Thermodynamics of Aqueous Atmospheric Aerosols Citation Stelson, Arthur Wesley (1982) Thermodynamics of Aqueous Atmospheric Aerosols. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/m9ac-pe87. https://resolver.caltech.edu/CaltechETD:etd-09062006-113244 Abstract A novel application of classical thermodynamics is presented to understand the distribution of aerosol forming material between the gas and aerosol phases in the polluted troposphere. The particular system studied involves NH 4 NO 3 and its interactions with the environmental variables, temperature, relative humidity, droplet pH and aqueous (NH 4 ) 2 SO 4 concentration. In Chapter 1, the theoretical temperature dependence of the solid NH 4 NO 3 dissociation constant is compared to ambient ammonia-nitric acid partial pressure products and general agreement is shown. Also, temperature is demonstrated to be a determining factor for ambient aerosol nitrate formation. Chapter 2 discusses how an urban aerosol can be chemically characterized and that the aqueous electrolytic aerosol solutions are very concentrated (> 8 molal). Thus, any attempt to model ion interactions in aerosol solutions must be able to represent the concentrated solution regime. The ammonia-nitric acid partial pressure product for concentrated NH 4 NO 3 -HNO 3 -H 2 O solutions is shown to be sensitive to relative humidity but not to pH (1-7) in Chapter 3. Since the ammonia-nitric acid partial pressure product is insensitive to pH, the NH 4 NO 3 dissociation constant over NH 4 NO 3 -H 2 O solutions should typify the ammonia-nitric acid partial pressure product above slightly acidic solutions. The NH 4 NO 3 dissociation constant temperature and relative humidity dependence is evaluated and compared to ambient data in Chapter 4. General agreement between the predictions and the data exists but the possible effect of additional solutes in aerosol droplets is evident. Since NH 4 NO 3 and (NH 4 ) 2 SO 4 are present in atmospheric particles of similar size, it is appropriate to calculate the effect of (NH 4 ) 2 SO 4 on the relative humidity dependence of the NH 4 NO 3 dissociation constant. Chapter 5 shows the presence of (NH 4 ) 2 SO 4 reduces the amount of ammonia and nitric acid in the gas phase and that the NH 4 NO 3 dissociation constant is only 40% less for a 0.5 (NH 4 ) 2 SO 4 ionic strength fraction in aqueous solution. Also, methods for predicting the particle growth, the solution density and the refractive index of NH 4 NO 3 -(NH 4 ) 2 SO 4 -H 2 O solutions are outlined in Chapter 5. Good accordance between experimental data and predictions is demonstrated indicating the possible applicability of these techniques to more complex multicomponent solutions. In the Appendices, a density prediction technique for (NH 4 ) 2 SO 4 -H 2 SO 4 -H 2 O solutions is presented since this aspect of ambient aerosols is not contained in the major thrust of this work. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemical Engineering) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Seinfeld, John H. Thesis Committee: Seinfeld, John H. (chair) Cass, Glen Rowan Flagan, Richard C. Morgan, James J. Defense Date: 21 September 1981 Funders: Funding Agency Grant Number Caltech UNSPECIFIED Environmental Protection Agency UNSPECIFIED California Air Resources Board UNSPECIFIED Record Number: CaltechETD:etd-09062006-113244 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-09062006-113244 DOI: 10.7907/m9ac-pe87 Related URLs: URL URL Type Description https://doi.org/10.1016/0004-6981(79)90293-2 DOI Article adapted for Chapter 1. https://doi.org/10.1021/es00088a005 DOI Article adapted for Chapter 2. https://doi.org/10.1016/0004-6981(82)90185-8 DOI Article adapted for Chapter 3. https://doi.org/10.1016/j.atmosenv.2007.10.063 DOI Article adapted for Chapter 4. https://doi.org/10.1016/0004-6981(82)90142-1 DOI Article adapted for Chapter 5. https://doi.org/10.1016/0004-6981(82)90453-x DOI Article adapted for Appendix A. https://doi.org/10.1021/j150624a042 DOI Article adapted for Appendix B. Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 3359 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 25 Sep 2006 Last Modified: 24 Apr 2025 22:24 Thesis Files Preview PDF - Final Version See Usage Policy. 5MB Repository Staff Only: item control page

THERMODYNAMICS OF AQUEOUS ATMOSPHERIC AEROSOLS Thesis by Arthur Wesley Stelson In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1982 (Submitted September 21, 1981) ii © 1981 Arthur Wesley Stelson All Rights Reserved iii ACKNOWLEDGEMENTS I would like to thank the California Institute of Technology, the Environmental Protection Aqency and the CaliTornia Air Resources Board for funding this work and supporting me during my graduate years. Citing everyone at Caltech who made a contribution to this thesis would be a very CUMbersome task. Thanks for every smile, encouraging remark and carinq action that always came at the most appropriate times. To my closest coworkers, I wish the best. I will never forget three office mates; Fred Geloard, Stan Sander and Dale Warren. You will all go far. Lenore Kerner, your ~aqical ability to cope with my handwriting and Dr. Seinfeld's corrections is shown throuohout this volume. Dan Duan, you were a good room- mate and see .vou at the arranged meetino five years from now. Special thanks ooes to Dr. Glen R. Cass, Dr. Richard C. Flagan. Dr. Sheldon K. Friedlander, Dr. Gregory J. FkRae and my advisor, Dr. John H. Seinfeld. Their guidance led me into an area of personal and intellectual satisfaction. It has been appreciated. Final Qracious words are due my family. rt>m, Dad, Kim, Caren, Tom, Becky and John, let's oet together and celebrate. glad you fo1lm~ed and sunoorted me the whole way. Papa and ~randpa, I am iv ABSTRACT A novel application of classical thennodynamics is presented to understand the distribution of aerosol fanning material between the gas and aerosol phases in the polluted troposphere. The particular system studied involves NH 4No 3 and its interactions with the environmental variables, temperature, relative humidity, droplet pH and aqueous (NH 4 ) 2so 4 concentration. In Chapterl, the theoretical temperature dependence of the solid NH 4N0 3 dissociation constant is compared to ambient a1m1onia - nitric acid partial pressure products and general agreerr~nt is shown. Also, temperature is demonstrated to be a detennining factor for ambient aerosol nitrate fonnation. Chapter 2 discusses how an urban aerosol can be chemically characterized and that the aqueous electrolytic aerosol solutions are very concentrated(> 8 molal). Thus,anyattempttomodel ion interactions in aerosol solutions must be able to represent the concentrated solution regime. The am:ionia - nitric acid partial rressure product for concentrated NH 4No 3 - HN0 3 - H20 solutions is shown to be sensitive to relative humidity but not to pH (1-7) in Chapter 3. Since the armonia - nitric acid partial oressure product is insensitive to pH, the NH 4N0 3 dissociation constant over NH 4No 3 - H2o solutions should typify the ammonia - nitric acid partial pressure oroduct above sliahtly acidic solutions. The NH 4No 3 dissoci- ation constant temoerature and relative humidity dependence is evaluated and compared to ambient data in Chanter 4. General agreement between the predic- tions and the data exists but the ocssible effect of additional solutes in Since NH No 3 and UlH 4 ) 2so4 are present in atmo4 spheric particles of similar size, it is appropriate to calculate the effect of aerosol droolets is evident. v (NH 4 ) so 4 on the relative humidity dependence of the NH 4No 3 dissociation con2 stant. Chapter 5 shows the presence of (NH 4 ) 2so 4 reduces the amount of ammonia and nitric acid in the gas phase and that the NH 4No 3 dissociation constant is only 40% less ~or a 0.5 (NH 4 ) 2so 4 ionic strength fraction in aqueous solution. Also, methods for predicting the oarticle growth, the solution density and the refractive index of NH 4No 3 - (N~~J 2 sod - H20 solutions are outlined in Chapter 5. Good accordance between experimental data and predictions is demon- strated indicating the possible aoplicability of these techniques to nore conDlex nulticonoonent solutions. In the Appendices, a densitv prediction technique for (NH 4 ) 2so 4 - H2so 4 H 0 solutions is oresented since this asnect of ambient aerosols is not con2 tained in the major thrust of this work. vi TABLE OF CONTENTS PAGE ACKNOWLEDGEMENTS iii ABSTRACT iv TABLE OF CONTENTS vi CHAPTER 1 - A NOTE ON THE EQUILil3RIUM RELATIONSHIP BETWEEiJ AMMONIA AND NITRIC ACID AND PARTICULATE AMMONIUM NITRATE CHAPTER 2 - CHEMICAL MASS ACCOUNTING OF URBAN AEROSOL 5 CHAPTER 3 - RELATIVE HUMIDITY AND pH DEPENDENCE OF THE VAPOR PRESSURE OF AMMONIUM NITRATE - NITRIC ACID SOLUTIONS AT 25°C 15 CHAPTER 4 - RELATIVE HUMIDITY AND TEMPERATURE DEPENDENCE OF THE AMMONIUM fHTRATE DISSOCIATION CONSTANT 41 CHAPTER 5 - THERMODYNAMIC PREDICTION OF THE WATER ACTIVITY, NH 4N0 3 DISSOCIATION CONSTANT, DENSITY AND REFRACTIVE ItWEX FOR THE NH 4No 3 - (NH 4 ) 2so 4 H20 SYSTEM AT 25oC 71 CHAPTER 6 - FUTURE RESEARCH 100 APPENDIX A - ON THE DENSITIES OF AQUEOUS SULFATE SOLUTIONS 105 APPENDIX B - PREDICTION OF THE DENSITY OF AMMONIUM BISULFATE SOLUTIOtJS 113 1 CHAPTER 1 A NOTE ON THE EQUILIBRIUM RELATIONSHIP BETWEEN AMMONIA AND NITRIC ACID AND PARTICULATE AMMONIUM NITRATE Published in Atmospheric Environment 13, 369 - 371, 1981. 2 Atmosplterlc Enr>i-t vol 13, pp. 369-371 C Pergamon Pn:ss Ltd 1979. Printed in Great Bri1A1n. 0004--69lllf79/0301--0369 $02.00/1) A NOTE ON THE EQUILIBRIUM RELATIONSHIP BETWEEN AMMONIA AND NITRIC ACID AND PARTICULATE AMMONIUM NITRATE A. W. STELSON, S. K. FRIEDLANDER and J. H. SEINFELD Department of Chemical Engineering, California Institute of Technology, Pasadena, California, U.S.A. (First received 10 July 1978 and in final fonn 26 September 1978) Abstract - Theoretical predictions of the atmospheric equilibrium involving gaseous ammonia and nitric acid and solid ammonium nitrate are compared with atmospheric measurements of ammonia and nitric acid concentrations reported by Spicer (1974) at West Covina, California. Qualitative agreement between the equilibrium constant and the product of the measured NH 3 and HN0 3 concentrations is found. INTI!.ODUCTION Elucidation of the paths of formation of and the factors governing the concentration of atmospheric particulate nitrates is of substantial current interest (Orel and Seinfeld, 1977). Particulate nitrate concentrations have been measured by several investigators (Gordon and Bryan, 1973; Kadowaki, 1976; Moskowitz, 1977; Appel et al., 1978), frequently together with particulate ammonium levels. Figure 1 shows ammonium and nitrate concentrations reported in atmospheric particulate samples from a variety oflocations. Most of the data lie above the 1 : I mole ratio line. Recent studies have demonstrated that gaseous nitric acid is adsorbed onto the glass fiber filters used in many of the measurements shown in Fig. 1 (Schumacher and Spicer, 1976; Spicer and Schumacher, 1977; Witz and MacPhee, 1977). This process, which leads to artifact nitrate formation on the filter medium, if present, would lead to higher reported particulate nitrate levels than those actuaiiy existing. Correction for artifact nitrate formation would have the effect of shifting more points in Fig. 1 above the 1 : l mole ratio line. Sulfate ions in substantial amounts are almost always present in the atmospheric aerosol with the ammonium and nitrate ions, and mixtures of ammonium sulfate and nitrate .often represent a significant fraction of the atmospheric aerosol. However, the equilibrium vapor pressures of ammonia and sulfuric acid above solid ammonium sulfate are very low, compared with the vapor pressures of ammonia and nitric acid over ammonium nitrate. The purpose of this note is to review the equilibrium relationship between ammonia and nitric acid in the gas phase and solid ammonium nitrate, and to compare theoretical predictions with atmospheric measurements. The equilibrium analysis should apply either to pure solid ammonium nitrate or to a mixture of immiscible solid phases one of which is ammonium nitrate. The analysis would have to be modified, 369 • GORDON B BRYAN 119731 • GROSJEllN ET AL 119761 HIDY fT AL (1975'i • HIDY B BURTON 11975) 20 • KADOWAKI 11976) o O'BRIEN ET AL. 119751 , o PATTERSON B WAGMAN 119771 • f O 10 56 POINTS 1 \ NH~ 003 MOLAR RATIO ., 10 15 POINTS 20 30 40 50 N03 (µg m-3) Fig.!. Concentrations ofNHt and NO; in ambient aerosols reported by various investigators. however, if solid solutions are present (Denbigh, 1971, p. 160). At temperatures below l 70°C, solid ammonium nitrate exists in equilibrium with ammonia and nitric acid: NH,N0 3 (s) ~ NH 3 (g) + HN0 3 (g). (1) In the notation of Denbigh {1971, p. 143), the equilibrium constant for this reaction, is related to the partial pressures of NH 3 and HN0 3 by K~ = PNH,PHNo,. and K~ is related to the standard Gibbs free energy change for reaction, 6G}, by K;,. AG~= -RTlnK~. (2) Since the thermodynamic data for NH 4 N0 3 are limited, an extrapolation formula for the equilibrium constant as a function of temperature can be derived by integrating the van't Hoff equation, liH- + In K' = er - 0 , RT IT -I- IT" 29s RT 2 29s (C,,,.., + c,,,...,, - C,,,..""')dT'dT". (3) 3 A. W. STEl..SON, S. K. FRIEDLANDER and J. H. SEINFELD 370 Table l. Thermodynamic data at 298°K Species Standard free energy of formation (kcal g mol- 1 ) Heat of formation (kcal gmol- 1 ) Heat capacity (cal gmol- 1 ) NH 3 (g) HN0 3 (g) NH 4 N0 3 (s) -3.915 -17.690 -43.98 -10.970 -32.100 -87.37 8.515 12.748 33.3 Using the data in Table l and assuming the heat capacities are independent of temperature, we obtain from (3), In K = 70.68 - ' 24090 T - 6.04 In(_!__) ~8 21510 In K, = 62.296 - -T-. points which fall above would correspond to a nonequilibrium system or may result from experimental error. (4) where K, is the equilibrium constant in terms of concentration, having units of ppm 2 . Brandner et al. (1962) measured the dissociation pressure of solid NH 4 N0 3 from 76 to 165°C. Based on their least squares expression representing their data, the following expression for In K, is obtained, (5) Both formulas, (4) and (5) are shown in Fig. 2 and are seen to be in substantial agreement. It is of interest to establish whether the equilibrium relation, Equation (1), holds in the atmosphere. For this purpose, it would be desirable to have simultaneous measurements of P,.m, and PHNo, taken over a short time interval. We have not been able to find such data; however, Spicer (1974) has reported hourly data on the concentration of gaseous ammonia and nitric acid at West Covina, CA. From these data, we have calculated the product fNHlHNo , where fNH, and fHNo, denote the hourly average concentrations in ppm. The data points on Fig. 2 represent the fNHlHNo, products plotted vs T, the hourly average temperature. Hourly measurements with the nitric acid or ammonia concentration less than 2 ppb were not included in Fig. 2 because of experimental error. The relationship, Equation (I), should hold for solid ammonium nitrate in equilibrium with its dissociation products. At 25°C, solid ammonium nitrate de· liquesces at a relative humidity of 62%. The corresponding relative humidities at 20 and 30°C are 64 and 58~~. respectively (Dingemans, 1941). At these and higher relative humidities, solution droplets are present (at equilibrium) and the relationship shown in Fig. 2 would not be expected to apply. Clearly, the data at the highes1 relative humidity ( > 90°/o) are not in agreement with the equilibrium expression. The data corresponding to relative humidities less than 60"/o fall around the equilibrium lines but with considerable scatter in the lower concentration ranges where the percentage experimental error is greatest. The points which fall below the lines may correspond to concentrations too low for .a solid phase to exist. The JANAF (1971) JANAF (1971) Wagman er al. (1968) CONCLUSIONS If ammonium nitrate is present in the aerosol phase, a substantial amount of NH 3 and HN0 3 must be present in the gas phase at equilibrium. For example, at 25°C the mass concentration of NH 3 plus HN0 3 (equimolar basis) in the gas in equilibrium with solid ammonium nitrate is about 22 µg/m - 3 • This amount is of the same order or larger than the mass of aerosol ammonium nitrate usually reported in polluted atmospheres, The NH 3 /HN0 3 /NH 4 N0 3 equilibrium is very sensitive to the temperature. Over the range of 20-30°C, the equilibrium mass concentration in the gas phase of NH 3 and HN0 3 (equimolar) increases from l l.0 to 30 ?O \ \ REL~TIVE \OJ HLJM:o:n I • 90-IOC i li :~g=~ 60- 70 0 \ '60 \ 1 . .~\. \ I \, 0 .~~\ •• . 0 0 \ . .. \ I • o· ' \ . . l J \ \ \ -JANAF\1971) 13 WAGMAN ET AL. !1968i ---BRANDNER El AL 11962) \ \ \ \ 1o·•L...._....__ _L_ __,___i..__ _:.....t.._j 3.25 3.35 3.45 1000 (oK-1) 3.55 T fig. 2. The product c11 NO,CM<, calculated from the data of Spicer (1974) for West Covina (CA) compared with equilibrium theory,Equation (4)(-)and Equation (5) (---).Data for concentrations less than 2 ppb are not shown because of the large experimental error at the low concentrations. 4 Equilibrium relationship between ammonia and nitric acid and particulate ammonium nitrate 38 .4 µg m - 3 • Thus, small changes in the temperature of the sampling train or in the analytical procedure can have a marked effect on the distribution between the gas and aerosol phases. The effect of the presence of (immiscible) ammonium sulfate in the aerosol phase has also been evaluated. The available data show that the vapor pressure of the dissociation products of (NH 4 h SO 4 (s) are too low to affect the concentrations of NH 3 and HN0 3 in the gas. The analysis would have to be modified if solid solutions of ammonium sulfate and nitrate are present (Denbigh, 1971, p. 160). Acknowledgement - This work was supported in part by EPA Grant No. R805736. The contents do not necessarily reflect the view and policies of the Environmental Protection Agency. 371 Hidy G. M. er al. (1975) Characterization of aerosols in California. Rockwell Int. Rep. California Air Rc:sour. Bd., ARB Contract No. 358. Hidy G. M. and Burton C. S. (1975) Atmospheric aerosol formation by chemical reactions. Int. J. Chem. Kinetics Symp. 1, 509-541. JANAF Thermochemical Tables, 2nd Edn (1971). NSRDSNBS 37. Kadowaki S. (1976) Size distribution of atmospheric total aerosols, sulfate, ammonium and nitrate particulates in the Nagoya area. Atmospheric Environme111 10, 39-43. Moskowitz A. H. (1977) Particle size distribution of nitrate aerosols in the Los Angeles Air Basin. EPA Report No. 600/3- 77-053. O'Brien R. J., Crabtree J. H., Holmes J. R., Hoggan M. C. and Bockian A.H. (1975) Formation of photochemical aerosol from hydrocarbons; atmospheric analysis. Eni•iron. Sci. Technol. 9, 577-582. Orel A. E. and Seinfeld J. H. (1977) Nitrate formation in atmospheric aerosols. Environ. Sci. Technol. JI, IOOCH007. Patterson R. K. and Wagmaf'I J. (1977) Mass and com/ position of an urban aerosol as a function of particle size for several visibility levels. J. AerosPI Sci. II, 269-279. RE:f£1l.£NCES Schumacher P. M. and Spicer C. W. (1976) Interferences in Appel B. R., Kothny E. L., Hoffer E. M., Hidy G. M. and J. J. the sampling of particulate atmospheric nitrate. Presented Weslowski (1978) Sulfate and nitrate data from the Califorat the l 72nd ACS Meeting, San Francisco. Spicer C. W. (1974) The fate of nitrogen oxides in the nia Aerosol Characterization Experiment (ACHEX) Environ. Sci Technot. 12, 418-425. atmosphere. Batelle Columbus Rep. to Cocrdinating Res. Brandner J. D., Junk N. M., Lawrence J. W. and Robins J. Council and U.S. Environ. Protection Agency Rep. 600/3(!962) Vapor pressure of ammonium nitrate. J. Chem. 76-030. Engng. Data 7, 227-228. Spicer C. W. (1977} Photochemical atmospheric pollutants Denbigh K. (1971) The Principles of Chemical Equilibrium, derived from nitrogen oxides. Atmospheric Em•ironment 11, 1089-1095. 3rd Edn Cambridge University Press, London. Dingemans P. (1941) Die dampfspannung von gesiittighten Spicer C. W. and Schumacher P. M. (1977) lnterferences in sampling atmospheric particulate nitrate. Atmospheric NH.N0 3 losungen. Rec. Trav. Chim. 60, 317-328. Environment 11, 873-876. Gordon R. J. and Bryan R. J. (1973) Ammonium nitrate in airborne particles in Los Angeles. Environ. Sci. Technol. 7, Wagman D. D., Evans W. H., Parker V. B., Harlow I., Baily S. 645-647. M. and Schumm R.H. (1968) Selected values of chemical thermo<lynamic properties; tables for the first thirty-four Grosjean D., Doyle G. J., Mischke T. M., Poe M. P., Fitz D. R., Smith J.P. and Pitts J.M. (1976) The concentration, size elements in the standard order of arrangement, NBS distribution and modes of formation of particulate nitrate, technical note 270-3. Witz S. and MacPhee R. D. (1977) Effect of different types of sulfate, and ammonium compounds in the eastern part of glass filters on total suspended particulates and their the Los Angeles Basin. Presented at the 69th Annual chemical composition. J. Air Pollui. Conirol Ass. 17, Meeting of the Air Pollution Control Association, 239-241. Portland. 5 CHAPTER 2 CHEMICAL MASS ACCOUNTING OF URBAN AEROSOL Published in Environmental Science and Technology 15, 671 - 679, 1981. 6 Reprinted from ENVIRONMENTAL SCIENCE & TECHNOLOGY, Vol. 15, Page 671, June 1981 Cop~Tight © 1981 by the American Chemical Society and reprinted by permission of the copyright owner Chemical Mass Accounting of Urban Aerosol Arthur W. Stelson and John H. Seinfeld• Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125 1111 A chemical mass accounting technique emphasizing the importance of chemical speciation is developed for analyzing atmospheric-aerosol data. The technique demonstrates that total aerosol mass can generally be characterized from measurements of S0 4 , Cl, Br, N0 3 , NH 4 , Na, K, Ca, Fe, Mg, Al, Si, Pb, carbonaceous material, and aerosol water, the predominant species being S0 4 , N0 3 , NH 4 , Si, carbonaceous material, and aerosol water. Since water is the major species distributed between the gas and aerosol phases, the interrelation between water and electrolytic mass is explored. It is shown that aerosol water is significantly correlated with electrolyte mass. Calculated aerosol ionic strengths lie in the region where the relative humidity /ionic strength relation is most sensitive, thereby suggesting the importance of relative-humidity monitoring during aerosol sampling. Introduction The urban aerosol consists in general of a complex mixture of ionic salts, metal oxides, glasses, carbonaceous material, and water. Partitioning the aerosol into groups of materials with similar physical and thermodynamic properties can simplify the interpretation of experimental data and facilitate theoretical analysis. The main objective of this paper is to develop methods for obtaining an accurate overall aerosol mass balance from the least number of measured quantities. The urban aerosol usually exhibits a bimodal volume distribution (see Figure 1). The fine-particle mode generally results from gas-to-particle conversion, whereas the coarseparticle mode arises from mechanically generated particles. The coarse mode is usually basic since the particles are formed from basic materials such as soil, cement, and fly ash. The fine mode can be neutral or acidic depending on the relative degree of neutralization of acidic material. In the eastern United States, the fine-particle mode in the urban aerosol generally dominates the total mass, so that the net aerosol pH is likely to be acidic, whereas Western aerosol has a greater tendency to be basic (1, 3, 4). Because the nature of the atmospheric aerosol depends strongly on its chemical speciation, it is important to be able to estimate its chemical composition based on measurements of elemental composition. The atmospheric aerosol can be considered to consist of five major classes of constituents: ionic solids, electrolytes (dissolved ionic species), carbonaceous material, metal oxides and glasses, and water. An equation expressing this relation is TSP == L: L: [MiOil + L: (E;) + i j i L [CMd + L: [Id + [HzO] (1) where TSP == total suspended particulate matt.er (µg m- 3 ), [MiOi] =mass concentration of metal oxide or glass (µg m- 3 ), [Ei] = mass concentration of electrolyte i (µg m- 3 ), [CM;] == mass concentration of carbonaceous material i (µg m-3), [Ii] ==mass concentration of ionic solidi (µg m- 3 ), and [H 20] = aerosol water concentration (µg m-3). Electrolytes are dissociating ionic substances dissolved in water, whereas ionic solids are undissolved electrolytic material. Carbonaceous material refers to carbon-containing species, present as elemental carbon or organic or inorganic compounds. Metal oxides and glasses refer to oxidized elemental species, such as those present in soil and cement dust and fly ash. The water content refers to "free" water unassociated with hydrated salts. The object of this paper is to show that, by making assumptions about each term on the right-hand side of eq 1, one can calculate the total suspended particulate mass concentration on the basis of conventional aerosol measurements. From an accurate aerosol mass accounting, several important issues can be explored: (1) the possibility of biased total-mass measurements through alteration of the aerosol between sampling and analysis, (2) the relation between measured electrolyte mass-to-water ratios and solubilities of atmospherically significant electrolytes, (3) the aerosol ionic strength and possible dependence of aerosol water content on the prevailing relative humidity, (4) the net aerosol pH, and (5) the relative importance of different aerosol fractionselectrolytic, metal oxide and glass, carbonaceous, and aqueous-to the total aerosol mass and the possible interrelation between different fractions. Each of these issues will be evaluated and discussed with particular reference to the Los Angeles aerosol. 7 TSP = 2: 2: [MiOj] + 2: [E;] + 2: [CM,] + ACHEX i One of the most detailed urban aerosol studies involving chemical analysis was the California Aerosol Characteriz.ation Experiment (ACHEX) (5). Ambient atmospheric aerosol was deposited on high-volume filters (Whatman 41) and analyzed for many chemical species. In addition, fl-gauge, waterometer, and total-filter (47-mm Gelman GA-1 and Gelman A) measurements were performed. During some sampling periods, the aerosol carbonaceous material was analyzed (6). From the ACHEX data, 6 days are chosen for individual mass-balance analyses. More sampling periods would have been desirable, but these days were the only ones in which the aerosol was chemically analyzed for the major inorganic species, water, and carbonaceous material, in addition to continuous totalmass measurements. Even for these 6 days, the aerosol water content was not measured throughout the high-volume-filter sampling period. In Table I the sampling times and locations are summarized. Only at West Covina, CA (TC), did the aerosol water concentration and high-volume-filter sampling times totally overlap. Since the waterometer measurements overlapped the majority of the high-volume sampling period, it will be assumed that the time-averaged aerosol water concentration over its sampling time typifies the time-averaged aerosol water concentration over the total high-volume-filter sampling period. The ACHEX ambient atmospheric aerosol high-volumefilter samples were analyzed for many chemical species. When only the major species, S0 4 , Cl, Br, N03, NH 4 , Na, K, Ca, Mg, Al, Si, and Pb, were considered, greater than 90% of the measured moles, excluding water and carbonaceous material, were accounted for. Therefore, the major species will only be considered in this study. Equation l will be modified as 2.---.,-~~~.--~~,.,..,~.--~~~~~~~~~ • 5<:imp1n"lq !!l!tC1J~r'l<'!S~ fo, Q 11'~1' -ro101F.i1t"l'J~ - " ' 110< {11--., vOlu~ ~omple· perpend1c.,.10• 10 o 102 mph •ind (2i Go119t!(ll~ !1 I : . E. ~> 08 ACDC~t\"' 06 MODE \ j ,·\.· • I O< \ I. ~ BASIC ~MODE : /. \ /1. /;.\ ', ,". . ' K) 04 " ~ Q t~ IOO Figure 1. Time-averaged normalized aerosol volume distributions and sampler upper effective size limit ( 1, 2, 5). (See Table l for aerosol volume distribution sample code definition.) . j i where [N;] is the concentration of minor specie i (µg m- 3 ). ln Table II the sum of the minor species for the ACHEX data is listed. We see that this term is Jess than l % of the total for the 6 days. A basic object of this paper is to attempt to reconcile TSP measurements with eq 2 by studying the means of estimating the contributions of each of the terms on the right-hand side of eq 2. Although we focus on the ACHEX data, the techniques to be discussed will have general applicability. To evaluate the terms on the right-hand side of eq 2 other than 1:[Ni], one must make assumptions about the chemical form of the different species. Each term and the assumptions needed in evaluating each will now be discussed. Then, the right-hand side of eq 2 will be evaluated theoretically and compared with the total suspended particulate measurements fromACHEX. Aerosol Components Ionic Solids. Measurements of ionic-solid concentrations present difficult problems. In the measurement of the ion concentration in an aerosol, the filter is washed with a solvent and the ion concentration in the solvent is measured. Using this procedure, it is impossible to tell whether the ion was present in an ionic solid or an aqueous solution. Indirectly, the presence of ionic solids can be inferred. If the ambient relative humidity is less than the deliquescent humidity of the ionic solid, then it can be assumed that the salt is present as a solid. An additional check can be invoked if the solid is volatile, for example, NH 4 N0a (7). The gas-phase concentrations of the precursors can be measured along with the temperature, and, if the calculated equilibrium coefficient matches the theoretical equilibrium coefficient for the ionic solid, it is assumed that the ionic solid is present. Both indirect methods fail if solid or supersaturated solutions are present. For our analysis, it will be assumed that the ionic-solid concentration is zero. If the calculated ionic strength of the electrolytic aerosol solution is unreasonably high, then a correction must be made for the presence of ionic solids. For the mass accounting, it is immaterial whether the ionic-solid material is treated as an ionic solid or an electrolyte . Metal Oxides and Glasses. The major elements possibly occurring in the form of oxides and glasses are Al, Ca, Fe, Si, Mg, Pb, K, and Na. When one follows the approach of Macias et al. (8), the chemical form of these elements can be assigned (see Table III). The majority of the oxides listed in Table III are known to be formed in combustion processes (9, JO). Additionally, Biggins et al. (11) have identified Fe203, Al20a, and Table I. ACHEX Sampling Time and Location Summary (5) 8 Dominguez Hills. CA - Dominguez Hills. CA WL -· aample slle Rubidoux, CA VJ 10/4-10/5173 10/10-10/11/73 9/24-9/25/73 West Covina, CA TC 7124-1125173 West Covina, CA TD TE 818-819173 West Covina, CA WK 7/25-7/26/73 high-•olume total~fltter (HVM) sampling period (TF, TV) sampling period sampling period weterorneter (H20) sampling period 2100-2105 2100-2100 2300-1802 2320-1605 0500-1826 2100-2100 2100-2100 2100-2100 2300-1801 2300-1600 0500-1800 2100-2100 2100-2100 2100-2100 2300-1900 2300-1600 0500-1600 2100-1800 2115-1515 0000-1800 0400-1900 2300-1600 0445-1545 2200-1400 11-oauve (fJ) • HVM =total mass from Whatman 41 8 X 10 in. high-volume filter (µg m-3). TF =time-averaged total mass from Gelman GA-1, 47-mm fitters (µg m- 3). TV =time-averaged total mass from Getman A, 47-mm filters (µg m- 3 ), ~=time-averaged total mass from fl gauge (µg m-3). H,O =time-averaged total water concentration from waterometer (µg m- 3 ). tll72 Environmental Science& Technology 8 Table 11. Summary of Measured and Calculated Los Angeles Aerosol Concentrations (5)" oxide and glass concn, "9 m-S - 1"'203] [1'9203) [Ill<>:!) (PbO] [C..O] (lllgO] (K~) (Na20) WK 4.9 1.2 4.0 0.8 4.0 1.8 2.4 4.1 3.4 2.6 1.8 1.9 0.7 0.7 1.7 5.5 3.8 8.6 2.2 2.8 14.3 WL 3.2 2.2 2.8 1.9 3.0 1.8 1.9 1.4 1.0 0.9 """""'8 VJ TC 5.9 8.2 6.4 4.7 TO TE 13.4 28.5 27.4 19.8 16.5 5.2 3.7 2.6 3.0 1.5 5.3 3.9 3.4 -olyl• concn, I'll m-3 -..pie WK Wl VJ TC TO ]TE 1"°31 [Cl] 0.3 1.2 0.7 0.6 0.9 0.7 [Br) (NH4] (Na] (S04] (Pb] [Cli) (K] (lol!!] (HJ 4.1 1.1 3.8 0.7 1.3 0.6 2.2 1.1 31.4 4.2 2.0 0.6 1.5 0.3 0.1 0.2 3.9 2.9 2.5 26.3 16.6 6.5 3.6 2.9 2.1 1.7 2.9 2.4 1.6 1.1 1.1 1.8 1.1 0.5 0.4 0.2 0.9 0.2 7.3 11.8 1.2 0.1 6.7 3.1 4.7 9.9 12.0 0.7 0.5 9.5 8.1 7.2 0.4 3.2 2.0 1.4 1.2 0.8 0.7 1.2 IOHJ' (Hf 1.3 3.8 2.3 0.1 0.1 1.5 aummatkms, "9 m-3 -1• ~i:!:jMjO;J l:1Ii0ii101f Xii Mil ItlE1) Ii.E1f IdH1] Ii!CM1) IH20) WK 33.2 31.9 52.9 21.4 20.0 43.0 11.4 39.6 17.1 19.5 49.5 30.2 0.7 0.9 0.7 18.7 16.4 8.0 54.2 24.9 40.8 1.4 29.8 TO 55.9 42.6 u TE 34.1 11.7 10.8 WL VJ TC 29.9 23.B 10.8 22.0 16.1 38.5 28.9 60.2 47.9 12.7 18.2 27.4 23.5 47.5 0.8 34.5 75.2 74.4 29.7 =o . ...., = = •[A] = mass concentration of specie A. [HJ = hydi"ogen concentration calculated from electroneutrality when x.,, = 0, Xca 0,"" = 0, and x,.. 0. [HJ'<>< [OH]'= hy<lrogen <><hydroxyl ion concentration when x,,,, 1, Xca 1, x.., 1,"" = 1, and x,.. = 1. l,l1[M,OiJ =sum of metal oxide and glass concentrations when xPb 0, Xca 0, x.., 0, "' = 0, 0. l,l 1[M.O,]' =sum of metal oxide and glass concentrations when"""= 1, Xca = 1, x.., = 1, x, = 1, arod x,.. = 1. l,[M,] =sum of metal oxide and glass f0<ming elements assuming no oxygen is present and x,,,, = 1, Xe.= 1, """= 1, x. = 1, and xMo = 1. l 1[E1] =sum of electrolyte concentrations when x,,,, = 0, 0, """= 0, 0, and x,.. = O. l 1[E,]' =sum of electrolyte concentrations when x,,,, 1, 1, x,.. = 1, x. = 1, and "Mo= 1. l 1[N,] =sum of min<>< species concentrations. l 1[CM,] =sumo! cart>ooaceous material. = = = and.-...= = Xe.= Xe.= Al Ca Fe Si oalde tonn Al203 Cao• Fe203 Si0 2 = ""= = Table IV. Equilibrium Analysis of Hydroxide Formation Table Ill. Aerosol Metal Oxides -..1 = element Ir- ....,..llY of lonnatlof! data ( 12) oxide tonn Mg Mgo• Pb PbO Na Na,o• K K,O• •Assumed opecleo 60° 2118 , kcell(e-moll _... AG 0 2118 • kcel/(lt'f'IOI) CaO(s) -i44.4 PbO(sJ -45.25,. -45.05 b Ca(OH),(s) -214.33 -136.13 -199.27 Pb(OH),(s) -100.6 -54.64 MgO(s) Mg(OH)z(s) H:P(g) oxide reacUonu wtth water Si0 2 in roadside aerosol. The presence of CaO, MgO, and PbO can be examined from considerations of chemical equilibrium. Equilibrium constants for the reactions of CaO, MgO, and PbO with water are given in Table IV. The equilibrium analysis indicates that CaO and MgO should readily react to form Ca(OHh and Mg(OH)z, whereas the PbO should not. Na20 should readily react with water to form NaOH, and KzO should react similarly to CaO and MgO to form KOH. Biggins et al. (11) have measured Pb 3 0 4 in roadside dust in addition to elemental lead, lead sulfates, lead carbonates, and lead hydroxides. The assumed form of lead, e.g., Pb 3 0 4 , PbO, or Pb, will not substantially affect the mass balance because of the high molecular weight of lead. We will assume lead to exist as PbO. Reiter et al. (13) have measured insoluble CaO, in disagreement with the pure thermochemical analysis. Ca(OHh has a solubility similar to that of CaO, as shown in Table V. Thus, the insoluble CaO reported by Reiter et al. (13) could be Ca(OHb MgO, Na20, and K 20 have not apparently been identified in tropospheric aerosol. + + CaO(s) H 2 0(g) ~ Ca(OH)z(s) MgO(s) H2 0(g) ~ Mg(OH)z(s) PbO(s) + H2 0(g) ~ Pb(OH)z(s) -15.29 -8.5 -0.11.•-o.91" 6.0 x 10- 1 2 6.0 x 10- 7 o.3,•0.2° •Red fO<TTI. •Yellow fO<TTI. MgO, Na 20, K 20, and CaO could exist in the atmospheric aerosol in solid solutions with Si0 2, Al20a, and Fe203 in soil dust or rock flour. The ability to remove these elements by forming hydroxides depends on particle size, rock structure, and the acidic nature of the leaching agent. Goldich (14) measured the weathering loss in sedimentary rocks and obtained the following ordering: Na20, CaO, MgO, K20, Si02, Ah03 , and iron, where Na20 is the easiest to remove and iron is the hardest. This ordering supports the preceding thermodynamic and qualitative discussion. An additional calculation supporting the weathering ordering is obtained by using Volume 15, Number 6, June 1981 673 9 Table V. Solubility of Inorganic Salts -al oxides and glasses ~. • g/100 g ol H,,0 ref -..ioxldeoendet- - , , a f!1100 11 ol H,,0 .... Si02 insoluble in H,O 12 Na20 decomposes 12 Al,03 insoluble in H,O 12 MgO 12 Fe203 insoluble in H20 12 PbO 0.00863-0 0.0023 22 12 eao 0. 131 10 , decomposes 12 K20 very soluble 12 ~. • g/100 g of H,O ref - o l y t. . 27 NaCl KOH 113.225 11220 28 KCI NH.OH soluble 12 NH4 CI Mg(OH), 0.0009 18 0.162 20 12 MgCl2 27 CaCl2 -..iytes NaOH Ca(OHh Pb(OH), 0.0155 20 12 PbCl2 NaN03 91.79 25 27 NH4 HS0 4 KN0 3 31.620 19220 28 12 NH.N03 12s.220 13525 59.6 25 Mg(N03), Ca(N01h -.i>ffltJ, • g/100 11 of H,,0 .... 35.91 25 34. 7 20 27 39_525 54.25 20 27 81.9 25 1.0825 27 12 12 27 29 Mgso. 288 25 44 _520 ea so. 0.298 20 28 27 Pbso. 0.0042525 27 H2so. 12 12 12 27 HN03 27 HC! NaHso. 27.8 25 28.6 25 12 K,so. 1225 12 KHS0 4 51.4 20 28 KBr (NH4)2S0 4 76.925 101.520 27 NH.Br 972s 12 MgBr2 12 Pt>Br 2 0.0520 28 CaBr2 142 20 12 Pb(N01)2 Na 2so. 12 59.425 18 Her 19520 28 Na Br 90.5 20 65.2 20 28 28 • FOf example, 0.131 10 means a solubility of 0.131 g/100 g of H,O at 10 •c. Clarke and Washington's (15) average composition of igneous rocks. Using the measured aerosol Si0 2 concentrations and the appropriate metal oxide-to-Si0 2 ratios calculated from Clarke and Washington's analysis, one can calculate the amounts of CaO, Na20, MgO, and K20. The calculated K20 concentrations agree within 6% of measured K 2 0 concentrations, whereas the calculated and measured CaO, MgO, and Na 20 concentrations differ by greater than 40%. Thus, it seems that K 20 originates from soil dust and that the CaO, MgO, and the Na 2 0 come from preferentially enriched sources, i.e., sea salt, cement dust, or fly ash. In light of the possibility that Pb, Ca, Na, K, and Mg are in either the glass and metal oxide or electrolytic phases, the metal oxide and glasses mass balance can be written as MPbO I: I: (M;OJ] = (1 - Xpb) - (Pb]+ ; Mpb i (1- xc.l Mc.o [CaJ + (l - xM.l MMgO [Mg]+ Mc. MMg (1 - XK) MK,O [KJ + (l - XNal MNaz(J (Na]+ MK MN. MFe.,03 [Fe]+ MAlz03 [Al]+ Ms;o, [Si] 2MFe 2MA.1 Ms; (3) where MA is the molecular weight of species A and xpb, xc •. XK, XNa• and XMg are the fractions of Pb, Ca, K, Na, and Mg, respectively, in the ionic-solid or electrolytic form. Determination of xpb, xc •• XK, XN 8 , and XMg could be based on a chemical-source balance. Even if the source signature is known, determination of the chemical form may be difficult. For example, Pb resulting from automobile exhaust may either ~ electrolytic or not depending on the fraction of Pb emitted as PbO or Pb vs. halogenated forms. In our analysis 874 Environmental Science&. Technology we will examine the two extremes: XPb = x ea = x K = x Na = x Mg = l, and Xpb = XCa = XK = XNa = XMg = 0. Electrolytes. An expression for the electrolyte mass of the atmospheric aerosol, i.e., ionic species dissolved in water, is I: [E;] = [S0 4 ] + (Cl] + [N03] + [NH 4 ] + i [Br] + XPb[Pb] + xc.[Ca] + XK(K] + XNa(Na] + XMg[Mg] +(HJ + [OH] (4) The [HJ or (OH] must be calculated on the basis of electroneutrality. If the aerosol is acidic, then [OH] may be neglected and (HJ= MHl2(SO,J/Mso, + [Cl]/Mc1 + (N03JIMN0,, (NH4J/MNH 4 + (Brl/Ms, - l'.Na[NaJ/MNa - XK[K]/Mk 2xpb(PbJ/MPb - 2xc.(CaJ/Mc 0 - 2xMg[MgJ/MMgi (5) If [HJ< 0 from eq 5, then [OHJ = -MoH[H]IMtt. Of course, eq 5 is an expression for the net acidity. Actually, the tropospheric aerosol would likely contain a mixture of acidic and basic particles (16). Water. Ho et al. (17) have shown that the aerosol water content varies diurnally. Since the ACHEX chemical composition measurements were time-averaged, the aerosol water concentrations as measured by the waterometer were timeaveraged. Since the average aerosol water concentrations were determined by integrating waterometer measurements, no assumptions were made concerning the amount of water on the filter material; i.e., the aerosol water is not assumed to be equal to the unaccounted mass on the filter as is typically done. Carbonaceous Material. The carbonaceous fraction of the total aerosol mass must typically be estimated since carbo- 10 naceous aerosol concentration measurements are very limited. Interpretation of existing carbonaceous-material measurements is complicated by the different organic carbon extraction efficiencies of solvents and the mutual extraction of inorganic nitrates by polar solvents (18, 19). Therefore, a calculation procedure must be devised that utilizes existing data to obtain values reflective of the actual carbonaceous-material loading. Pierson and Russell (20) calculated for Denver a linear relation between the aerosol carbon, [C], and lead, [Pb], concentrations. [CJ = (5.84 ± 0.34)[Pb] - 0.85 ± 0.97 µg m-3 (6) In Figure 2 this correlation is compared to data for aerosol lead and carbon measurements. The Los Angeles and Denver trends are similar except that, as [Pb] - 0, the Los Angeles data approach 10 µgC m- 3. The combined Los Angeles, San Jose, and Los Alamitos data indicate that eq 6 overpredicts the aerosol-carbon loading at high lead concentrations. An additional correlation between total carbonaceous material and lead can be derived by utilizing data of Grosjean et al. (23), who reported an average noncarbon-to-carbon ratio of 0.37 in the organic aerosol fraction for 2 days in 1973 at Pasadena, CA. (The noncarbon material is nitrogen, oxygen, and hydrogen associated with carbon in organic molecules.) Thus, the total carbonaceous aerosol mass loading, ~i[CMi], can be approximated by multiplying the Pierson and Russell correlation by 1.37 have solubilized in the CH30H-CHCh solution or some measurement error must have been present. Thus, the points plotted in Figure 3 represent the minimum aerosol carbonaceous material. As can be seen, the Los Angeles data are not well correlated with eq 7. The correction for aerosol nitrate in the CH 3 0H-CHC1 3 extractable mass is significant and can be shown by the following approximation: [N03] = (MNo/MNH,No,l x [CH 30H-CHCia-extractable mass] X (1 - [carbon fraction][carbon + noncarbon fraction]/ {carbon fraction j) (NOa] = 62 /81.J (CH30H-CHCh-extractable mass] X (l - l.37[carbon fraction]) (8) assuming nitrate is present as ammonium nitrate and that the CHaOH-CHCl 3 -extractable mass has the same noncarbonto-carbon ratio as that measured by Grosjean et al. (23) for the organic aerosol fraction in Pasadena. The total noncarbon-to-carbon ratio of Grosjean is similar to those measured by Cukor et al. (24) and Ciacco et al. (25) in New York City. Based on their data for chloroform, 2-propanol, and methanol extractions, calculated noncarbon-to-carbon ratios varied between 1.36 and 1.49. Therefore, the total organic noncarbon-to-carbon ratio of Grosjean should approximate that in the CH30H-CHCh-extractable mass. In Figure 4 nitrate O HIDY ET AL (5) 8 APPEL ET AL.(61° I: [CMd = (8.02 ± 0.47)[Pb] - 1.17 ± 1.33 µg m-3 (7) In Figure 3 this correlation is compared with ACHEX aerosol lead and carbonaceous-material estimates using the data of Appel et al. (6). The CH 3 0H-CHCh extractables were corrected for the solubilization of ammonium nitrate by assuming that all of the nitrate measured was ammonium nitrate and subtracting the value obtained from the CH 3 0H-CHCh extractables. Subsequently, the CH 30H-CHC1 3 -extracted carbon value was subtracted from the total CH30HCHC13-extractable mass. This procedure led to negative mass concentrations in 7 out of 11 cases. To check the extreme case, we subtracted the sum of the nitrate and CH 30H-CHCl 3extractable carbon loadings from the total CH 3 0H-CHC1 3 extractable mass. This procedure led to negative values in 3 out of 11 cases. Therefore, either all of the nitrate must not ~ + HIDY ET AL (5) 8 APPEL ET AU6 lb 40 ~ 30 ~ :I! 20 0 w·-10 o""'-.......==-~-'--~~~-'--~~~---~~~-'-~~~--' 3 2 0 [Pb) L ~E ry ::i._ 40 4 µ.g m-3 5 Figure 3. Relation between aerosol carbonaceous material and aerosol lead: (a) Pb from Whatman 41 high-volume filter; (b) time-averaged Pb from 47-mm Gelman GA-1 filters. + c LEW!S 8 MACIAS (211- CHARLESTON, W v 50 + 0 .£ "' PIERSON 8 RUSSELL 1201- DENVER. COL o HIDY ET AL !518 APPEL ET AL (61-LOS ANGELES CAO 'E • HIDY ET AL !5)8 APPEL ET AL 161- LOS ANGELES: CAb O APPEL ET AL (22)-SAN JOSE 8 LOS ALAMITOS,CAc ~ • APPEc ET ALl22J-SAN JOSE 8 LOS ALAMITOS,CAd l.U 4D .... 30 <[ a:: .... z 30 0 u • • 20 f;l 2D a:: :::> en .... <[ l.U 10 :I! 10 [MEASURED NITRATE] = + 0 ~o~~~~~~~~3~~~~~~~~6~~---~--'e [Pb) µg m-3 Figure 2. Relation between aerosol carbon and aerosol lead: (a) Pb from Whatman 41 high-volume filter; (b) lime-averaged Pb from 47-mm Gelman GA-1 fitters; (c) Pb from 47-mm Fluoropore filter; (d) Pb from Spectrograde high-volume filter. Solid lines: minimum and maximum of Pierson and Russell (217/ correlation. 1.02 (CALCULATED NITRATE] + + 1,96 (r.a,986) + 0 D 10 20 30 40 50 CALCULATED NITRATE, µ.g m-3 !Figure oil. Measured nitrate vs. calculated nitrate. Solid line: linear least-squares lit to data. Volume 15, Number 6, June 1981 Gl75 11 values calculated from eq 8 are compared with the measured values of Hidy et al. (5). Mueller et al. (26) measured aeroaol carbonate carbon in Pasadena, CA, and determined it to be consistently less than 5% of the total carbon present. In light of the previously dis. cussed inaccuracies, the carbonate fraction of the aeroaol will be assumed to be negligible. In summary, the total carbonaceous aerosol concentration can be estimated from the sum of the benzene- and CH30H-CHC1 3 -extracted mass minus nitrate as ammonium nitrate plus the estimate for the maximum elemental carbon aerosol loading of Appel et al. (6). The carbonaceous aerosol concentration as calculated by the above procedure should generally reflect the atmospheric carbonaceous-material loading and is the best obtainable using the existing data. seen in the results in Table VII is that the fl-gauge measurements are consistently lower than the other calculated and measured total-mass concentrations. (Possibly the instrument gain was set too low.) The mass ratio, S, of electrolytic material to water can be calculated by S = ( ~ [E;]!H20) x 100 g/100 g of HzO (9) Calculated values of S are listed in Table VIII for the two extreme cases of the distribution of Pb, Ca, K, Na, and Mg between the metal oxide-glass subset and the electrolyte subset. The values calculated for S and S' are within the typical range of solubilities of electrolyte materials listed in Table V. Since the calculated mass ratios vary between 50 and 125 g/100 g of HzO, it can be inferred that the electrolyte portion of the atmospheric aerosol at these sampling locations is dominated by soluble sulfates, nitrates, and chlorides. The chemical analysis summary shows the dominance of nitrate and sulfate (Table lI). Ochs and Gatz (30) recently measured the fraction of water-soluble material in particles of >4.6-µm radius as ---0.3. Using data from Tables II and VI, we compute the soluble fraction in the Los Angeles aerosol to lie between 0.15 and 0.35. Older Los Angeles aerosol data of Cadle (31) list water and volatile organics as 0.15 of the total aerosol mass, with a water-soluble fraction of0.15. The ionic strength of the aerosol solution can be calculated by Aerosol Mass Accounting Table II presents a summary of the data used for the mass accounting calculation. The calculated and measured totalmass data are summarized in Table VI. In Table VI, M 1 is the total mass calculated by assuming XPb = 0, xea = O,xK = 0,XNe = 0, and XMg = 0, and M 2 is that when Xpb = 1,xc. = l, XK = 1, XNa = 1, and XMg = 1. M 3 is the calculated total mass assuming that the total mass is the sum of the measured species. Thus, no assumptions are made concerning chemical speciation in the calculation of M 3 . All three mass calculation procedures (M 1 , M2, M 3 ) yield similar values but disagree with the total-mass concentrations calculated from the fJ gauge, total filters, and high-volume filters. To evaluate the trend among these seven variables, M 1 , M2, M3, ~. TF, TV, and HVM, we performed a least-squares analysis between all pairs (see Table VII). (VJ was omitted from the least-squares analysis since a TV measurement was not performed.) All measured and calculated total suspended mass techniques correlated significantly. A notable feature (10) where Mi is the molecular weight and z i is the charge of species i. Calculated values of I are listed in Table VIII for the two extreme cases of the distribution of Pb, Ca, K, Na, and Mg. The range of ionic strengths at each sampling location is compared with the ionic-strength dependence of water activity Table VI. Calculaled and Measured Total Mass (µg m-3 ) (5} oample .,, ... WK 146.6 WL 91.2 VJ llf3 "fl i'F TV HVM 144.5 133.8 105.7 113.5 127.7 148 92.4 82.4 77.7 101.5 107.5 115.6 115.1 96.0 85.8 160.9 114 211 TC 209.8 207.4 192 0 173.1 210.9 215.4 241 m 168.3 165.0 153.9 137.8 176.9 176.0 194 TE 93.6 92.5 82.3 87. 1 101.0 113.4 123 Table VII. least-Squares Analysis of Measured and Calculated Total Mass HVM .,, 1162 1163 0.974 0.975 0.972 0.929 -10.4 ~ i'F TV 0.905 -8.1 0.867 -13.3 Ti' TV 0.986 0.997 0.933 0.870 m 5.4 b 0.738 -4.8 -12.3 least aquMH parameters a 0.976 0.977 0.974 1.00 0.981 0.995 1.26 -4.6 1.23 -2.4 1. 18 -7.9 1.00 0.0 1.26 -5.5 1.18 -11.4 0.935 0.936 0.933 0.981 1.00 0.995 0.941 0.918 0.879 0.766 1.00 0.918 m 9.4 11. 1 5.1 8.5 0.0 18.9 b 0.955 0.956 0.995 1.00 1.02 -1G.2 0.952 0.974 0.995 1.04 0.842 1.08 -19.0 1.00 m 0.0 b -12.5 -15.2 • r = correlation coefficient; m = slope; b = intercept. 876 "fl 0.999 Environmental Scienell & Technology -8.3 m b 12 Table VIII. Calculated Electrolyte-to-Water Mass Ratios and Ionic Strengths for los Angeles Aerosol " ........ s S' WK 73.4 91.3 WL VJ 68.7 121.3 56.5 63.2 83.8 80.1 64.4 92.3 TC TD TE 51.7 61.3 = = , 18.6 14.2 8.0 13.4 10.0 11.6 = + (NH4 1i_ SO,. (32) 22.2 25.9 16.5 15.4 11.5 18.3 • S calculated mass ratio when """ 0, Xe. 0, x,.., = 0, >\< = 0, and x.., = 0, g/100 g of H,,O. S' =calculated mass ratio when = 1, Xe.= 1, x,.., = 1, >\< = 1, and x.., = 1, g/100 gof H,O. I= ionic strength when"""= 0, Xe.= 0, x... = 0, _.. = 0, and = 0, mov1000 g of H,O. f =ionic strength when """'= 1, Xe.= 1, ""'"= 1, XI(= 1, and x.., = 1, mol/1000 g of H2 0. x,,. x... 0 NH 4 N03 o HC! (33) • .,,so. {33) (34) u. > ~ 40 _1 RANGE oi:- CALCULATED IONIC STRENGTHS F O R 4 - W ACHEX IONIC for several electrolytes at 25 °C in Figure 5. All of the calculated ionic strengths are in the region where the relative humidity-ionic strength variation is strongest, indicating the importance of the prevailing relative humidity and the aerosol chemical nature in determining the atmospheric aerosol water content. The net aerosol pH was calculated for both extreme distributions of Pb, Ca, K, Na, and Mg (see Table II). Samples TC and TD were the only ones that were definitely acidic, whereas WK, WL, VJ, and TE could be basic or acidic. Although Liljestrand (4) measured net basic aerosol pHs in Los Angeles, his measurements and those reported in ACHEX (5) were taken by using quite different experimental techniques that might have different cutoff diameters. Since the coarse mode is generally basic and the fine mode acidic, a lower cutoff would lead to a lower net pH. Combining the coarse and fine modes can also lead to sampling errors (35). The metal oxide-glass, electrolyte, carbonaceous, and water fractions are of equal in1portance in the total aerosol mass (see Table II). The dominance of different fractions at different locations and sampling periods is evident. In sample VJ the metal oxide-glass fraction was largest, and in WK, TC, and TD the water fraction predominated. In TE and WL the aerosol was fairly evenly distributed among the metal oxide-glass, electrolytic, and water fractions. Finally, the electrolytic mass and the aerosol water concentrations are well correlated, indicating the presence of electrolytic solutions (see Figure 6). DATA o:: 3 ~oo·':::-'-'--........=u:.o,-,-'--'-w....=_,-'-'-..J...J.='-,'_--'-'--'-' 10 100 STRENGTH Figure 5. Water activities for typical electrolytes as a function of ionic strength ( r = 25 °C). ";' 80 E 0 j'._ 70 H20 = l.59(I [E,) )+ .9 (r = .9451 z Q 60 I- <! er I- z 50 lLJ u z 40 0 u er lLJ I- H2o = 1. s2 (I [ E, ]') - 12. 9 ( r =.925) 30 <! '?: ....) 20 0 (j) 0 er lLJ <! 0 0 IO 20 30 ELECTROLYTE 40 50 60 CONCENTRATION 70 80 /.Lg m- 3 Figure 6. Aerosol water vs. electrolyte concentration. Solid lines: linear ieasi-squares iits to data. Implications for Measurement Techniques Several important experimental questions need to be considered when comparing the total suspended mass measurements obtained by using glass-fiber filters, cellulose filters, cellulose triacetate filters, and the ,B gauge: (I) Does the ,B gauge measure only suspended particles and not exhibit a relative-humidity interference? (2) Do filtration-efficiency differences have a significant influence on total-mass measurements? (3) Are the samplers' upper and lower aerosol size cutoffs similar? (4) What effect does equilibrating the filters to 55% relative humidity at 25 °C have on the water adsorbed or absorbed on the filter material and the water contained in the aerosol? (5) How important is filter artifact in prejudicing aerosol nitrate and sulfate measurements? Landis (36) has reported a large positive interference in /3-gauge measurements at high relative humidity (>75%). Data of Husar (37) and Yamamoto (38) do not show this interference but show the thermodynamically predicted absorption of water on filter-deposited NaCl and (NH 4 )zS04 aerosols as the relative humidity is increased above the deliquescence point. Additionally, ACHEX data using the ,B gauge do not show instrument saturation during times of high relative humidity as would be predicted by Landis' measurements. Landis' Figure 3 shows that ,8-gauge measurements are consistently lower than or equal to the total filter measurements. If the instrument responded to high relative humidity and had a response greater than the manufacturer's calibration for atmospheric aerosol, the filter-sample data should be less than the /3-gauge measurements. Since the measured effect is the opposite of the calibration results, some inconsistency exists. Therefore, the /3-gauge measurements were not considered in error and have been compared here to other mass measurement techniques. Shown in Figure 7 is the initial filtration efficiencies of different filter materials vs. face velocity. The most recent data of John et al. (39) show that the efficiencies of Gelman GA-1 and Gelman A should be greater than 99% over the op· erating range of interest for a polydisperse room aerosol. Even though the data indicate higher efficiencies than those found by Appel et al. (40), the maximum discrepancy would account for an error of only 5%. The data for Whatman 41 filters do not agree as well with the other data in Figure 7. These differences can result from filter maturation, material construction variation, and different particle concentration measurement techniques. Since the filtration efficiency curves for Whatman Volume 15, Number 6, June 1981 177 13 HIGH VOLUME FILTER OPERATING RANGE 99.99---_.c:=:p.----- ,------,-----, >- 99 u z w u u.: LL 90 w z 80 0 f:: <! a:: f- _J WHATMAN 41 u.: • NRL from Rim berg (41) , Lindekin el al from Rimberg (41) c John et ol (39) •Stafford et al (421 + R1mberg (41) •Appel el al (40) I 0.5.._ _ _ _ _..__ _ _ __.__ _ _ __,__ ___, 0 50 100 FACE VELOCITY ( cm/s ) 150 Figure 7. Filtration efficiencies for Whatman 41, Gelman A, and Gelman GA-1. 41 are lower than the curves for Gelman GA-1 and Gelman A, the effect of filtration loss niust be evaluated. Lindeken et al. (43) and Stafford et al. (42) measured the increase in filter efficiency for Whatman 41 as a function of time. Using their data and making very conservative estimates, one can estimate the maximum error due to the initial filter inefficiencies as I% for all samples. \.\'hen one considers that the average standard deviation error of the three filter total suspended mass measurement techniques is 8%, initial filtration inefficiency differences cannot be the major source of error. Shown in Figure 1 are the time-averaged normalized aerosol volume distributions for four sampling periods. Also, shown in Figure 1 are the sampler cutoffs for sampling in stagnant air (J ). The value for the high-volume sampler is a more recent one than that reported in ACHEX (i.e., 60 µm). Wedding et al. (2) measured the sampling effectiveness of a high-vohime sampler perpendicular to a 10.2 mi/h wind. Figure 1 shows that the presence of wind can significantly affect the fraction of the coarse mode sampled. Since the wind effect on the sampling efficiency of the total filter setup or the {3 gauge has not been mea~ured, it is assumed that wind affects all samplers similarly. Thus, the ambient aerosol should not be significantly preferentially measured by any sampler. The filters used in ACHEX were equilibrated to 55% relative humidity and 25 °C as prescribed by NASN procedures. Tierney et al. (44) and Demuynck (45) showed that glass-fiber filters lose their adsorbed or absorbed water when equilibrated to NASN conditions. Demuynck demonstrated that Whatman 41 cellulose filters irreversiblv absorb water. When Demuynck's data and the ratio of-filter surface areas are used, this interference would amount to 107 µg m- 3 for a 24-h high-volume filter. In Table VI, HVM is consistently higher than TV, verifying the irreversible absorption of water by Whatman 41. The cellulose triacetate filters did not irreversibly absorb water, as seen by comparing TF and TV values in Table VI. Whether the filter drying process removed water from the aerosol is very important. Table II and VI show that 678 Environmental Science & Technology the aerosol contains between 20 and 45% water. If the water is removed, then 20-45% of the aerosol mass is unaccountable. This fraction is unreasonably high; therefore, only the loosely held absorbed water on the filter surface is removed by the initial drying. Whether the aerosol is a supersaturated solution or more dilute cannot be determinined from existing data. Corrections for artifact nitrate and sulfate were not performed since assigning a correction would be somewhat arbitrary with current knowledge. Maximum artifact values can be calculated from the results of Appel et al. (22). The maximum artifact sulfate would be -2 µg m- 3 and nitrate would be-26 µg m- 3 (10 ppb 24-h average HN0 3 (g) concentration) for Whatman 41 high-volume filters. The measured sulfate values used in this study were consistently above 2 µg m- 3 , whereas the nitrate values were below 26 µg m- 3 (see Table II). Thus, the sulfate data are presumed to be more accurate than the nitrate data, but no measured values were corrected since assignment of corrections could not be quantitatively performed. Recent work by Appel et al. (46) indicates that positive and negative nitrate artifacts exist, making corrections even more difficult to assign. Conclusions The foregoing analysis demonstrates several important points concerning mass accounting, the presence of electrol)rtic solutions, and aerosol pH. Mass Acccounting. A reasonably accurate mass balance for the Los Angeles aerosol has been obtained from measurements of S0 4 , Cl, Br, N0 3 , NH 4 , Na, K, Ca, Fe, Mg. Al, Si, Pb, carbonaceous material, and aerosol water, the predominate species being S0 4 , N0 3 , NH 4 , Si, carbonaceous material, and aerosol water. Chemical speciation was assigned, and the presence of oxygen in metal oxides and glasses was' accounted for. The addition of metal oxide and glass oxygen to the mass balance did not have a significant effect on the total-mass correlations. The assignment of oxide forms to certain elements is, however, physically important, since metal oxides tend to be water insoluble. Thus, no "free" water would be associated with these oxides. Since aerosol carbon measurements are limited, the aerosol carbon concentration typically must be estimated. The Pierson and Russell (20) correlation was examined and does not seem to apply to the Los Angeles aerosol data (Figure 2). In addition to quantification of the aerosol carbon concentration, determination of the associated oxygen, nitrogen, and hydrogen in the carbonaceous material is important. As indicated by Appel et al. (6), Grosjean (18), Gordon and Bryan (19), and this work, the CH30H-CHCh-extractable mass contains considerable nitrate. Thus, a correction to this measurement for dissolved inorganics would improve future mass accounting calculations. Since certain chemical species are distributed between the gas and aerosol phases, the total aerosol mass, the aerosol water concentration, the relative humidity, and the temperature should be continuously monitored during sampling. Ideally, other volatile species that are distributed between the gas and aerosol phases should also be monitored, i.e., NH:;, HN0 3 , HCl, and organics. By analyzing continuous data, one can determine the distribution of material between the gas and aerosol phases and the possibility of aerosol alteration between sampling and measurement due to volatilization, uptake of water, or displacement reactions. Since mass is re· versibly distributed between the gas and aerosol phases, care must be taken when determining the total suspended particulate mass from filter samples such that the filters are equilibrated with a known relative humidity and temperature at the time of weight measurement. Ideally, filter weight measurements should be performed at several relative humidities. 14 Presence of Electrolyte Solutions. The calculated electrolyte-to-aerosol water mass ratios are typical of atmospherically significant electrolyte solutions near saturation (Tables V and VIII). By assigning valences to the electrolyte species. we have calculated the ionic strength. From the ionic strengths calculated and compared with typical ionic-st.-ength dependence of water activities in binary electrolyte solutions, the electrolyte material appears to be present in highly concentrated solutions and/or ionic solids. The amount of water in the aerosol phase is very dependent on the chemical nature of the electrolytes and the prevailing relative humidity (Figure 5). Since the aerosol water and electrolyte concentrations are interdependent, a correlation between electrolyte mass and aerosol water was evaluated. The significant correlation between electrolyte mass and aerosol water highlights an important point, namely, that electrolyte material can cause greater visibility reduction per unit mass than organics or metal oxides because of hygroscopicity. Aerosol pH. The fraction of electrolyte material for Ca, Pb, K, Na, and Mg must be determined to perform an accurate chemical mass and acidity balance. Biggins et al. (1 J) and Reiter et al. (13) recognized the importance of differentiating between water-soluble and -insoluble Pb and Ca. Depending on the assumptions of chemical speciation for Ca, Pb, K, Na, and Mg, metal oxide vs. electrolyte, the net aerosol pH may be basic or acidic (Table II). Knowing the net aerosol pH would improve the aerosol mass balance because an additional variable would exist to check chemical speciation assumptions or measurements. Recent aerosol data include aerosol pH measurements but do not have detailed chemical analyses and aerosol water measurements to perform a mass balance (3, 47). An additional factor important to determining the net aerosol pH is the upper cutoff of the aerosol sampler. This point is graphically illustrated by Figure 1. Acknowledgment We extend appreciation to Bruce Appel for his helpful comments. Literature Cited ( l) National Research Council, Subcommittee on Airborne Particles .. Airborne Particles"; University Park Press: Baltimore, MD, 1979; Chapter J. (2) Wedding. J.B.; McFarland, A. R.; Cermack, J.E. Environ. Sci. Technol 1977, 1 J, 387. (3) Tanner. R. L.: Cederwall, R.; Garber, R.; Leahy. D.; Marlow, W.; Meyers. R.; Phillips, M.; Newman. L. Almos. Environ. 1977, 11, 955. (4) Liljestrand, H. M. Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 1980. (5) Hidv. G. M., et al. ""Characterization of Aerosols in California'", Rock.;,,ell International Report, California Air Resources Board, ARB Contract No. 358, 1975. (6) Appel, B. R.; Colodny. P.; Wesolowski, J. J. Environ. Sci. Technol 1976. 10, 359. (7) Stelson, A. W.; Friedlander, S. K.; Seinfeld, J. H. Atmos. Environ. 1979, 13. 369. (8) Macias, E. S.; Blumenthal, D. L.; Anderson. J. S.; Cantrell, B. K "'Size and Composition of Visibility-Reducing Aerosols in South· western Plumes"', presented at the Conference on Aerosols: Anthropogenic and Natural-Sources and Transport. New York Academv of Sciences, New York, Jan 9-12, 1979. (9) Bryers~ R. W. ""Influence of the Distribution of Mineral Matter in Coal on Fireside Ash Deposition", ASME Paper No. 78-W A/ CD-4, 1978. (10) Henry, W. M.; Knapp, K. T. Environ. Sci. Technol. 1980, 14, 450. (11) Biggins, P. D. E.; Harrison, R. M. Environ. Sci. Technol. 1980, 14.336. (12) Weast, R. C., Ed. "Handbook of Chemistry and Physics", 54th ed.; CRC Press: Cleveland, OH, 1973. (13) Reiter, R.; Sladkovic, R.; Potzl, K. Atmos. Environ. 1976, 10, 841. (14) Pettijohn, F. J. "Sedimentary Rocks"; Harper and Brothers: New York, 1957; Chapter 11. (15) Mason, B. "Principles of Geochemistry"; Wiley: New York, 1966; Chapter 3. (16) Brosset, C. Atmos. Environ. 1978, 12. 25. (17) Ho, W.; Hidy, G. M.; Govan, R. M. J. Appl. Meteorol. 1974, 13, 871. (18) Grosjean, D. Anal Chem. 1975, 47, 797. (19) Gordon, R. J.; Bryan, R. J. Environ. Sci. Technol. 1973, 7. 645. (20) Pierson. W.R.; Russell, P.A. Atmos. Environ. 1979, 13, 1623. (21) Lewis, C. W.; Macias, E. S. Atmos Environ. 1980, 14, 185. (22) Appel, B. R.; Tokiwa, Y.; Wall, S. M.; Hoffer, E. M.; Haik, M.; Wesolowski, J. J. "'Effect of Environmental Variables and Sampling Media on the Collection of Atmospheric Sulfate and Nitrate"; Final Report, California Air Resources Board, ARB Contract No. 5-1032, 1978. (23) Grosjean, D.; Friedlander, S. K. J. Air Pollut. Control Assoc. . 1975, 25, 1038. (24) Cukor, P.; Ciaccio, L. L.; Lanning, E.W.; Rubino, R. L. Environ Sci. Technol. 1972, 6, 633. (25) Ciaccio, L. L.; Rubino. R. L.; Flores, J. Environ. Sci. Technol 1974, 8, 935. (26) Mueller, P. K.; Mosley, R. W.; Pierce, L. B. In "'Aerosols and Atmospheric Chemistry"; Hidy, G. M., Ed.; Academic Press: New York, 1972. (27) V+t' est, C. J., Ed. "International Critical Tabies of Numerical Data, Physics, Chemistry and Technology"; McGraw-Hill: New York, 1933; Vol. IV. (28) Lange, N. A., Ed. "Handbook of Chemistry", 5th ed.; Handbook Publishers: Sandusky, OH, 1944. (29) Tang, I. N.; Munkelwitz, H. R. J. Aerosol Sci. 1977, 8, 321. (30) Ochs, H. T., Ill; Gatz, D. F. Atmos. Environ. 1980, 14, 615. (31) Cadle, R. D. "Particles in the Atmosphere and Space"; Reinhold: New York, 1966; Chapter 2. (32) Wishaw, B. F.; Stokes. R H. Trans. Faraday Soc. 1954, 50. 952. (33) Hamer, W. J.; Wu, Y. C. J. Phys. Chem. Ref. Data 1972, 1, 1047. (34) Robinson, R. A.; Stokes, R. H. "Electrolyte Solutions; The Measurement and Interpretation of Conductance, Chemical Potential and Diffusion in Solutions of Simple Electrolytes"', 2nd ed. (revised); Butterworths: London, 1959. (35) Brosset, C. "Possible Changes in Aerosol Composition Due to Departure from Equilibrium Conditions during Sampling"; Swedish Water and Air Pollution Research Laboratory; Goteborg, 1978; PB-298 947 . (36) Landis, D. A. Atmos. Environ. 1975, 9, 1079. (37) Husar, R. B. Atmos. Environ. 1974, 8, 183. (38) Macias, E. S.; Husar, R. B. In ""Fine Particles. Aerosol Generation, Measurement, Sampling, and Analysis"; Liu. B. Y. H., Ed.; Academic Press: New York, 1976. (39) John, W.; Reischl, G. Atmos. Environ 1978, 12, 2015. (40) Appel. B. R.; Wesolowski, J. J. In "The Character and Origins of Smog Aerosols; A Digest of Results from the California Aerosol Characterization Experiment (ACHEX)"; Hidy, G. M., Mueller, P. K., Grosjean, D., Appel, B. R., Wesolowski. J. J., Eds.; Wiley: New York, 1980. (41) Rimberg. D. Am. Ind. Hyg Assoc. J. 1969, 30. 394. (42) Stafford, R. G.; Ettinger, H.J. Am. Ind. Hyg Assoc. J. 1971, 32, 319. (43) Lindeken, C. L.; Margin, R. L.; Petrock. K. F. Health Phys 1963, 9, 305. (44) Tierney, G. P.; Conner, W. D. Am. Ind. Hyg. Assoc. J. 1967, 28, 363. (45) Demuynck, M. Atmos. Environ. 1975, 9, 523. (46) Appel. B. R.; Tokiwa, Y.; Haik. M. Atmos. Environ., 1981, 15, 283. (47) Stevens, R. K.; Dzubay. T. G.; Russwurm. G.; Rickel. D. Atmos Environ. 1978, 12, 55. Received for review May 16, 1980. Accepted February 17, 1981. This work was supported by U.S. Environmental Protection Agency grant R806844 and by State of California Air Resources Board contract A7-169-30. Volume 15. Numbers. June 1981 679 15 CHAPTER 3 RELATIVE HUMIDITY AND pH DEPENDENCE OF THE VAPOR PRESSURE 0 OF AMMONIUM NITRATE - NITRIC ACID SOLUTIONS AT 25 C Accepted for publication in Atmospheric Environment. 16 RELATiVE HUMIDITY AND pH DEPENDENCE OF THE VAPOR PRESSURE OF AMMONIUM NITRATE - NITRIC ACID SOLUTIONS AT 25oC Arthur W. Stelson and John H. Seinfeld Department of Chemical Engineering California Institute of Technology Pasadena, California 91125 ABSTRACT Quantitative expressions for the arnmonia-nitric acid equilibrium product and the partial pressures of ammonia and nitric acid over non-ideal nitric acid-arnmonium nitrate solutions are developed. The relative humidity and pH dependence of the equilibrium product and the partial pressures are obtained from free energy thermodynamic data. The thermodynamic predictions show the arnmonia-nitric acid equilibrium product is inversely related to relative humidity. strated. The importance of correcting for non-ideality is demon- The assumption of ideality for arnmonium nitrate in solution incurs an error of an order of magnitude in the a1T1110nia-nitric acid equilibrium product prediction at the point of deliquescence and of 20 percent in the relative humidity of deliquescence. The trends indicated by the analysis are consistent with the filter study results of Forrest et al. (1980) and Appel et al. (1980). 17 INTRODUCTION The presence of armionium nitrate in atmospheric aerosols has been confinned by a number of investigators (Lundgren, 1970; Stephens and Price, 1972; Gordon and Bryan, 1973; Mamane and Pueschel, 1980). The studies of Doyle et al. (1979) and Stelson et al. (1979) have inferred the existence of an equilibrium between arrrnonium nitrate precursors, arrrnonia and nitric acid, and solid particulate arrrnonium nitrate. Using the ambient arrrnonia and nitric acid data of Spicer (1974) at West Covina, CA, Stelson et al. (1979) showed that the measured and predicted concentration products, K = PNH PHNO , were in essential agreement. 3 3 Doyle et al. (1979) demonstrated the same phenomenon at Riverside, CA based on FT-IR arrrnonia and nitric acid measurements. Significant problems in the measurement of aerosol nitrate have been experienced. Smith et al. (1978) found substantial losses of particulate nitrate and arrrnonium from high volume glass fiber filter samples taken at Riverside, CA when stored at room temperature. The data of Smith et al. (1978) are re-interpreted in Fig- ure 1, where a least squares fit of the molar arrrnonium and nitrate losses produces a line with slope 1.094, strongly indicative of NH No volatilization. 4 3 Forrest et al. (1980) spiked filters with NH No and drew ambient air through 4 3 the filters for three to five hours. The greatest NH 4No 3 losses occurred at re·.ative humidities below 60 percent, whereas at 100 percent relative humidity, no NH 4No was lost. Appel et al. (1980) measured NH 3 and HN0 concentration 3 3 products, ~H pHNO , at Pittsburg, CA using filter techniques and obtained 3 3 values generally below those needed for saturation even though aerosol nitrate was present. Stelson and Seinfeld (1981) have shown that Los Angeles aerosols contain ionic solids or concentrated solutions, 8 to 26 molal. The ionic strengths 18 1.6 -E ..., 1.2 I 0.4 b. [NH:]= (1.094 :to.01s)a [ NOi] + (o.1s1 to.011) h" .986) o.oo.o 0.4 0.8 1.2 3 ~ (NOi) (µ.moles m- ) Figure 1. Molar ammonium and nitrate losses from high volume glass fiber filters stored at room temperature. _ _ Linear least square fit + Data of Smith et al. (1978) 19 corresponding to these concentrations lie in the range where ionic strength is most sensitive to relative humidity, suggesting that relative humidity is an important detenninant of aerosol water content. The object of this work is to further our understanding of the NH 3-HN0 3- H2o system by studying the role of relative humidity and pH on the system's equilibrium. One issue that can be addressed with such a study. for example, is explanation of the filter results of Appel et al. (1980) and Forrest et al. (1980). Specifically, we wish to carry out a thermodynamic analysis of the NH 3-HN0 3-H 2o system at 25°c for pH varying from 1 to 7 and relative humidity varying between O and 100 percent. In our analysis no assumptions concerning the ideality of solutions will be made. The results can be compared to those of ideal solution theory as well as to the semi-quantitative ones of Tang (1980a). No corrections will be made for the Kelvin effect. since the aero- sols of interest have been shown generally to exceed 0.5 µm diameter (Lundgren, 1970; Mamane and Pueschel, 1930). A calculation procedure for the arrrnonia-nitric acid equilibrium product relative humidity dependence over solid and aqueous anmonium nitrate is developed. Then, expressions for the individual a111ll0nia and nitric acid partial pressures over non-ideal arrrnoniurn nitrate-nitric acid solutions are derived. Finally, the influence of pH on the partial pressures of arrrnonia and nitric acid is explored. 20 AMMONIA-NITRIC ACID EQUILIBRIUM PRODUCT OVER SOLID AND AQUEOUS AMMONIUM NITRATE Below 62 percent relative humidity at 25°c, arrmonium nitrate should be present as a solid, and above this value it should be in solution (Stelson et al., 1979). Although recent work of Tang (1980b) indicates arrmonium nitrate does not exhibit traditional deliquescence but is hygroscopic at relative humidities greater than about 30 percent, we will assume arrrnonium nitrate deliquesces at 62 percent relative humidity for the purpose of this work. Recent available free energy data for the NH -HN0 3-H 20 system are given in 3 Table 1, from which the equilibrium constants for the NH -HN0 - H 0 system in 3 3 2 Table 2 can be calculated. The equilibrium constants in Table 2 and throughout this paper are thermodynamic equilibrium constants where pressure is referenced to one atmosphere and aqueous solute concentration to unit molality. The dif- ferences between the values for reactions 4 to 6 and those of Tang (1980a) are less than 6 percent. A 21 percent difference exists between the equilibrium constant used for reaction 3 by Tang (1980a) and the value in Table 2. The equilibrium constants listed in Table 2 can be tested for internal consistency in two ways. First, K2 should equal K K4K ;K . Based on the values 5 3 6 . given, K5K4 K3!K = 2. 4 6xl0 -18 versus K2 = 2 .7lxl0 -18 , an error of 9 . 2 percent. 6 Second, K1 should equal K2 aNH NO where aNH NO 4 3 4 = saturated arrmonium nitrate of Hamer and Wu (1972), K1 = 3 solution activity. Using the value of aNH NO 4 3 3.14xlo- 17 , which agrees well with K = 3.03xlo- 17 as calculated and given in 1 Table 2. For arrmonium nitrate at 25°c below 62 percent relative humidity, the equi1 ibrium product is K . 1 Above 62 percent the equilibrium product is given by 21 Table 1. Free Energy Data for the NH 3-HN0 3-H 2o System at 298°K Species tiG/R,°K-l NH 3 (g) - 1,977 Parker et al. (1976) HN0 3(g) - 8,903 JANAF ( 1971) NH 4No 3(c,IV) -22,220 Parker et al. (lg76) NH 4N0 3 (aq, m=l) -22,940 Wagman et a1. (1968) No3(aq, m=l) + H (aq, m=l) + NH 4 (aq, m=l) H20(£) -13,410 Parker et al. (1976) 0 Parker et al. (1976) - 9,558 Parker et al. (1976) -28,530 Parker et al. (1976) NH 3·H 20(aq) -31, 730 Wagman et al. (1968) OH-(aq, m=l) -18,925 Parker et a1. (1976) Table 2. Equilibrium Constants for the NH 3-HN0 3-H 20 System at 298°K Reaction 1 NH 4N0 3(c,IV) ~ NH 3 (g) + HN0 3 (g) 2 NH 4N0 3 (aq) t NH 3 (g) + HN0 3(g) 3 NOj(aq) + H+(aq) t HN03(g) 4 NH3·HzO(aq) t Hz0(£) + NH3(g) 5 NH;(aq) + OH-(aq) t NH 3·H 20(aq) H+(aq) + OH - (aq) ::;: H20(£) 6 Reference Equilibrium Constanta 3.03xlo- 17 aValues calculated from the free energy data of Table 1. 2. 7lxl0- 18 2.72xl0-7 l.65xl0 -2 5.37xl04 9.79xl0 13 22 where pNH , pHNO 3 3 = the partial pressures of arrrnonia and nitric acid; YNH , YNO = the molal activity coefficients of the NH; and NOj ions; 4 + 3 - , mNO , mNH NO = the molalities of NH 4 , N0 3 and NH 4N0 3 and {y+)NH NO 4 3 43 -43 the mean molal activity coefficient for NH 4No 3 . Using the NH 4No 3 solution activity coefficient data from Hamer and Wu (1972), the equilibrium product rnNH can be calculated as a function of NH 4No 3 rnolality. The relative humidity, R.H., over the solution can be calculated as a function of NH 4No 3 molality from the molal osmotic coefficients in Hamer and Wu (1972), -2 R.H. = 100.0 aw = 100.0 exp ( -3.6027x10 mNH NO ¢m) 4 (2) 3 where aw = the water activity, and ¢m = the molal osmotic coefficient at mNH NO . 4 Since the equilibrium product and the relative humidity over solution 3 are both solely dependent on mNH NO , the equilibrium product - mNH NO 4 3 4 func3 tionality can be replaced by a function relating the equilibrium product directly to the relative humidity, as in Figure 2. Note that the product, pNH PHNO , 3 3 is expressed in units of ppb 2 in Figure 2 for convenience in atmospheric appliThe effect of non-ideality can be examined by assuming ¢m and (y:_)NH N 4 03 are unity. (See the curve labelled ideal solution in Figure 2.) The ideal cations. solution curve ends at mNH NO 4 3 = 25.954, saturated NH 4No 3 solution at 25°c, which shows the ideal solution approach grossly mispredicts the deliquiescence relative humidity. The approach of Tang (1980a) can also be used to evaluate the product, pNH PHNO for pH, 1 to 7, and arrrnonium nitrate concentrations, 1.0 to 10.5 3 3 23 41 10 2 10 BRANDNER ET AL. (19621 •••••••••••••••••••••••• - _SJS.,L~Clt'l- - H. ~L... (.L9l~ _. NON-IDEAL NH4 N03 SOLUTION 1 10 NON- I DEAL SOLUTION K-M SOWTION PERCENT RELATIVE HLMIDITY Figure 2. Effect of relative humidity on ammonianitric acid partial pressure product. 24 molar. Over this range of hydrogen, armionium and nitrate concentrations, the amount of undissociated nitric acid predicted by the approach of Tang (1980a) was less than 0.3 percent. Thus, it is appropriate within this regime to consider the amount of undissociated nitric acid to be zero, i.e. purely an ionic solution. For very acidic solutions, pH < l, the presence of undissoci- ated nitric acid must be taken into account. The pNH PHNO 3 3 values shown in Fig- ure 2 on the curve labelled Tang (1980a) represent the limit as pH~ 7, although the variation between pH = l and 7 is not large. The water activity was determined assuming the solution was purely armionium nitrate. The molal osmotic coefficient data from Hamer and Wu (1972) were used to calculate the water activity, and the molar to molal concentration conversion was carried using NH No solution density data of Adams and Gibson (1932). 4 3 lated result is shown in Figure 2. out The calcu- The solid NH 4No 3 vapor pressure product calculated using a least squares fit of the data of Brandner et al. (1962) and the thennodynamic prediction of Stelson et al. (1979) are also shown in Figure 2. The new solid vapor pressure product prediction and the non-ideal NH 4No 3 solution curve at saturation join closely, indicating the improved quality of this prediction for the NH 4No 3 solid vapor pressure product at 2s 0 c over that of Stelson et al. (1979). Finally, curves labelled non-ideal and K-M solution are shown in Figure 2. The K-M solution curve was calculated by multiplying arrmonia and nitric acid partial pressures determined from equilibria 3-6 in Table 2. The non-ideal solu- tion curve serves as a check of the assumptions used in deriving quantitative expressions for the arrmonia and nitric acid partial pressures. The procedure used in calculating the individual nitric acid and arrmonia partial pressures will now be developed. 25 NITRIC ACID PARTIAL PRESSURE The nitric acid partial pressure is determined from the equilibrium of reaction 3 in Table 2, ( 3) + + where yH = the molal activity coefficient for H ion and mH = H ion molality. Kusik and Meissner (1978) developed an expression for predicting the activity coefficient of a salt in a multicomponent electrolytic mixture from which the YHYNO product can be evaluated, 3 (4) where x = mH/mN 03 ated nitric acid. Table l, and h:::_lH,N0 =mean molal activity coefficient for dissoci3 Using the value for K3 determined from thermodynamic data in l+x 1-x 2 PHNO = 272 (y+)H NO (y:_)NH NO x mNO (ppb) 3 -.3 43 3 (5) By specitying mH, mN and mNH , the ionic strength, I, is determined by I 03 4 mN + mNH , and only (y:_)H NO needs to be evaluated to calculate the nitric acid 03 '4 ' 3 partial pressure. The ionic strength functional dependence of (y:_)H,N0 must be 3 calculated by an indirect method which is different from the usual experimental activity coefficient determination methods, vapor pressure, freezing point depression or electrochemical, since nitric acid does not totally dissociate in water. The degree of dissociation of nitric acid in water as a function of acid concentration can be determined using the approach of lf6gfeldt (1963), in which the dissociation of nitric acid is represented by three equilbria; 26 = [HN0 3(H 2o) 3 ] {H+}{NOjHH 0J 3 2 = [HN0 3(H 20)] + {H }{N0 HH 0} 3 2 [HN0 ) 3 {H+}{N03} where [) represents molar concentration and {} refers to the activity. Ka, Kb and Kc are 3.63xlo- 2 , 8.13xl0- 3 and 1.66xl0- 4 , respectively (Hogfeldt, 1963). Hogfeldt (1963) assumes the molar activity coefficients of the un- dissociated aqueous nitrate species to be unity. When converting to a molal basis, the undissociated nitric acid species molal activity coefficient, y , u is not unity, but rather is given by (6) where d and d0 are the nitric acid solution and pure water densities in gm ml- 1 , = the molecular weight of nitric acid, and ms = the stoi3 chiometric nitric acid molality. Using Hogfeldt's equilibria and Equation (6), respectively, MHN0 the fraction of nitric acid that is dissociated, a, can be calculated from 2 doysms a =1 Yu 3 (K a + Kba + Kc) a w w where ys = the stoichiometric molal nitric acid activity coefficient. (7) The dissociation of nitric acid can be calculated using the stoichiometric molal nitric acid activity and water activity data fit of Hamer and Wu (1972), pure water density and nitric acid molecular weight of Weast {1973), and the nitric acid solution density interpolation formula of Granzhan and Laktionova 27a (1975). The dissociation calculated from Equation (7) is compared to the dissociation data of Krawetz (1955) and Redlich, et al. (1968) in Figure 3. The agreement. especially with the data of Redlich et al. (1968), is good. The total nitric acid dissociation constant can be expressed in terms I( N = 1 (8) 3 K a +Kba +K a w w c Using Hogfeldt's equilibrium constants and noting that aw= 1.0 at infinite dilution, ~ = 22.4, which compares favorably with values of 15.4, 20.0 and 26.8 from Davis and De Bruin (1964), Redlich et al. (1968) and Young et al. {1959), respectively. The mean molal ionic activity coefficients for the H+ and N0-3 ions, (y+)H NO • can be found from - ' 3 (9) Using Equations {6), (7) and (9), (y.!.)H,N0 can be calculated as a function of ionic strength. 3 The maximum ionic strength is about 8.3 tt~1al and occurs between 17 to 21 stoichiometric nitric acid molality. The mean molal ionic activity coefficient polynomial regression up to 7.5 molal is tn{y ) = - 1· 17625 /r + 2.260xl0- 1I - 4.722xl0- 2I 2 !. H,ND3 l+l.44 Ir (10) where the standard deviation is.:_ 0.0022. Although {y+)H NO should also be - • 3 a function of the undissociated nitric acid concentration. the effect of undissociated nitric acid will be shown to be negligible up to 7.0 ionic strength. 0.6 0.8 LL 0.1 o.o • 0.2 u 0.4 <( a:: ~ 0 z z ~ <t a:: ~ w LO 1111 llJi ~- • II • ' I 1.0 I . . l Figure 3. . Ionization of nitric acid. I JOO.O . . . ... I ' OF NITRIC ACID 10.0 I ' ' I •I STOICHIOMETRIC MOLALITY • • I T • 25°C 111 KRAWETZ (1955) • REDLICH,DUERST,, S MERBACH ( 1968) ... ' er ....., N 28 AMMONIA PARTIAL PRESSURE The partial pressure of armionia over the solution is (Tang, 1980a) K4K5 YNH 4 mNH 4 (11) PNH3 = K6 YH m-; By specifying mNH , mH and ~O , the ionic strength is determined, and 4 3 yNH /yH depends on the ionic strength. From the approach of Kusik and Meissner 4 (1978) (12) and Equation (11) simplifies to (y+)NH NO PNH 3 1-x = 9.05x10 -3 ( - ) 4 3 ( ~x~ ) (ppb) Y:_H,N0 (13) 3 with the values for the equilibrium constants from Table 2. VARIATION OF AMMONIA AND NITRIC ACID PARTIAL PRESSURES AS A FUNCTION OF pH The variation of the armionia and nitric acid partial pressures as a function of pH can be evaluated using the expression for (y+)NH NO from - Hamer and Wu (1972) and Equations (5), (10) and (13). 4 3 The water activity of the NH 4No 3-HN0 3 solution, (aw)MIX' is given by (14) where (aw)H,N0 is obtained from Equation (10) and the Gibbs-Duhem relationship 3 (Kusik and Meissner, 1978). The variation of pNH and pHNO with pH is shown 3 in Figure 4 for a relative humidity of 94.5 percent. 3 Also, shown are the 29 results of Tang (1980a) and those calculated assuming an ideal solution. The solid lines labelled Tang (1980a) were taken directly from Tang (1980a), and the points labelled Tang (1980a) were calculated using his procedure to insure an accurate duplication of that work. Figure 4 shows the approach of this work and that of Tang (1980a) differ in both the individual anmonia and nitric acid partial pressures, differences that become larger so the relative humidity decreases or ionic strength increases. The product of the ammonia and nitric acid partial pressures calculated from Equations (5) and (13) as a function of relative humidity is compared to the equilibrium product calculated using armionium nitrate activities in Figure 2. By comparing the curves labelled K-M solution and non-ideal NH 4No 3 solution, the agreement is shown to be good. The major source of dis- agreement between the K-M solution and the non-ideal NH 4No 3 solution curves The insensitivity of PNH PHN0 3 3 to pH can be seen in the range of relative humidity variation by multiplying is the 9.2~ difference between K5K4K3iK6 and K2 . Equations (5) and (13), As the relative humidity decreases, the maximum x, which occurs at pH = 1, becomes smaller. Thus, the difference between an acidic ammonium nitrate solu- tion (pH > 1) and a pure ammonium nitrate solution partial pressure product decreases with relative humidity. 30 2 10 \ I I RH= 94.5 % T = 25° C \ \ \ I I \ I \ PHNO \ 3\ I \ I I PNH 3 I I .0 \ -w \ \ a. 10 1 a. I I \ - I I I I \ a::: \ \ ::> CJ) en I \ w 8 TANG (1980a) A IDEAL SOLUTION I I -TANG (l980a) I \ s: I ---K-M SOLUTION I \ I ...J I <( t- a::: 1cf <( Q. I A I \ I \ I \ I I I I 10 1 1 0 !! \ \ / \ \ \ I \ \ I 2 1\~ 3 4 5 I 6 pH OF SOLUTION Figure 4. Effect of pH on the ammonia and nitric acid partial pressures. I 7 31 EFFECT OF NEGLECTING UNDISSOCIATED NITRIC ACID AND ION-PAIRING In developing quantitative expressions for the arrrnonia and nitric acid partial pressures, two assumptions were invoked. dissociated nitric acid on the (y.::_)H,N0 First, the effect of un- ionic strength functionality is small 3 below 7.0 molal. Second, ion-pairing of NH~ and N03 ions has a minimal effect on the anmonia partial pressures predicted. Equation (15) requires as x ~ 0, the solute activity approaches (y+)~H NO m~N NO . 2 quires YHl'N0 - to approach (r.::_)H,N0 3 4 3 3 as x 4" Similarly, Equation (4) re- 4 3 1. Inherent in Equations (4) and (15) are the correct limits but neither equation gives insight into the effect of these two assumptions. By an alternative expression for (y+)~H NO , - 4 3 (16) where yNH /yH and YHYNO are evaluated independently from NH 4 No 3 , the rela4 3 tive error can be ascertained. 2 The YHYN0 product will be given by (y.::_)H,N0 which assumes the undisso3 3 ciated nitric acid contribution is small. The arrrnonium to hydrogen ion activity coefficient ratio, Y.,u /yH, can be 11114 I evaluated from mean molal activity coefficients of an arrrnoniated salt, NH 4 X, and the acid with the same anion, HX, provided the acid completely dissociates. The ammonium to hydrogen ion activity coefficient ratio can be calculated noting that ( 17) where (y.::_)NH X = the mean molal activity coefficient of salt NH 4X and (y+)HX = 4 the mean molal activity coefficient of acid HX. This approach was tested with five different anions, Ct-, No3. I-, Br- and Cto4. (See Figure 5.) The assump- tion that HCt, HBr, HI and HCt0 4 totally dissociate in solutions below 7 molal + tt I J IONIC 0.1 I I ' ' II I I I I ' ' I 1.0 I STRENGTH (MOLALITY) I I • 10.0 I ' I I I I T• 2~· C' Effect of ionic strength on calculated annnonium/hydrogen ion mean molal activity coefficient ratio. I I ROBINSON 8 STOKES ( 1959) NH..O...(\-·HCL04 HAMER 8 WUU972) • NH4 1 ... Ht A NH4NO,-HNO, HAMER8 WUU972)and HOOFELDTU963) 1111 NH 8r-HBr ROBINSONS STOKES (1959) 4 o NH4 Cl-HCl HAMER 8 WU (1972) Figure 5. 0.01 ' 0.0I NH" 0.1 rH+ 1' 1.0~~~~~ w N 33 or saturation is appropriate since the dissociation constants are very large, 7 > 10 (Mccoubrey, 1955; Bockris and Reddy, 1970). It is incorrect to assume that HN0 3 completely dissociates, so the NOj curve was calculated using (y:_)H,N0 as previously derived. Lee and Wilmshurst (1964) have shown that a 5 molar NH Ct solution forms 4 ion-pairs. The observed mean molal activity coefficient, (y+)NH X,must be - corrected as follows (Bockris and Reddy, 1970), 4 (18) where (y+)NH X = the corrected mean molal activity coefficient for salt NH X 4 4 and e = the fraction of NH and X ions forming ion-pairs. Equation (18) as4 sumes the ion-pairs are syrrrnetric (Robinson and Stokes, 1959). Also, the ionic strength would be corrected to (l-6)mNH x· The net effect of ion-pairing 4 on the curves in Figure 5 is not obvious since the NH X mean molal activity 4 coefficient would increase and the ionic strength would decrease. Using density data of Pearce and Pumplin (1937), a 5-molar NH Ct solution is approxi4 mately 6.25-molal. The NH Ct-HC£ al1il10nium to hydrogen ion activity coeffi4 cient ratio is used to represent yNH /yH to 7.0 molal. 4 Thus, some NH 4Ct ion- pairing must be present above 6.25 molal. With Equations (1), (10), (16), and (17) and replacing K by K K K /K , 2 54 3 6 the effect of ion-pairing and the undissociated nitric acid can be ascertained. We refer the reader to the curve labelled non-ideal solution in Figure 2. water activity was calculated from Equation (2). The The agreement between the non-ideal, non-ideal NH No , and K-M solution curves supports the assumptions 4 3 3 34 of neglecting both the influence of undissociated nitric acid on the mean molal activity coefficient of dissociated nitric acid, (y.!.)H,N0 ' and the 3 presence of ion-pairing in calculating yNH /yH. By comparing the K-M and 4 non-ideal solution curves, the maximum possible error in the individual partial pressures can be ascertained as about 30~. Assuming YHYNo=(Y+l~ NO 3 - ' and Equation (17) holds, the YHYNO 3 product and 3 the yNH /yH ratio calculated cannot be used for calculating the individual 4 partial pressures of arrmonia and nitric acid because yHyNO goes to the wrong 3 limit as x • 0 and yNH NH goes to the wrong limit as x • 1. Even though these 4 expressions cannot be used for the individual partial pressures, they can be multiplied together to check the ammonia-nitric acid partial pressure product ca~culated from Equations (1) and (15) and the possible significance of ion- pairing and the undissociated nitric acid in calculating (y.:_)H,N0 . 3 35 DISCUSSION This approach gives theoretical justification for the results of Forrest et al. (1980) and Appel et al. (1980). As the relative humidity approaches 100 percent, the equilibrium vapor pressure product sharply decreases by several orders of magnitude. At 98 percent relative humidity and 2s 0 c, the mass concentration of NH 3 plus HN0 3 (equimolar basis) in the gas in equilibriu~ with an aqueous. ammonium nitrate solution is about 1.9 ~g m- 3 versus 17.9 ~g m- 3 needed if ammonium nitrate is present as a solid. Thus, the observation of Forrest et al. (1980) that greatest arrrnonium nitrate filter losses occurred at relative humidities below 60 percent, and no losses occurred at 100 percent relative humidity, and the observations of Appel et al. (1980) that nitrate aerosol is present even though the equilibrium product of a111110nia and nitric acid is much less than the solid equilibrium product are consistent with this work. The ammonia-nitric acid equilibrium product relative humidity functionality does not significantly change when the pH is varied between 1 and 7. The insensitivity of the arrrnonia-nitric acid equilibrium product with pH variation results from the arrrnonia-nitric acid equilibrium product being dominantly dependent on ionic strength. As the pH decreases below 1, the approach used in this work is not applicable since the role of undissociated nitric acid becomes significant and similarly for high pH undissociated dissolved arrmonia would appear. From the electroneutrality balance and the average aerosol water data in Stelson and Seinfeld (1981), a range of possible mass distribution averaged pHs between 2 and 12 is calculable for several locations in the Los Angeles Basin. and basic particles, Since the atmospheric aerosol is often a mixture of acidic 36 a distribution of aerosol pH would exist, the basic particles existing predominantly in the coarse mode (> 1 µm) and the acidic particles in the fine mode (< 1 wm). Thus, these results have limited applicability to the pos- sible range of existing ambient aerosol acidity. Qualitatively, the result of adding an unreactive solute on the vapor pressure product-relative humidity curve can be discussed. The unreactive solute would lower the water vapor pressure but would not affect the a1m1onianitric acid vapor pressure product. Thus, the resulting situation would be a measured vapor pressure product and relative humidity location lying below the NH 4Nc non-ideal vapor pressure product-relative humidity curve in Figure 2. 3 The presence of a saturated arrnonium nitrate solution around a solid arnr:ionium nitrate aerosol core can be examined. Since the saturated solution must be in equilibrium with solid arwionium nitrate, the vapor pressure product must be the same over the saturated solution as for the solid a11TT10nium nitrate. Thus, the presence of a saturated aqueous layer around a solid arrrnonium nitrate core at relative humidities below 62 percent would not affect the equilibrium vapor pressure product prediction. An additional important thermodynamic concept is the Gibbs-Duhem relationship which shows the solute activities determine the water activity. Thus, the equilibrium product and the relative humidity cannot be varied independently and to be theoretically consistent the solute or water activity must be determined by the other activities. Equation (14) shows the water activity can be taken as the water activity of a pure a1m1oni um nitrate solution s i nee the so 1utions are greater than 90 percent ammonium nitrate and the correction to make this theoretically rigorous is sma 11 . 37 Finally, this work illustrates an important concept in devising methods for performing equilibrium analysis. The equilibrium approach must be consis- tent, and certain limits must be satisfied. Internal consistency was demon- strated by the agreement between K2 and K5K4K3;K6 and by the arrrnonia-nitric acid vapor pressure products of solid anmonium nitrate and a saturated arnrnonium nitrate solution being equal. CONCLUSIONS Some important conclusions are evident from this work: (1) The ammonia-nitric acid equilibrium product is strongly and inversely dependent on the relative humidity. (2) A consistent set of free energy data exists such that the armionia-nitric acid equilibrium products for solid anmonium nitrate and for a saturated arrrnonium nitrate aqueous solution are equal; i.e. no discontinuity exists in the arrrnonia-nitric acid equilibrium product prediction at the relative humidity of deliquescence at 2s 0 c. (3) The ammonium to hydrogen ion molal activity coefficient ratio is not unity for concentrated ionic solutions. By assuming it is unity, sig- nificant error in the calculated ammonia partial pressure results. (4) The predicted relative humidity dependence of the arrrnonia-nitric acid equilibrium product is consistent with filter study results of Forrest et al. (1980) and Appel et al. (1980). ACKNOWLEDGMENT This work was supported by Environmental Protection Agency grant R806844 and State of California Air Resources Board contract A7-169-30. 38 REFERENCES Adams L.H. and Gibson R.E. (1932) Equilibrium in binary systems under pressure. III. The in6luence of pressure on the solubility of arrmonium oitrate in water at 25 C. J. Amer. Chem. Soc. 54, 4520-4537. Appel B.R., Wall S.M., Tokiwa Y. and Haik M.(1980) Simultaneous nitric acid, particulate nitrate and acidity measurements in ambient air. Atmospheric Environment li• 549-554. Bockris J. O'M. and Reddy A.K.N. (1970) -Modern Electrochemistry; An Introduction to an Interdisciplinary Area, Volume 1, Plenum Press. New York. Brandner J.D., Junk N.M., Lawrence J.W. and Robins J. (1962) 227-228. sure of amr:ioniurn nitrate. J. Che"-. Engng. Data z, Vapor pres- Davis W. Jr. and De Bruin H.J. (1964) New activity coefficients of 0-100 per cent aqueous nitric acid. J. lnorg. Nucl. Chem. 26, 1069-1083. Doyle G.J., Tuazon E.C., Graham R.S., Mischke T.M., Winer A.M. and Pitts J.N. Jr. (1979) Simultaneous concentrations of ammonia and nitric acid in a polluted atmosphere and their equilibrium relationship to particulate ammonium nitrate. Environ. Sci. Technol. ll• 1416-1419. Forrest J., Tanner R.L., Spandau 0., D'Ottavio T. and Newman L. (1980) Determination of total inorganic nitrate utilizing collection of nitric acid on NaC£-irnpregnated filters. Atmospheric Environment J.i, 137-144. Gordon R.J. and Bryan R.J. (1973) Ammonium nitrate in airborne particles 645-647. in Los Angeles. Environ. Sci. Technol. z, Granzhan V.A. and Laktionova S.K. (1975) The densities, viscosities, and surface tensions of aqueous nitric acid solutions. Russ. J. Phys. Chem. 49, 1448. Hamer W.J. and Wu Y.C. (1972) Osmotic coefficients a8d mean activity coefficients of uni-univa1ent e1ectro1ytes in water at 25 C. J. Phys. Chem. Ref. Data l· 1047-1099. Hogfeldt E. (1963) The comple~ formation between water and strong acids. Acta Chemica Scandinavica ll• 785-796. JANAF Thennochemical Tables, 2nd Edn (1971), NSRDS-NBS 37. Krawetz A.A. (1955) A Raman Spectral Study of Equilibria in Aqueous Solutions of Nitric Acid, Thesis, University of Chicago. Kusik C.L. and r1eissner H.P. (1978) Electrolyte activity coefficients in inorganic processing. A.I.Ch.E. Symp. Ser • .J.1l, 14-20. Lee H. and Wil~hurst J.K. (1964) Observation of ion-pairs in aqueous solutions by vibrational spectroscopy. Aust. J. Chem. lZ_, 943-945. 39 Lundgren D.A. (1970) Atmospheric aerosol composition and concentration as a function of particle size and of time. J. Air Pollut. Control Ass. 20, 603-608. Mamane Y. and Pueschel R.F. (1980) A method for the detection of individual nitrate particles. Atmospheric Environment li· 629-639. Mccoubrey J.C. (1955) The acid strength of the hydrogen halides. Soc. Trans . ..[!_, 743-747. Faraday Parker V.B., Wagman D.D. and Garvin D. (1976) Selected thermochemical data compatible with the CODATA recorrrnendations. NBSIR 75-968. Pearce J.N. and Pumplin G.G. (1937) The apparent and partial molal ~olumes of ammonium chloride and of cupric sulfate in aqueous solution at 25 C. J. Amer. Chem. Soc. ~. 1221-1222. Redlich o., Duerst R.W. and Merbach A. (1968) Ionization of strong electrolytes. XI. The molecular states of nitric acid and perchloric acid. J. Chem. Phys. 49, 2986-2994. Robinson R.A. and Stokes R.H. (1959) Electrolyte Solutions; The Measurement and Interpretation of Conductance, Chemical Potential and Diffusion in Solutions of Simple Electrolytes, 2nd. Edn. Butterworths, London. Smith J.P., Grosjean D. and Pitts J.N. Jr. (1978) Observation of significant losses of particulate nitrate and arrmonium from high volume glass fiber filter samples stored at room temperature. J. Air Pollut. Control Ass. 28, 930-933. ~ Spicer C.W. (1974) The fate of nitrogen oxides in the atmosphere. Batelle Columbus Rep. to Coordinating Res. Council and U.S. Environ. Protection Agency Rep. 600/3-76-030. Steison A.W., Friedlander S.K. and J.H. Seinfeld (1979) A note on the equilibrium relationship between armionia and nitric acid and particulate ammonium nitrate. Atmospheric Environment ]l, 369-371. Stelson A.W. and Seinfeld J.H. (1981) Chemical mass accounting of urban aerosol, submitted to Environ. Sci. Technol. Stephens E.R. and Price M.A. (1972) Comparison of synthetic and smog aerosols. J. Coll. Int. Sci. 39, 272-286. 40 Tang I.N. (1980a) On the equilibrium partial pressures of nitric acid and almlonia in the atmosphere. Atmospheric Environment.!.!· 819-828. Tang I.N. (1980b) Oeliquescence properties and particle size change of hygroscopic aerosols. In Generation of Aerosols, Ch. 7, ed. by K. Wi1leke, Ann Arbor Science Publisher, Ann Arbor, Michigan. Wagman O.D., Evans W.H., Parker V.B., Harlow I., Baily S.M. and Schuf11Tl R.H. (1968) Selected values of chemical thermodynamic properties; tables for the first thirty-four elements in the standard order of arrangement, NBS technical note 270-3. Weast R.C. (1973) Cleveland. Handbook of Chemistry and Physics, 54th. Edn. CRC Press, Young T.F., Maranville L.F. and Smith H.M. (1959) Raman spectral investigation of ionic equilibria in solutions of strong electrolytes. In The Structure of Electrolytic Solutions, Ch. 4, ed. by W.J. Hamer, John Wiley & Sons, New York. 41 CHAPTER 4 RELATIVE HUMIDITY AND TEMPERATURE DEPENDENCE OF THE AMMONIUM NITRATE DISSOCIATION CONSTANT Accepted for publication in Atmospheric Environment. 42 RELATIVE HUMIDITY AND TEMPERATURE DEPENDENCE OF THE AMMONIUM NITRATE DISSOCIATION CONSTANT A. W. Stelson and J. H. Seinfeld Department of Chemical Engineering California Institute of Technology Pasadena, California 91125 ABSTRACT Expressions for predicting the temperature and relative humidity dependence of the NH 4No dissociation constant are derived from funda3 mental thennodynamic principles. The general trends predicted by the theory agree with the atmospheric data of Appel et al. (1979, Pitts (1978, 1979) and Tuazon et al. (1980). 1980), 43 INTRODUCTION Ammonium nitrate has been identified in atmospheric aerosol (Lundgren, 1970; Stephens and Price, 1972; Gordon and Bryan, 1973; Mamane and Pueschel, 1980). An understanding of the temperature and relative humidity dependence of the relationship between NH 4No 3 and its precursors, NH 3 and HN0 3, is desirable. Stelson et al. (1979) and Doyle et al. (1979) showed that measured atmospheric ammonia-nitric acid partial pressure products scattered about the thermodynamically predicted solid NH 4N0 3 dissociation constant, indicating the likelihood of chemical equilibrium existing in this system. Stelson and Sein- feld (198la) demonstrated that Los Angeles aerosols contain ionic solids or concentrated solutions, B to 26 molal, indicating that any thermodynamic analysis must account for non-idealities present in concentrated solutions. Stelson and Seinfeld (1981b) calculated the ammonia and nitric acid partial pressures over ammonium nitrate-nitric acid solutions accounting for nitrate, hydrogen and ammonium ion non-idealities. Their analysis showed the ammonia- nitric acid partial pressure product is sensitive to relative humidity but insensitive to pH(l-7). Thus, the aqueous NH 4No 3 dissociation constant at a specific temperature and relative humidity should typify the arrrnonia-nitric acid partial pressure product of a slightly acidic armionium nitrate solution. Atmospheric gas phase arrrnonia and nitric acid and particulate nitrate measurements demonstrate important trends. Significant amounts of ammonium nitrate precursors, ammonia and nitric acid, have been found in urban air 44 accompanied by strong diurnal trends (Spicer, 1974; Pitts, 1978, 1979; Appel et al., 1979; Tuazon et al., 1980). Stelson et al. (1979) and Doyle et al. (1979) explained these observations through temperature dependence of the solid NH 4No 3 dissociation constant. Appel et al. (1979) observed that measured am- monia-nitric acid partial pressure products were less than the predicted dissociation constant even though aerosol nitrate was present. Forrest et al. (1980) spiked filters with NH 4No 3 and drew ambient air through the filters for three to five hours. The greatest NH 4 No 3 losses occurred at relative humidi- ties below 60 percent, whereas at 100 percent relative humidity, no NH 4No 3 was lost. Stelson and Seinfeld (198lb) were able to explain the results of Appel et al. (1979) and Forrest et al. (1980) by the relative humidity dependence of the NH 4No 3 dissociation constant at 25°c. Appel et al. (1980) observed a temperature and relative humidity dependence of measured a!Ti11onia-nitric acid partial pressure products. The object of this work is to derive expressions for the temperature and relative hu~idity dependence of the NH 4No 3 dissociation constant based on fundamental thermodynamic principles. The temperature dependence of the solid dissociation constant will be calculated using the method developed by 3 Stel son et al. ( 1979). The regions where anvnonium nitrate is in the sol id form NH 4No or in aqueous solution will be determined from expressions for the NH 4N0 3 relative humidity of deliquescence and solubility. For aqueous armionium nitrate, the NH 4No 3 dissociation constant and solution relative humidity will be calculated by non-ideal aqueous solution thermodynamics. Using appropriate express- ions for the NH 4N0 3 dissociation constant, a diagram can be constructed for the temperature and relative humidity dependence of the NH 4No 3 dissociation constant. Finally, the thennodynamic predictions are compared with ambient measurements of Appel et al. (1979, 1980), Pitts (1978, 1979) and Tuazon et al. (1980). 45 THEORY AND THERMODYNAMIC DATA FOR THE AMMONIUM NITRATE SYSTEM Solid NH 4No 3 Dissociation Constant At temperatures below 170°c, solid anrnonium nitrate exists in equilibrium with ammonia and nitric acid: ( 1) The equilibrium constant for this reaction, K~, is related to the partial press u res of N"~3 and HNO - .K'p -- ·oNH pHN0 ' and K'p is related to the standard Gi· bbs ' 3 bv 3 3 free energy change for reaction, lG~. by lG~ = - RT £n K~ ( 2) Since the thennodynamic data for NH 4 N0 3 are limited, an extrapolation formula for the equilibrium constant as a function of temperature can be derived by integrating the van't Hoff equation, £n K'p J 298 J( T" T 1 RT " 2 298 + C C PHNO PNH 3 3 ) dT' dT" - C . PNH NO 4 3 where a = integration constant, lH 0 = change in enthalpy at 298°K, and C PNH 3 respectively. , No NH and HN0 = the heat capacities of NH , , C C 3 3 4 3 PNH N0 PHN0 4 3 3 Using the data in Table 1 and assuming the heat capacities are independent of temperature, we obtain from (3), T 24220 tn K = 84. 6 - - T - - 6. 1 £n ( 298 ) where K is the equilibrium constant in units of ppb2. (4) (3) 46 Table 1. Thermodynamic Data for the Ammonium Nitrate System at 298°K LG o -1 LH o -1 c __£ Species R' K R' K NH 3(g) - 1,977* - 5,526* 4.285 Parker et al. (1976)* and JANAF ( 1971 ) HN0 3 (g) - 8~903 -16,155 6.416 JAN,A.F (1971) NH 4N0 (c,IV) 3 -22,220* -44,080* 16.8 Parker et a 1 . (1976)* and Wagman et al. ( 1968) NH 4N0 3(aq,m=l) -22,940+ -40,880+ -0.505 Wagman et al. (1968)+ and Roux et al. (1978) LG = Standard free energy of formation lH = Heat of formation Cp = Heat capacity R Reference 47 Relative Humidity of Oeliguescence and Solubility Up to the relative humidity of deliquescence, armionium nitrate should be present as a solid. The results of Tang (1980 ) indicate NH 4No 3 aerosol is quite hygroscopic at ~30% relative humidity versus '""62% observed for bulk NH 4No 3 at 25°c (Dingemans, 1941; Adams and Merz, 1929; Edgar and Swan, 1922; Prideaux, 1920). Whether the observation of Tang (1980 ) is the result of a property unique to the size of the NH 4No 3 aerosol or the presence of an impurity is difficult to ascertain. Prideaux (1920) observed that the presence of a small amount of sodium nitrate in arrrnonium nitrate significantly reduced the relative humidity of deliquescence. Since we cannot adequately evaluate the observations of Tang (1980 ), we will assume NH 4No 3 exhibits traditional deliquescence as implied by the majority of the literature. An expression can be derived for the saturated solution relative humidity 1 ) + £n (RHD)298 L ( fl - 298 £n(RHD) = - R (5) where RHO = percent relative humidity of deliquescence and L =water heat of fusion (Denbigh, 1971). Using the water heat of fusion from Weast (1973) and the rela- tive humidity of a saturated NH 4No 3 solution at 298.15°K from Harner and Wu (1972), tn (RHO) = 72 ~· 7 + 1.7037. (6) Equation (6) agrees well with the least square expression derived from the data of Dingemans (1941), in (RHO) = 856 · 2 ~= 13 · 25 + 1.2306 .:_ 0.0439 (7) 48 Equations (6) and (7) are shown with experimental data in Figure 1. For an ideal solution, the solubility temperature dependence is (a ~n(m2)) = Ro-hs ClT \ (8) RT2 p where m = NH 4N0 3 molality, R0 ,.. the NH 4 ~10 3 partial molal enthalpy at infinite dilution and hs = enthalpy of crystalline NH 4No 3 . 1) 0 (R -hs)(l tn m = - ~ T - 298 is obtained. By integrating Equation (8), (9) + tn(m)298 Using the thennodynamic data in Table 1 and noting that (m) 298 25.954 from Harner and Wu (1972), + 8.6228 Xn m = - 1600 T ( 10) Equation (10) agrees well with the least squares expression for the data of Stephen and Stephen (1963), ' ~n m -- - 1837 · 3=18 · 0 + 9 • 4235~0 - . 0602 • T ( 11) Equations (10) and (11) are shown with the data of Stephen and Stephen (1963) in Figure 2. Figures 1 and 2 sho1-1 the strong temperature dependence of the relative humidity of deliquescence and the solubility of ammonium nitrate. This tempera- ture dependence is an unfortunate complication when attempting to extrapolate aqueous arrrnonium nitrate thermodynamic data to temperatures above 2s 0 c. Aqueous NH 4No 3 Dissociation Constant Analogous to the solid NH 4No 3 dissociation constant derivation, an expression for the equi]ibriUl'C constant over aqueous NH 4No 3 can be derived, T £n K*p J" J J( _l_ 298 RT" 2 298 C PNH3 - C PHN03 - r 0 PNH4N0 3 ) dT' dT" (12) !.150 40 !.200 30 • 10~0 3.350 20 •c • •I{' TEMPERATURE , 3.450 , ~ PRIDEAUX OHO) & !.!3 00 i JlNECKE Ii RAHl..'5(11 1111 PRIDEAUX Ii CAY!N (1911) 6 o EDGAR & SWAN ( 1122) a ADAMS 8a MERZ UHi) e ~MANS (194U ......... 10 (15), (21) and (22). NH No relative humidity of deliquesc ence temperatu re dependenc e: 4 3 (•-•-•) Equation (6); (~) Equation (7); (- - -) Equations (11), 3.800 3.0!'JO 4.000 Figure 1. .5 0:: - :c 0 - 4.200 00 . w ~ ~ ~ 48 ~ 50 t"" ~ 0:: LIJ _. e:: C( ! 0 • w~_. ~-0 ~ (/) lro"" w~ IO ~ \0 ...... ....... 3.25 3.35 20 3.45 ........... ~... .... - 10 0 I 33.12 54.60 ,... I:: .! - t Figure 2. 2.50 3.05 3.00 12.18 3.675 NH No solubility temperature dependence: (~) Equation (11); 4 3 (- - ) Equation (10); Data from Stephen and Stephen (1963). ~··•c·• 3. 55 i 20.09 z-J! :I 'i .... ......... 30 i ... 3.15 ...... ...... 40 ~ 3.50 ...... ..... 50 ~ ~ -....> 4.00 TEMPERATURE, •c 0 V1 51 2 -o - ±2 I where K~ = PNH3PHN03/aNH4N03 - KP aNH4N03' aNH4N03 - YNH4N03m CPNH4ND3 - I NH 4No 3 partial heat capacity at infinite dilution, and y~H NO 4 ionic activity coefficient of dissolved NH 4No 3 . = mean molal 3 Using the data in Table 1 and assuming the heat capacities are independent of temperature, we obtain from (12), in K* = £n a = 54.18 K NH 4No 3 2 where K* has units of ppb 2 molal- . 15 60 ~ + 11.206 £n( 2 ~8 ) (13) 4 03 can The temperature variation of y~H N be calculated from -o -HH (14) = RT 2 where R =the NH 4 No 3 nartial molal enthalry ?tt m (nenhiah, 1971, o. 279). Bv integrating (14), (15) is obtained, where dilution and m, c0 , L = NH4 No 3 partial molal heat capacities at infinite resp:cti~ely, and (RRP.o) 298 = the normalized NH 4No 3 relative partial molal enthalpy difference between infinite dilution and mat 298.15°K. To evaluate (£n y~H NO ) , the concentration dependence of (£n y~H NO ) , 4 3 298 4 3 T 0 (C-c ) --o (HRH )298 and \~ must be known. The expression of Hamer and Wu (1972) can 4 03 ) 298 to be used to represent the concentration dependence of (in y~H N ,.~ -c-o ) R-Ro) 25.954 molal. Obtaining expressions for (-R~ 298 and ( ~ is more complicated. 52 Relative apparent molal heat content data can be obtained from Wagman et al. (1968) and Vanderzee et al. (1980). Since the data of Vanderzee et al. (1980) are more recent and span a larger concentration range, they will be used to represent the variation in enthalpy with concentration. A polynomial regression can be calculated using ideal gas constant normalized relative apparent molal heat content data of Vanderzee et al. (1980) between 0.1 and 25 molal. The partial molal enthalpy was derived using Equation (8-2-7) from Harned and O;;en ( 1958), as where ~L = relative apparent molal heat content at m. The resulting poly- nomial regression is - -o 312 - 133.86m 2 297.85 m112 - 983.98m + 508.08m (H-H ) R 298 + 19.328m 512 - l.207lm 3 (17) where the standard deviation for the normalized relative apparent molal heat content polynomial regression is.:!:. 3.54 oK- 1 . The error in the relative partial molal enthalpy polynomial regression is unknown since it was obtained using the normalized relative apparent molal heat content polynomial regression and (16). Roux et al. (1978) measured the apparent molal heat capcity, ¢cp' of aqueous ammonium nitrate at 25°c to 22.4 molal. data, Their expression for their 53 oc 312 --2= - 0.505 + 3.482 m112 + 3.159 m - 1.605 m R 2 - 0.0161 m5/2 + 0.274 m (18) agrees well with the measurements of Gucker et al. (1936) and Sarina et al. (1977). Using Equation (8-4-7) from Harned and Owen (1958), cl<tc ct. cp +m--P. (19) am the partial molal heat capacity can be calculated from (18) as, c 3 --2. = - 0.505 + 5.223 m112 + 6.318 m - 4.013 m 12 R 2 + 0.822 m 5/2 - 0.0564 m . (20) The data of Sorina et al. (1977) extend to 50 molal, supersaturation at 25°c. With relative apparent molal heat content and solute activity data to 50 molal, + the temperature extrapolation of y-NH No 0 at so c. 4 could be performed to saturation 3 Unfortunately, the relative apparent molal heat content data are limited to 25 molal (Vanderzee et al., 1980). Even though (20) is based on data to 22.4 molal, it will be used to 25 molal. Within the region 22.4-25 molal, (20) is a smoothly continuous extrapolation of the data below 22.4 molal and represents the data of Gucker et al. (1936) and Sarina et al. (1977) fairly well. + Once (tn YNH N )T has been calculated, the osmotic coefficient of the 4 03 solution, ¢T' can be derived from the Gibbs-Duhem equation, 54 1 + ~ m J m d(in y~H 0 4 NO )T (21) 3 The percent relative humidity at te~pernture T, RHT' can be calculated from RHr = 100 exp ( - ·v m M::T ) 1000 (22) where ·J = the nuf'.lber of moles of ions formed by the ionization of one mole of solute and M =molecular weight of water. 55 RESULTS By using appropriate expressions for the temperature dependence of solid or aqueous phase NH 4No 3 thermodynamic properties, the dissociation constant can be calculated at a specific temperature and relative humidity. With (7), the for:i' of armionium nitrate, solid or aqueous, can be detennined. At a spe- cific temperature the NH 4No 3 dissociation constant is invariant below the relative humidity of deliquescence and can be obtained from (4). Above the rela- tive humidity of de1iquescence, the NK 4N0 3 dissociation constant re1ative humidity dependence can be calculated from (13), (15), (21) and (22) to 25 molal. Equation (11) is used to calculate the solubility temperature depende- ence. Figure 3 has been constructed using the previously mentioned techniques. Notice discontinuities exist between the solid NH 4No 3 dissociation constant and the dissociation constant for a saturated solution at 25°c and below. The possible sources of these discontinuities at temperatures below 25°c are manifold and the relative error from each source is difficult to evaluate. First, the temperature extrapolations for the solid NH 4No and the 3 aqueous NH 4No 3 dissociation constants are based on different thennodynamic data sets so an inconsistent value in one data set can cause discontinuity. Second, the relative humidity of deliquescence is obtained by different methods for solid NH 4Nc 3 and aqueous NH 4No 3. The relative humidity of deliquescence for solid NH 4No was calculated from (7) and aqueous NH 4No from (11), (15), 3 3 (21) and (22). The relative error can be seen by comparing the solid and dashed curves in Figure 1. Third, error is introduced by differentiating the polynomial regressions obtained for the relative apparent molal heat content and the apparent molal heat capacity to get expressions for the partial molal enthalpy and heat capacity. The amount of error is known for the original 56 4 10 253 50-C \ \ \ \ 101 80.0 40*C -:::c \ \ \ 2 10 O'I \ E 25.3 30•c E 0 CD ..... 2s•c 1a1 0 S.00 2o•c 11111 .a an ..,N Q. Q. ~ 0 'E 100 2.53 10-C "'::l I"' -1 0.80 iO ~ VJ < 1f!' o•c ~ ·3 10 ~-~~~~..-~~.......~~--.......~~.......~~~--~.....i...a... """ 50 60 70 80 90 RELATIVE HJMIDITY • o/o Figure 3. NH No dissociation constant temperature and 4 3 relative humidity dependence: (- - -) solid NH No to aqueous NH No solution transition 4 3 4 3 predicted from Equation (7); (~) Isothermal prediction of NH No dissociation constant for 4 3 solid NH No and non-ideal NH No solutions at 4 3 4 3 indicated temperatures; ~···) Extrapolation between predicted solid and maximum calculable aqueous NH No dissociation constant. 4 3 57 po1ynomial regressions but not for the derived regressions. Finally, the error must be introduced by the enthalpy, heat capacity, relative humidity of deliquescence or solubility data or the temperature extrapolation technique, since the free energy data are consistent at 298°K (Stelson and Seinfeld, 198lb). Above 25°c. an interpolation must be performed between the relative humidity corresponding to 25 molal and saturation. Since the curves are fairly flat in the region between 25 molal and saturation, a linear interpolation between the dissociation constant at 25 mo1al and at saturation should approximate the dissociation constant in this region. The temperature dependence of the saturated solution relative humidity can be calculated using (11), (15), (21) and (22) for temperatures below 25°c. A curve calculated using this method is shown in Figure 1. Data for the molal variation of the solution relative humidity at various temperatures are shown in Figure 4. The data scatter is considerable and shows no definite temperature variation trend. Curves for the relative 0 humidity concentration dependence were calculated at 0, 25 and 5o c using (15), (21) and (22) and are shown in Figure 4. The predictions coincide with the general area of the data but do not show agree~~nt with any particular data set. Also shown in Figure 4 is the relative humidity concentration depend- ence for an ideal NH 4No 3 solution which poorly predicts the non-ideal NH 4No 3 behavior. Figure 4 illustrates the infeasibility of attempting to use water activities at higher temperatures, 25-S0°c, and the Gibbs-Duhem equation to calculate solute activities. The data have too much scatter and are too sparse at any particular temperature. Furthermore, the maximum concentration of existing water activity data is 29.2 molal and saturation is 42 molal at so0 c. 58 • O'"C - FlltlCKE 0129) II iO"'C - Fma<E Ii HAVESTADT('l927) e BO'"C -AUCK£ ( 1129) 0 '!O"'C -CAM PB ELL ET AL. ('1956) O 40'"C-CAMPBELL ET Al..(1956) II \ \ \ \ \ \ A 40•c-PR1DEAux &CAVENC19!9l • !IO'"C -CAMPBELL ET AU 1956) \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \ IDEAL SOLUTION - - " ' \ \ \ \ \ \ \ I ·'~~'~'L..&..'~~---''--~~~'~~~··~' 50~~~.......1'~~~~'~~-D Figure 4. 5 ID ~ ~ ~ ~ Temperature and concentration dependence of NH No solution relative humidity: (- - -) 4 3 ideal solution prediction; ( - - ) non-ideal solution predictions at O, 25, and 50°c. ~ 59 DISCUSSION Atmospheric measurements of simultaneous a1m10nia, nitric acid, temperature, relative humidity, aerosol ammonium and aerosol nitrate are very limited. With partial data sets, the merit of the thermodynamic calculations can be demonstrated. Figure 5 shows diurnal variation of the measured arrrnonia-nitric acid partial pressure product and the respirable aerosol nitrate at Pittsburg, Ca. (Appel et al., 1979). The trends of the curves are very similar. If the similarity between the diurnal variation of the ammonia-nitric acid partial pressure product and the respirable aerosol nitrate resulted strictly from atmospheric dilution effects, these data when cross plotted, should result in a single curve. The data were analyzed by this method and the test failed. Thus, the similar trend between the observed ammonia-nitric acid partial pressure product and the respirable aerosol nitrate cannot be merely attributed to atmospheric dilution. Also shown are the daily maximum bulk NH 4No 3 dissocia- tion constants calculated frorr. the daily maximum temperature and (4). Amonia- nitric acid partial pressure products below the daily maximum bulk NH 4No 3 dissociation constant can result from the lack of aerosol ammonium nitrate, the presence of an unreactive solute, the temperature being less than the daily maximum or the relative humidity being greater than the deliquescence point. Ammonia-nitric acid partial pressure products above the daily maximum bulk NH 4No 3 dissociation constant could be explained by kinetic limitations or Kelvin effects. Kinetic limitations are doubtful since the ammonia-nitric acid reac- tion is very fast (Kaiser and Japar, 1978; Morris and Niki, 1971). tal errors could result in positive or negative deviations. Experimen- 60 ------------ 1.0 ... ~------------ o.o l!I II JL 0.15 _J 0.10 TIME(PST) Figure 5. Experimental diurnal NH -HN0 product and aerosol 3 3 nitrate trends at Pittsburg, CA (Appel et al.,1979): (o-o) Product calculated from NaCl impregnated Whatman 41 filter gaseous HN0 3 measurements; (a-a) Product calculated measurements; 3 dissociation constant based on the from Duralon nylon filter gaseous HN0 (- - -) Maximum NH No 4 3 daily maximum temperature and Equation (4); pNH PHNO in 3 3 p~2 61 The effect of an unreactive solute in solution with al1lT10nium nitrate on the a1TB11onia-nitric acid partial pressure can be evaluated qualitatively. From the Gibbs-Duhem equation, (23) where m = molality of inert solute and a =activity of inert solute. 1 1 ing the inert solute is ideal and undissociated, Assum- (24) Equation (24) shows the addition of an ideal inert solute would decrease the relative humidity above an a1TT110nium nitrate solution for a specific a1TB11onium nitrate molality. Since the additional solute is assumed to be non-interactive with the dissolved a1TB11onium nitrate, the ammonia-nitric acid partial pressure product would be the same as the situation without any inert solute. Thus, the presence of an inert solute results in an al1lT10nia-nitric acid partial pressure product being observed at a lower relative humidity than would be predicted from the pure a1TB11onium nitrate-water system. The Kelvin effect for solid NH N0 can be evaluated using an expression 4 3 derived by Banic and Iribarne (1980), 4 c- M oRT £n S (25) NH 4No 3 surface tension, dp = particle diameter, M = NH No molecular 4 3 weight, p = NH No density and S = the saturation ratio which equals K for 4 3 where a curved surface/K for flat surface. The N~N0 surface tension was approximated 3 62 as 108.4 dynes/cm at 25°c by the approach of Rehbinder (1926). The surface tension is approximate because it required extrapolation from 168.5°c across three different NH 4N0 3 crystalline structures (Nagatani et al .• 1967). With the NH 4No 3 density and molecular weight from Weast (1973), (25; simplifies to d = 8.lxlO p -3 ( 26 ) in S In Figure 5, saturation ratios greater than 5 are observed. (Compare observed ammonia-nitric acid partial pressure products and the daily maximum bulk NH No 4 3 dissociation constants in Figure 5.) Can these supersaturations be attributed to the Kelvin effect? dia~eter For a saturation ratio of 5, the calculated particle is O.OCS u~ which is too small to be atmospherically realistic since 0.005 -..r particles would be readily scavenged by larger particles. The relative hu~idity dependence of the ammonia-nitric acid product at Clare~ont, datu~ Ca is displayed in Figure 6 (Appel et al., 1980). Next to each is the temperature in centigrade at the time of measurement. te~peratures Underlined refer to points positively deviating from the dissociation constant calculated at the temperature and relative humidity of each measurement. Also shown are NH 4No 3 dissociation constant isotherms, 20, 25 and 30°c, calculated using the procedures developed in this work. The data show scatter but are in general agreement with the predictions of this work. Figure 7 shows the diurnal variation of the arrrnonia-nitric acid product calculated fro~ measurements at Riverside, Ca (Pitts, 1978, 1979; Tuazon et al., 1980). Also shown are the diurnal variations of the solid NH4No 3 dissoci- ation constant calculated fro~ (4) and the average temperature profiles for all days and episode days (maximur o3 > 0.2 ppm) between May and October 1976 63 . ~29.9 l9.o 25 45 rr. 55 RELATIVE HUMIDITY, 9/o Figure 6. Experimental relative humidity and temperature dependence of the NH -HN0 product at Claremont, CA 3 3 (Adapted from Appel et al., 1980): (~)Predicted NH No dissociation constant relative humidity 4 3 0 dependence at 20, 25, and 30 C; Values next to data from Appel et al. (1980) are the temperatures in centigrade. P. ) ca 0 0 "' + • 12001 0 --- ~ 1300 i II I ... 0 •• ~ ,,...... ~' ....... i l!SOO 1600 i ·--.. -- TIME OF DAY MOO 0 Ill j ' '' 1800 '•a' 1700 ·~.. •' • 1900 '' NH No dissoc iation consta nt diurna l trend calcula ted from Equatio n (4) 4 3 and the average temper ature profile for episode days (maximum o > 0.2 ppm), 3 May - Octobe r 1976 (Pitts, 1978); (- - -) solid NH No dissoc iation 4 3 consta nt diurna l trend calcula ted from Equatio n (4) and the average temper ature profile for all days, May - Octobe r 1976 (Pitts, 1978); Differe nt data symbol s refer to differe nt days of measur ement; pNH pHNO 2 3 3 i n PP b Diurna l NH -HN0 produc t trend calcula ted from FT-IR measur ements 3 3 at Rivers ide, CA (Pitts, 1978; Tuazon et al., 1980): (~) solid 0 v a . .-------- . . . e , .... • • O 1111 1100 1.0 F1 2.0 3HM05 Figure 7. IOQ ( D 30....-.........-....----....----..----.,.......--~--.........,l""""""--'T'""................, + + ~ O'\ 65 (Pitts, 1978). Note the strong diurnal pattern with the peak occurring between 1400 and 1600 which corresponds to the daily maximum temperature and minimum relative humidity region. Finally, some comments on how this work should be applied are in order. Figures 6 and 7 show the trends predicted by the thennodynamics generally follow the atmospheric data trends though positive and negative deviations from the pure NH 4No 3 thermodynamics are apparent. Negative deviations can be explained by the presence of additional solutes in solution. explained with current theoretical development. Positive deviations cannot be The polluted atmospheric aerosol can be multicomponent or supersaturated which leads to deviations from the pure NH 4No 3 theoretical predictions. Thus, this work should be used as guidance to identify important parameters in aerosol measurement, give a relative feeling for what the distribution of nitrate is between the gas and aerosol phases and a basis for assembling more detailed multicomponent theories. Additionally, Figure 3 merits comment. The right ordinate of Figure 3 is lK, expressed as nitrate, ug m- 3 , at 25°c and 760 rrrn Hg. Typical aerosol nitrate values range between 0 and 40 µg m- 3 (Stelson et al., 1979). spanned by the ordinate of Figure 3. This range is Thus, the importance of accurately moni- taring temperature and relative humidity during aerosol nitrate measurement is apparent. CONCLUSIONS Some important conclusions are evident from this work: 1. A thermcdynamic extrapolation method was developed to predict the ternperature and relative humidity variation of the NH 4No 3 dissociation constant. 2. The approach of using existing water activity data at temperatures other than 25°c to calculate solute activities is shown to be infeasible. 66 3. The general trends predicted by the thennodynamic model agree with the atmospheric observations of Appel et al. (1979, 1980), Pitts (1978, 1979), and Tuazon et a 1. ( 1980). 4. Positive deviations of measured ammonia-nitric acid partial pressure products from the solid NH 4N0 3 dissociation constant at the temperatures of measurement cannot be readily explained other than on the basis of experimental error. ACKNOWLEDGMENT This work was supported by Environmental Protection Agency grant R806844 and State of California Air Resources Board contract A?-169-30. 67 REFERENCES Adams J.R. and Merz A.R. (1929) Hygroscopicity of fertilizer materials and mixtures. Ind. Eng. Chem. £!_. 305-307. Appel B.R., Tokiwa Y., Hoffer £.M., Kothny E. l., Haik M. and Wesolowski J.J. 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Atmospheric Environment _ll, 369-371. Stelson A.W. and Seinfeld J.ll. (1981a) Chemical mass accounting of urban aerosol. Environ. Sci. Technol. ~. 671-679. Stelson A.W. and Seinfeld J.H. (198lb) Relative humidity and pH dependence of the vapor pressure of arrrnonium nitrate-nitric acid solutions at 25°c. Accepted for publication in Atmospheric Environment. Stephen H. and Stephen T. ed. (1963) Solubilities of Inorganic and Organic Compounds. Vol. 1, Part 1, Macmillan, New York, p. 217. Stephens E.R. and Price M.A. (1972} J. Coll. Int. Sci. 39, 272-286. Comparison of synthetic and smog aerosols. Tang I.N. (1980) Deliquescence properties and particle size change of hygroscopic aerosols. In Generation of Aerosols, Chap. 7, ed. by K. Willeke, Ann Arbor Science Publisher, Ann Arbor, Michigan. Tuazon E.C., Winer A.M., Graham R.A. and Pitts J.N. Jr. (1980) Atmospheric measurements of trace pollutants by kilometer pathlength FT-IR spectroscopy. Adv. Environ. Sci. Technol. lQ_, 259-300. Vanderzee C.E., Waugh D.H. and Haas N.C. (1980) Enthalpies of dilution and relative apparent molar enthalpies of aqueous a1T111onium nitrate. The case of a weakly hydrolysed (dissociated) salt. J. Chem. Thermodynamics_!£, 21-25. 70 Wagman D.D., Evans W.H., Parker V.B., Harlow I., Baily S.M. and Schumm R.H. (1968) Selected values of chemical thermodynamic properties; tables for the first thirtyfour elements in the standard order of arrangement, NBS technical note 270-3. Weast R.C. ed. (1973) Handbook of Chemistry and Physics, 54th Edn. Chemical Rubber Publishing Company, Cleveland, p. D-159. 71 CHAPTER 5 THERMODYNAMIC PREDICTION OF THE WATER ACTIVITY, NH No DISSOCIATION CONSTANT, DENSITY AND REFRACTIVE INDEX 4 3 FOR THE NH No - (NH ) so - H o SYSTEM AT 25 C 2 4 2 4 4 3 Submitted for publication in Atmospheric Environment. 72 THERMODYNAMIC PREDICTION OF THE WATER ACTIVITY, NH 4No 3 DISSOCIATION CONSTANT, DENSITY AND REFRACTIVE INDEX FOR THE NH4N0 3-(NH 4 )2so4-H 2D SYSTEM AT zs 0 c A. W. Stelson and J. H. Seinfeld Department of Chemical Engineering California Institute of Technology Pasadena, California 91125 ABSTRACT The thermodynamic properties, water activity, density and refractive index, of NH 4No 3-(NH 4) so 4-H 20 aerosols are estimated from binary solution 2 data and existing mixing rules. Particle growth is shown to be predictable from the particle composition, the NH 4No 3-(NH 4 ) 2so 4-H 2D phase diagram and the water activity calculation technique of Kusik and Meissner (1978). Good agreement between the theoretical predictions and the experimental measurements of Tang et al. (1981), Thudium (1978) and Emons and Hahn (1970) is shown. Also, the effect of (NH 4 )2so4 on the relative humidity dependence of the NH 4No 3 dissociation constant is evaluated. 73 INTRODUCTION Arrrnonium, nitrate and sulfate comprise a significant portion of the atmospheric aerosol (Appel et al., 1978; Stevens et al., 1978). Two probable chemical forms for the nitrate and sulfate species are arrrnonium nitrate and anrnonium sulfate. Since the arrmonium, nitrate and sulfate ions occur in par- ticles of similar size, a thennodynamic study of the interaction between a1TTI1onium nitrate and arrmonium sulfate would provide a foundation for understanding atmospheric processes involving these species (Cunningham et al .• 1974; Patterson and Wagman, 1977; Harrison and Pio, 1981). The prediction of the size, water activity and NH 4No 3 dissociation constant for aqueous NH 4No 3-(NH 4 )2so 4 aerosols is necessary. Previously, the thermodynamic analysis of this system has been limited by the non-ideal nature of these solutes. This paper will show how the growth, water activity and NH 4No 3 dissociation constant can be calculated from the temperature, relative humidity and NH No ;(NH 4 ) so 4 ratio. Also techniques for predicting the solu4 3 2 tion density and refractive index will be discussed. The theory, though specifically applied to the NH 4No 3-(NH 4 )2so 4-H 20 system, can easily be generalized to ll()re complex electrolytic mixtures. BACKGROUND Growth Studies The thermodynamic growth properties of atmospheric electrolytic aerosols have been explored extensively (Orr et al., 1958; Winkler and Junge, 1972; Winkler, 1973; Chen, 1974; Tang et al., 1978; Thudium, 1978; Hanel and Zankl, 1979; Saxena and Peterson, 1981; Tang et al., 1981). Tang et al. (1978) demonstrated that mixed salt aerosol particles can undergo stepwise growth 74 and showed the utility of phase diagrams for understanding these processes. Chen (1974), Thudium (1978), Hanel and Zankl (1979), and Saxena and Peterson (1981) have studied methods for predicting the water activity or osmotic coefficient of a multicomponent aerosol droplet from binary data*. Winkler and Junge (1972) and Winkler (1973) studied the growth of multicomponent atmospheric and synthetic salt aerosols. They observed that the ambient aerosol composite exhibited smooth growth which contrasts with the stagewise growth of the single particle studies of Tang et al. (1978). Orr et al. (1958), Winkler and Junge (1972), and Tang et al. (1981) studied hysteresis effects of drying aerosols, and Orr et al. theoretically and experimentally demonstrated that particles deliquesce at lower relative humidities as their size decreases. The volatility of solid NH 4No 3 in atmospheric aerosols has been studied by Stelson et al. (1979) and Doyle et al. (1979). In particular, Stelson and Seinfeld (198la, 198lb) have evaluated the temperature, relative humidity and pH dependence of the NH 4No 3 dissociation constant in concentrated solutions of arrmonium nitrate and nitric acid. Tang (1981) explored the role of sulfate on the individual an1110nia and nitric acid partial pressures above NH 3-HN0 3H2so4-H2o solutions. *Thudium (1978) has shown the mixture rule of Chen (1974) is physically incorrect. 75 Relation to Ambient Aerosol Sampling From understanding the role of {NH ) so on the volatility of NH No , 4 2 4 4 3 the effect of (NH 4 ) 2so on the sampling of a1TJT1onium nitrate aerosol can be 4 evaluated. Appel and Tokiwa {1981) showed that the reaction of strong acids, H2so4 and HCt, with NH No leads to the loss of aerosol nitrate. A question 4 3 of importance is - What effect would the internal mixing of a pure (NH ) so 4 2 4 aerosol with a pure NH No aerosol have on the NH No dissociation constant? 4 3 4 3 Ahlberg and Winchester {1978) identified a1TJT10nium sulfate as the major sulfate species in Florida aerosol by following the relative humidity dependence of the aerosol sulfur mass median aerodynamic diameter. Another question is - How would the presence of NH No affect an aerosol identification technique that 4 3 utilizes particle growth resulting from water condensation? Finally, Clark et al. (1976) measured the effect of aerosol sulfate fonnation on aerosol nitrate fonnation. As the rate of aerosol sulfate formation increased, that of aerosol nitrate formation decreased. A further question is - Is the reduc- tion in the nitrate aerosol formation rate during simultaneous sulfate aerosol formation the result of a change in the distribution of nitric acid between the gas and aerosol phases or is the total amount of nitrate formed reduced? The thermodynamic theories developed in this paper will give insight into the answers of these questions. 76 NH4N03-(NH4)zS04-HzO PHASE DIAGRAM The NH 4No 3-(NH 4 ) 2so4-H 2o phase diagram can be constructed from the data in Silcock (1979) and Emons and Hahn (1970) and is shown in Figure 1. The phase diagram shows several interesting items. By equating chemical potentials at eutonic points, E1 and E2 , the NH 4N0 3 chemical potential can be shown to be constant along the solubility curve between pure NH 4No 3 in water and E3 and in the regions I, I & II, II, II & III, III and III &IV. If the NH 4N0 3 chemical potential is constant throughout these regions, then the NH 4N0 3 dissociation Similarly, the (NH 4 )2so 4 chemical potential must constant must be invariant. be constant along the solubility curve between pure (NH 4 )2so 4 in water and E1 and in the regions IV, III & IV, III, II & III, II and I & II. If the chemi- cal form of the aqueous solutes is the same along the solubility curve between E1 and E3 then by equating chemical potentials and by using the Gibbs-Ouhem equation, the solution relative humidity should be constant. In Table 1, relative humidity measurements of saturated aqueous NH 4No 3-(NH 4 )2so 4 solutions from Emons and Hahn (1970) are shown. "Their data show that the relative humidity varies between E and E3 , indicating a new dissolved species must be formed. 1 Finally, Figure 1 illustrates a problem when attempting to describe multicomponent aqueous mixtures up to saturation. Since (NH4 )2so4 precipitates at a lower ionic strength then NHANO~. there is a prob1em in describing the region J ~ of the phase diagram where the ionic strength is greater than the maximum ionic strength of the least soluble species. For the NH 4No 3-(NH 4 )2so 4-H 20 system, this region lies between the solubility curve and the dashed line in Fig. 1. In the next section, this problem will be discussed in more detail. 77 :z 80 0 I- I u er <{ I.I.. I- :r 60 -C> w ~ 20 20 40 60 80 100 (NH4) 2 504 WEIGHT FRACTION Figure 1. NH No -CNH ) so -H o phase diagram at 25°c. 4 3 4 2 4 2 0 - Emons and Hahn (1970); o, +, .Da- Silcock (1979) 78 ESTIMATION OF THE WATER ACTIVITY AND THE NH 4No 3 DISSOCIATION CONSTANT Expressions developed by Kusik and Meissner (1978) can be used to estimate the water activity and the solute activity coefficients for the NH No 4 3 (NH4)2so4-H20 system. The NH 4No 3 activity, a 12 , is given by o 3-3Y o tn a 12 = -2+4Y 3- tn y 12 + - 4- tn y 14 (1) + tn { 2;v } vr2 where y~ 2 , y~ 4 = the activity coefficients of NH 4 No 3 or (NH 4 ) 2so 4 alone in water at-I, Y =the ionic strength fraction of NH 4No , 3 and I= the total solution ionic strength. The (NH 4 J2so4 activity, a14 , is tn a 14 = 2Y tn y~ 2 + 1243Y tn y~ 4 (3) From Equations (1) and (3) and the Gibbs-Duhem equation, followed by integration, the water activity can be calculated as tn aw = ( 2; Y ) Y .tn a 0 + wl2 (2; Y) (1-Y) YM I - 60~0 (1-Y) (4) where a0 , a0 the water activities of NH 4No 3 or (NH 4 )2so4 aqueous soluwl2 W14 tions at I, and~= the molecular weight of water. The integration was 79 performed in deriving Equation (4) instead of using the generalized expression in Kusik and Meissner (1978) • Equations (1), (3) and (4) can be used to evaluate the activities up to an ionic strength of 17.5 molal, the solubility of (NH ) so in water at 25°c. 4 2 4 Expressions for the ionic strength dependences of the NH No activity coeffi4 3 cient and water activity were obtained from Hamer and Wu (1972). The expres- sions used for the (NH ) so activity coefficient and water activity ionic 4 2 4 strength dependences were based on the isopiestic measurements of Wishaw and Stokes (195~). The solution osmotic coefficients were calculated using the method outlined in Staples and Nuttall (1977) and referenced to the ionic strength dependence of the NaC£ os~otic coefficient of Hamer and Wu (1972). The more recent NaC~ expression of Gibbard et al. (1974) was not used since it is in good agreement with the work of Hamer and Wu (1972). The resulting (N~ ) so 4 2 4 osmotic coefficient data were fit to a polynomial and, with the Gibbs-Duhec equation, the following ionic strength dependence for the {NH ) so 4 2 4 activity was obtained, -2.3525/T 8.369xl0 -2 I + 7.635xl0-3 I 2 1+1.02.'r - 3.307x10- 4 I 3 + 5.783x10- 6I 4 where the standard deviation of the original regression was 7.55x10 -4 . (5) Still unresolved is how to predict the activity coefficient of {NH ) so in the 4 2 4 region of the phase diagram between the dashed line and the solubility curve . •An error exists in the expression designed to evaluate the extreme right te~ in Kusik and Meissner's version of Equation (4). 80 The activity coefficient of (NH4 )2so 4 at ionic strengths greater than its solubility in water can be approximated four ways from existing data. First, Emons and Hahn (1970) measured the water activity along the solubility From Equation (4), the data of curve for the NH 4 No 3 ~(NH4 ) 2 so 4 -H 2 o system. Emons and Hahn (1970) and the NH4 No 3 water activity ionic strength dependence, the hypothetical (NH4 ) 2so 4 water activity can be calculated to 26.0 molal, the solubility of NH 4No 3 in water. By using the Gibbs-Duhen equation, the (NH 4 ) 2so 4 activity coefficient can be obtained. Second, the dissolved anmoni- um sulfate activity must be constant along the solubility curve between (NH4 )2so4 in pure water and E1. Thus, the hypothetical (NH4 )2so4 activity coefficient ionic strength dependence can be calculated from the solubility data in Silcock (1979), the NH 4No 3 activity coefficient ionic strength dependence, the activity of a saturated aqueous (NH 4 ) 2so 4 solution and Equation (3). Third, the (NH 4 ) 2so 4 activity coefficient data below 17.5 molal can be linearly extrapolated to higher ionic strengths. Fourth, Equation (5) could be used above 17.5 molal. The results of the four techniques were compared. The second method ex- hibits a higher ionic strength dependence than the other three. The first method results scattered about the predictions of the third and fourth with neither method showing better agreement. Thus, Equation (5) was used to repre- sent the ionic strength dependence of the (NH 4 ) 2so 4 activity coefficient above as well as below 17.5 molal. Using Equation (4), the water activities of NH 4No 3-(NH 4 )2so 4 solutions were predicted and compared to the data of Emons and Hahn (1970) and Thudium {1978). See Tables 1 and 2. The agreement between the predictions and data is good even though the data were taken using distinctly different experimental techniques. The maximum error was 3.7%. Table 1 and Table III of Saxena 81 Comparison of Calculated and Measured Water Activities Along the NH 4No -(NH 4 ) 2so 4 Aqueous Solubility Curve 3 Table 1. y aw (Cale.) aw (Meas.) Error % Solid Phase* 17.46 0.000 0.800 0.801 - 0. 12 (NH 4 )2so 4 18. 06 o. 126 0.775 0.767 1. 04 (NH 4 ) 2so 4 19. 64 0.371 0.725 0.727 - 0.28 (NH 4 ) 2so 4 20.76 0.457 0.701 0.700 0. 14 (NH 4 }2so 4 23.25 0.614 0.655 0.655 0.00 (NH 4 ) 2so4 23.84 0.640 0.645 0.662 - 2.57 2NH 4N0 3 ·(NH 4 l 2so 4 24. 54 0.697 0.634 0.657 - 3.50 2NH 4N0 3 ·(NH4 )2so 4 25.02 0.758 0.627 0.651 - 3.69 2NH 4N0 3·(NH4 )2so 4 25. 91 0.793 0.616 0.625 - 1.44 2NH 4N0 3·(NH4 )2so 4 25.30 1.00: 0.62E 0.615 1. 79 NH 4N0 3 t Emons and Hahn ( 1970) *Silcock (1979) Table 2. Comparison of Calculated and Measured Water Activities for Dilute NH4ND3-(NH4)2S04 y aw (Ca1c.} aw* (Meas.} Error O' " 1.288 0.25 0.9791 0.9788 0.03 0.882 0.25 0.9852 0.9852 0.00 0.597 0.25 0.9897 0.9896 0. 01 0.289 0.25 0. 994 7 0. 9948 -0.01 *Thudiurn (1978) 82 and Peterson (1981) are directly comparable. Saxena and Peterson (1981) used Their maximum error was Bromley's model with higher order coefficients. 12.3%. Thus, the approach of Kusik and Meissner (1978) is better suited for NH 4N0 3-(NH 4 ) 2so 4 mixtures. Finally, the influence of (NH4 ) 2so4 on the NH 4No 3 dissociation constant can be calculated. The appropriate equilibria for the NH 4No 3-(NH 4 ) 2so 4-H 20 system are listed in Table 3. As stated in the phase diagram discussion, the NH 4No 3 dissociation constant would be invariant along the solubility curve between pure NH 4No 3 in water and E3 and in the regions I, I & II, II, II & III, III and III & IV and is given by the equilibrium constant of Reaction 1 in Table 3 and is independent of relative humidity. Within the aqueous solution region of the phase diagram, the NH 4No 3 dissociation constant varies and is a function of Y and the ionic strength. From Equations (1) and (4) and the equilibrium constant for Reaction 2 in Table 3, the water activity or reiative humidity and the Y dependence of the NH 4No 3 dissociation constant can be evaluated andare shown in Fig. 2. The dashed curve is obtained by calcu- lating the relative humidity and the NH 4No 3 dissociation constant along the solubility curve between E3 and pure (NH 4 ) 2so 4 in water. A striking feature of Fig. 2 is the insensitivity of the NH 4No 3 dissociation constant to the ionic fraction of nitrate. For example, the NH 4No 3 dissociation constant for Y = 0.5 varies from that of pure NH 4No 3 in water by only 40%. In addition to the NH 4No 3 dissociation constant, the (NH 4 ) 2so 4 dissociation constant relative humidity dependence can be evaluated from Equations (3) and (4) and Reactions 3 and 4 of Table 3. Evaluation of the (NH 4 ) 2so 4 dissociation constant is generally not merited because the dissociation T= 2s•c N ..0 0.. 0. '' '' \ \ \ \ \ \ \ \ \ '' ~ I I Figure 2. The effect of (NH 4 ) so on the relative humidity dependence of 2 4 the NH No dissociation constant. 4 3 84 Table 3. Equilibrium Constants for the NH 4N0 3-(NH4 ) so4-H o 2 2 System at 298 K. Equilibrium Constant * Reaction 1. NH 4N0 3 (c,IV) ; NH 3 (g) + HN0 3 (g) 3.03xl0- 17 2. NH 4N0 3 (aq) ; NH 3 (g} + HN0 3 (g) 2.7lxlo- 18 3. (NH 4 )2so 4 (c); 2NH 3 (g) + H2so4 (g) 2.33xlo- 38 4. (NH4lzS04(aq) ; 2NH3(g) + HzS04(g) 2.62xlo- 38 Free Energy Data Sources: NH 3 (g}, NH 4N0 3 (c,IV) Parker et al. (1976) HN0 (g), H so4 (g) 2 3 JANAF (1971) *Thermodynamic equilibrium constants - pressures in atmospheres, aqueous concentration in molality. 85 constant is small at 2s0 c. The amount of (NH 4 ) 2so4 precursor in the gas phase, the cubic root of the equilibrium constant for Reaction 3 expressed as (NH ) so , is about 0.002 µg m- 3• Thus, the relative humidity dependence 4 2 4 of the (NH 4 )2so 4 dissociation constant is not presented in detail. PARTICLE GROWTH BY PHASE TRANSITION AND WATER CONDENSATION In addition to the relative humidity and compositional dependence of the NH 4No 3 dissociation constant, it is desirable to predict the growth of a particle by water condensation. The salt weight fraction, xs, of a particle growing in the aqueous solution region of the NH 4No 3-(NH 4 )2so 4-H 2o phase diagram can be calculated from x s =1 - 1000 1000 + ( YM 1 (6) +(13Y) M2}I where M , M =the molecular weights of NH 4No 3 and (NH 4 )2so 4 , respectively. 1 2 The water activity over the particle can be predicted from Equation (4). Figs. 3 and 4 compare the theoretical predictions with the experimental data of Tang et al. (1981) for two different NH 4No 3/(NH 4 )2so4 molar ratios. Fig. 4 is more complex than Fig. 3 because the aerosol particle goes throught two phase transitions, and part of the particle is solid in some regions. The process in Fig. 4 is shown on the NH No 3-(NH 4 )2so 4-H 20 phase diagram, Fig. 1, 4 by the line A-B-C-0 (Tang et al., 1981). The aerosol is a solid core surrounded by a saturated solution of composition E3 from A until the particle reaches B. to C. After B the particle grows along the saturation curve from £3 From C to 0, the particle growth is governed by Equation (6). £3 and C the particle growth can be calculated from Between > &u 0.640 0.701- Figure 3. ~ ti w 0:: 0.80 <t i )-- 0.90L 1-- 0.2 0.4 0.5 \0 0.6 0 0.7 SALT WEIGHT FRACTION 0.3 \ 0.8 [NH4 N0 3] [(NH4)2 S04] ::: 1/0.486 0.9 by wt. (NH ) so l~ - NH No mixture. 4 2 4 3 o - Tang et al. (1981); Solid lines are the theoretic al predictio ns. . I 1.0 Salt concentra tion dependenc e of the water activity for a 44.5-55.5% 0.1 "" ---.----·- · r-- -------. "" co >- ti3= a:: w <t u t- > - t- Figure 4. I 0.640 0.70 I 0.801 0.901- 0.2 I I I . 0.4 I Q5 c - I 0.6 0.7 I o~ 4 4 3 I 0.8 0.9 \:·E~I 0 1.0 ~ o - Tang et al. (1981); .6 - Emons and Hahn (1970); Solid lines are the theoretical predictions. 4 2 SALT WEIGHT FRACTION 0.3 &.. Salt concentration dependence of the water activity for a 82.6-17.4% by wt. (NH ) so - NH No mixture. 0.1 I ~ ,---.------- 1--- --.---- (NH4N03] - / [(NH4)2 S04] - I 2.875 I ----.-----T co -...,J 88 (7) ZD (y I) s + 1000 l M l where (yI)s = the NH 4No 3 molality along the saturation curve between E3 and C and z~ = the NH 4No mass fraction in the dry particle. Essentially, NH 4No 3 3 is being used as a tracer between E3 and C since it is completely dissolved in the aqueous phase. From E3 to C on Fig. 4, the growth curve was calcu- lated from Equations (4) and (7) and the solubility data in Silcock (1979) and Emons and Hahn (1970). Also shown in Fig. 4 are growth data calculated from the so1ubi1ity and water activity data presented in Emons and Hahn {1970), In the region between E3 and xs = 1, the water activity is constant and equals that at E3 . The agreement between the theoretical predictions and the experimental data in Figs 3 and 4 is quite encouraging and indicates these techniques may be applicable to more complex multicomponent particles. PREDICTION OF THE SOLUTION DENSITY The density, d, of a multicomponent electrolytic solution can be calculated from d =do+ io6o I c;(M; - do¢;) (8) . of water, g cm-3 , C; = the molarity of solute i, moles where do = the d ens1ty 1 1 £- • Mi= the molecular weight of solute i, g mole- , and ¢i =the molal volume ) . -1 3 . 1 f from Xoung's rule and the o so ute 1, cm mole . Equation (8 is derivable definition of the molal volume of a solute (Young and Smith, 1954). The molal v~lumes in Equation (a} dre .Getennined at the total molar ionic strength. For the aqueous NH 4No 3-(NH 4 ) 2so 4 system, the NH 4No 3 molal volume ionic strength dependence was calculated using the polynomial fit of Gucker (1934) 89 which is based on the density data of Adams and Gibson (1932). The polynomial 3 molal volumes calculated from density data in Beattie et al. (1928), Campbell et al. (1953) and Geffcken and fit of Gucker (1934) was compared to NH4No Price {1934). The agreement was good with the Geffcken and Price data show- ing some scatter at dilute concentrations. The (NH 4 ) 2so4 molal volume ionic strength dependence was obtained by a polynomial regression of molar volume data calculated from the density data in Beattie et al. (1928). The solute molecular weights and the pure water density were taken from Weast (1973). In Fig. 5 the theoretical predictions are compared to experimental measurements for aqueous NH 4N0 3-(NH 4 )2so 4 solutions from Tang et al. (1981). The maximum error between the data and predictions is 0.20% indicating the possibility of using Equation (8) for more complex multicomponent electrolytic aerosol solutions. PREDICTION OF THE REFR~CTIVE INDEX Using the approach developed in Moelwyn-Hughes (1961), the refractive index of an aqueous multicomponent electrolytic solution can be predicted from density and refractive index data for single salts dissolved in water. The refractive index, n, is given by n = (2R+V)l/2 V-R (9) where R =the mean molar refraction, cm 3 mole- 1 , and V =the mean molar volume, cm 3 mole- 1, and where (10) 90 1.20 1/2.875 1/0.486 .., I 1.15 E c.J E C" (NH4N03J I (<N~)zS04) : 1, 0.0 )- ..... tn z w 0 1.10 1.05 I 0.1 Figure 5. 1 I 0.2 0.3 0.4 0.5 N~N03 WEIGHT FRACTION 0.6 Solution density concentration dependence for various NH No : (NH ) so molar ratios. 4 3 4 2 4 o - Tang et al. (1981); A - Adams and Gibson (1932); Solid lines are the theoretical predictions. 91 1 3 \\•here R; = the partial molar refraction of species i, cm mole- • and xi the mole fraction of species i. The mean molar volume is V=~ (11) where M = the mean molecular weight, g mole -1 • (12) The solution density prediction technique was described in the preceding section. The partial molar refraction for water was calculated from the refractive index and density data in Cheneveau (1928) and Stott and Bigg (1928), for (NH 4 )2so 4 from Flottmann (1928), Pulvermacher (1920) and Rimbach and Wintgen (1910), and for NH 4No 3 from Kruis (1936), Llihdemann (1935) and Geffcken and Price (1934). used. For all cases the 0.5893 µwavelength refractive indices were The partial molar refractions for (NH4 )2so4 and NH 4No 3 were insensi- tive to ionic strength and varied over the range 23.33-23.98 and 15.20-15.32, cm 3 mole -1 , respectively. 15.20 and R(NH ) SO 4 2 4 In Fig. 6 the theoretical predictions for RNH NO = 4 3 = 23.65 are compared with the experimental measurements of Tang et al. (1981). The agreement between theory and data is quite good indicating the possible applicability of Equations {9-12} to more complex multicomponent aerosol solutions. 92 1.40 1.39 1/0.486 L38 x w 0 z 1.37 w > I- u <:r 1.36 a:: lL w 0::: 1.35 l.33o 0.08 0.16 0.24 NH4N03 WEIGHT FRACTION Figure 6. Refractive index concentration dependence for various NH No : (NH ) so molar ratios. o - Tang et al. (1981); 4 3 4 2 4 a - Kruis (1936); ¢ - Geffcken and Price (1934); .6:.. - Luhdemann (1935); V- Pickard et al. (1928); Solid lines are the theoretical predictions. 93 DISCUSSION In the Background section, several questions were highlighted concerning the applicability of the thennodynamic theories presented to aerosol sampling and evaluation methods. From the theories discussed in this paper, answers to these questions can be advanced. 1. What effect would the internal mixing of a pure aqueous (NH 4 ) 2so 4 aero- sol with a pure aqueous NH4No 3 aerosol have on the NH 4No 3 dissociation constant? By examining Fig. 2, this question can easily be answered. Since the relative humidity remains constant, the mixing process would follow a relative humidity isopleth. From the mixing process, Y would decrease and like- wise [NH 3 J[HN0 3 J would decrease. Thus, the net effect would be to absorb more nitric acid from the gas phase into the aerosol phase provided sufficient alTITlonia is present. 2. How would the presence of NH 4No 3 effect an aerosol identification tech- nique that utilizes particle growth resulting from water condensation? The increase in particle radius due to water condensation is given by (13) where r 2 , r 1 =the final and initial particle radii, d2 , d1 =the final and initial particle density and x52 , x51 = the final and initial salt weight fraction. From the preceding discussions on predictive techniques for particle growth, water activity and solution density, the effect of NH 4No 3 on the volumetric growth of a (NH ) so aerosol particle can be evaluated for any 4 2 4 NH4N03/(NH4)2S04 ratio. 94 3. Is the reduction in the nitrate aerosol fonnation rate during simultane- ous sulfate aerosol fonnation the result of a change in the distribution of nitric acid between the gas and aerosol phases or is the total amount of nitrate fonTied reduced? This question has already been partially addressed in the answer to question 1. The presence of (NH4 )2so4 should decrease the amount of HN0 in 3 the gas phase. Thus, if the aerosol sulfate was (NH ) so4 , the amount of 4 2 aerosol nitrate should increase provided enough arrmonia is present. The re- duced nitrate formation rate observed by Clark et al. (1976) could result from the displacement of HN0 3 by H2so 4 from NH 4No 3 on the filter material as studied by Appel and Tokiwa (1981). Finally, the results of Clark et al. could be explained by the aqueous competitive or inhibited oxidation of nitrite to nitrate. Definitely their results are not due to the presence of (NH ) so 4 2 4 alone. CONCLUSIONS The prediction of the thennodynamic properties of NH 4No 3-(NH 4 )2so 4-H 0 2 aerosols from binary solution data is shown to be feasible. The water activity is obtained using the approach developed by Kusik and Meissner (1978), the solution density from Young's rule and the refractive index from the discussion in Moelwyn-Hughes (1961). The agreement between experimental measure- ments and theoretical predictions indicates the applicability of these approaches to more complex electrolytic solutions. Particle growth is calcul- able from the NH 4No 3-(NH 4 ) so -H 0 phase diagram, the initial particle compo2 4 2 sition and the water activity prediction technique. Finally, the effect of (NH 4 ) so 4 on the relative humidity dependence of the NH 4No 3 dissociation con2 stant is shown to be less than 40% for nitrate ionic strength fractions greater than 0.5. 95 ACKNOWLEDGMENT This work was supported by U.S. Environmental Protection Agency grant R806844. We would like to thank James J. Morgan for helpful discussions. 96 REFERENCES Adams l.H. and Gibson R.E. (1932) Equilibrium in binary systems under pressure. III. Th9 influence of pressure on the solubility of anmonium nitrate in water at 25 C. J. Amer. Chem. Soc. 54, 4520-4537. Ahlberg M.S. and Winchester J.W. (1978) Dependence of aerosol sulfur particle size on relative humidity. Atmospheric Environment .!.f.., 1631-1632. Appel B.R., Kothny E.L., Hoffer E.M., Hidy G.M. and Wesolowski J.J. (1978) Sulfate and Nitrate Data from the California Aerosol Characterization Experiment (ACHEX). Envir. Sci. Technol. _lg_, 418-425. Appel B.R. and Tokiwa Y. (1981) Atmospheric particulate nitrate sampling errors due to reactions with particulate and gaseous acids. Atmospheric Environment l?.· 1087-1089. Beattie J.A., Brooks, B.T., Gillespie L.J., Scatchard G., Schumb W.C. and Tefft R.F. (1928) Density (specific gravity) and thennal expansion (under atmospheric pressure) of aqueous solutions of inorganic substances and of strong electrolytes. In International Critical Tables of Numerical Data, Physics, Chemistry and Technology, Vol. III, pp. 51-111, McGraw-Hill, New York. Campbell A.N., Gray A.P. and Kartzmark E.M. (1953) Conductances, densities and fluidities of solutions of silver nitrate and of anmonium nitrate at 35 6 . Can. J. Chem . .J.1, 617-630. Chen C.S. (1974) Evaluation of the vapor pressure over an aerosol particle. J. Atmos. Sci. I!_, 847-849. Cheneveau C. (1928) Refractivity of selected solids and liquids. In International Critical Tables of Numerical Data, Physics, Chemistry and Technology, Vol. VII, pp. 12-16. McGraw-Hill, New York. Clark W.E., Landis D.A. and Harker A.B. (1976) Measurements of the photochemicai production of aerosols in ambient air near a freeway for a range of so 2 concentrations. Atmospheric Environment lQ., 637-644. Cunningham P.T., Johnson S.A. and Yang R.T. (1974) Variations in chemistry of airborne particulate material with particle size and time. Envir. Sci. Technol . .§_, 131-135. Doyle G.J., Tuazon E.C., Graham R.A., Mischke T.M., Winer A.M. and Pitts, J.N. Jr. (1979) Simultaneous concentrations of a1M10nia and nitric acid in a polluted atmosphere and their equilibrium relationship to particulate arrrnonium nitrate. Envir. Sci. Technol. 11· 1416-1419. Emons H.H. and Hahn W. (1970) Dampdruckmessungen in system alT'ITlOnnitratarrrnonsul fat-wasser. Leuna Technischen Hochschule fur Chemie. Wissenschaftliche Zeitschrift Jl., 129-132. 97 Flottmann Fr. (1928) Uber loslichkeitsgleichgewichte. Z. Anal. Chem. 73, 1-39. Geffcken W. and Price 0. (1934) Zur frage der konzentrationsabhangigkeit des scheinbaren mo1vo1umens und der scheinbaren mo1refraktion in verdJnnten losungen. z. Physik. Chem. B26, 81-99. Gibbard H.F. Jr., Scatchard G., Rousseau R.A. and Creek J.L. (1974) Liquidvapor equili~rium of aqueous soldium chloride, from 298 to 373K and from 1 to 6 mol kg- , and related properties. J. Chem. Engng. Data Ji, 281-288. Gucker F.T. (1934) The calculation of partial molal solute quantities as functions of the volume concentration, with special reference to the apparent molal volume. J. Phys. Chem. 38, 307-317. Hamer W.J. and Wu Y.-C. (1972) Osmotic coefficients ang mean activity coefficients of uni-univalent electrolytes in water at 25 C. J. Phys. Chem. Ref. Data.!... 1047-1099. Hanel G. and Zankl B. (1979) uptake by mixtures of salts. Aerosol size and relative humidity: Tellus ll_, 478-486. Water Harrison R.M. and Pio C.A. (1981) Apparatus for simultaneous size-differentiated sampling of optical and suboptical aerosols: Application to analysis of nitrates and sulfates. J. Air Po1lut. Control Assoc. ll_, 784-787. JANAF Thennochemical Tables, 2nd Edn. (1971). NSRDS-NBS 37. Kruis A. (1936) Die aquivalentdispersion von starken elektrolyten in losung. I. Die messung der konzentrationsabhangigkeit der aquivalentrefraktion im sichtbaren. Z. Physik. Chem. 834, 13-50. Kusik C.L. and Meissner H.P. (1978) Electrolyte activity coefficients in inorganic processing. A.I.Ch.E. Symp. Ser. ~. 14-20. Luhdemann R. (1935) Uber die konzentrationsabhangigkeit der aquivalentrefraktion einiger salze unde sauren in wasseriger 1osung. Z. Physik. Chern. 829, 133-149. Moe1wyn-Hughes E.A. (1961) mon Press, New York. Physical Chemistry, 2nd Rev. Ed, p. 397. Perga- Orr C. Jr., Hurd F.K. and Corbett W.J. (1958) humidity. J. Coll. Sci. Jl_, 472-482. Aerosol size and relative Parker V.B .• Wagman O.D. and Garvin D. (1976) Selected thennochemical data compatible with the CODATA reco!Tillendations. NBSIR 75-968. 98 Patterson R.K. and Wagman J. (1977) Mass and composition of an urban aerosol as a function of particle size for several visibility levels. J. Aer. Sci. ~. 269-279. Pickard R.H., Houssa A.H.J. and Hunter H. (1928) Refractivity of mixtures. In International Critical Tables of Numerical Data, Physics, Chemistry and Technology, Vol. VII, pp. 63-108. McGraw-Hill, New York. Pulvennacher 0. (1920) 1J.l, 141-148. Zur kenntnis waBriger losungen. Z. Anorg. Chem. Rimbach E. and Wintgen R. (1910) Uber den einfluss der komplexbildung auf raumerfullung und lichtbrechung geloster korper. Z. Physik. Chem., Steich. and Verwand. 74, 233-252. Saxena P. and Peterson T.W. (1981) Thennodynamics of multicomponent electrolytic aerosols. J. Coll. Int. Sci. 79, 496-510. Silcock H.L. (1979) Solubilities of Inorganic and Organic Compounds, Vol. 3, Part 2, pp. 157-159. Pergamon Press, New York. Staples B.R. and Nuttall R.L. (1977) The activity and osmotic coefficients of aqueous calcium chloride at 298.15 K. J. Phys. Chem. Ref. Data.§_, 385-407. Stelson A.W., Friedlander S.K. and Seinfeld J.H. (1979) A note on the equilibrium relationship between ammonia and nitric acid and particulate ammonium nitrate. Atmospheric Environment Jl., 369-371. Stelson A.W. and Seinfeld J.H. (1981a) Relative humidity and temperature dependence of the anmonium nitrate dissociation constant. Atmospheric Environment ]2, XXX-XXX. Stelson, A.W. and Seinfeld J.H. (198lb) Relative humidity and pH dep 0ndence of the vapor pressure of ammonium nitrate-nitric acid solutions at 25 C. Atmospheric Environment ]2, XXX-XXX. Stevens R~K., Dzubay i.G., Russwurm G. and Rickel D. (1978} Sampling and analysis of atmospheric sulfates and related species. Atmospheric Environment J1, 55-68. Stott V. and Bigg P.H. (1928) Density and specific volume of water. In International Critical Tables of Numerical Data, Physics, Chemistry and Technology, Vol. III, pp. 24-26. McGraw-Hill, New York. Tang I.N., Wong W.T. and Munkelwitz H.R. (1981) The relative importance of atmospheric sulfates and nitrates in visibility reduction. Atmospheric Environment ]2, XXX-XXX. 99 Tang I.N. (1980) On the equilibrium partial pressures of nitric acid and anmonia in the atmosphere. Atmospheric Environment J.!. 819-828. Tang I.N .• Munkelwitz H.R. and Davis J.G. (1978) Aerosol growth studies - IV. Phase transformation of mixed salt aerosols in a moist atmosphere. J. Aer. Sci. ~. 505-511. Thudium J. (1978) Water uptake and equilibrium sizes of aerosol particles at high relative humidities: Their dependence on the composition of the water-soluble material. Pageoph l.1.§., 130-148. Wagman D.D .• Evans W.H., Parker V.B .• Harlow I .• Baily S.M. and Schurrrn R.H. (1968) Selected values of chemical thennodynamic properties; tables for the first thirty-four elements in the standard order of arrangement. NBS technical note 270-3. Weast R.C. ed. (1973) Press, Cleveland. Handbook of Chemistry and Physics, 54th Edn. CRC Winkler P. (1973) The growth of atmospheric aerosol particles as a function of the relative humidity - II. An improved concept of mixed nuclei. Aerosol Science!· 373-387. Winkler P. and Junge C. (1972) The growth of atmospheric aerosol particles as a function of the relative humidity. Part I: Method and measurements at different locations. J. Rech. Atmos. (Memorial Henri Dessens) 1972, -617-638. Wishaw B.F. and Stoke~ R.H. (1954) Activities of aqueous arrrnonium sulphate solutions at 25 C. Trans. Faraday Soc. 50, 952-954. Young T.F. and Smith M.B. (1954) Thermodynamic properties of mixtures of electrolytes in aqueous solutions. J. Phys. Chem. 58, 716-724. 100 CHAPTER 6 FUTURE RESEARCH 101 In many ways the approaches developed in this thesis can be expanded and and applied to urban aerosol problems. Some examples of these areas are outlined in the following sections. I. Displacef'lent Reactions The heterogeneous reactions of gaseous acids, HBr, HCl, H2so 4 and HN0 3 , with pre-existing solid or aqueous aerosols is an area needing experimental and theoretical work. A typical reaction studied by Robbins et al.(1959) is NaCl(s or aq) + HN0 3 (g) #NaN0 3 (s or aq) + HCl(g). ( 1) The role of the displacement reaction, (2) on filter deposited aerosol material has been explored by Apoel and Tokiwa (1981). T~us, an understanding of these reactions is important for ambient aerosol chemistry as well as sampling. TI. Heterogeneous Neutralization Reactions '" 's area is similar to Tooic I but involves the reaction of a gaseous acid with an aerosol base or vice versa. Robbins and Cadle(1958) studied the reaction of gaseous ammonia with sulfuric acid droplets. A typical examole of the alternate reaction scheme, gaseous acid reacting with an aerosol base, is Thi HN0 (g) + NaOH(ari) 4'9NaCl(ari ors)+ H20(g). 3 ( 3) These reactions have an important role in gaseous or aerosol acidic deposition process2s. 102 III. Photo - Oxidation of Nitrite to Nitrate The oxidation of nitrite to nitrate in sunlight has been shown by Dahr et al.(1934,1936). They demonstrated this oxidation is greatly accelerated by the presence of titanium, zinc and iron oxides (Ti0 2 , ZnO and Fe o ). 2 3 Since soil dust is a source of large ambient aerosol particles and soil contains Ti0 and Fe o , this mechanisn may be an important source for large 2 3 2 particle nitrate formation (Stelson and Seinfeld, 1981). !V. Refractive Indices and Densities of Multicomoonent Ambient Aerosol Solutions In Chapter 5 equations were derived that enabled the calculation of the refractive index and the density of aqueous multicomponent ionic solutions. These equations were tested on data for the NH 4 N0 - (NH 4 ) so 4 - H o system 3 2 2 and excellent aqreement was obtained. The ambient aqueous aerosol solutions cannot be merely described by NH 4N0 and (NH 4 ) 2so and are complex multi3 4 component mixtures (Stelson and Seinfeld, 1981). Therefore, these equations should be more rigorously tested before beinq apolied to visibility model lino and imoroved samoling techniaues. V. Atmospheric Aerosol Density Monitoring from aerosol mass and volume distrihution d~ta, the si:e dependence of the aerosol densit~ can be calcul~ted. In addition, size composition data are desirable. The mass distribution can be measured with a cascade impactor and the volume distribution with an optical particle counter and an electrical aerosol ana1yzer. Chemical comoosition data are obtainable by some combined size classification and filter measurement technique. The typical ambient aerosol density can vary from 1.00 g cm -3 for water to 9.5 g cm -3 for lead oxide (Lanoe, 1944). Thus, a reasonable range for density measurements exists. These measurements can be used to answer several important questions. 103 l) Does the correction from aerodynamic diameter to true partic1e diameter significantly alter the aerosol mass distribution? 2) Can the density data, composition size distribution and total chemical composition data be used to improve observed aerosol to source signature balances? 3) Thermodynamic analysis indicates the aerosol density should decrease as the 1·elative humidity increases. Does this occur and at what rate? 4) Jf the aerosol is predominantly an aqueous electrolytic solution, how do the density nredictions from Equation (8) in Chanter 5 compare with ambient measurements? 104 REFERENCES Aopel B.R. and Tokiwa Y. (1981) Atmospheric particulate nitrate sampling errors due to reactions with particulate and gaseous strong acids. AtMospheric Environment~. 1087-1089. Dhar N.R. and Tandon S.P. (1936) Oxidation of nitrites to nitrates in sunlight. J. Indian CheM. Soc. Jl_, 180-184. Dhar N.R., Tandon S.P., Biswas N.N. and Bhateacharya A.K. (1934) Photooxidation of nitrite to nitrate. Nature ]ll, 213-214. Lange N.A. (1944) Handbook of CheMistry, 5th Ed, oo. 154-265. Publishers, Sandusky, Ohio. Handbook Robbins R.C. and Cadle R.D. (1958) Kinetics of the reaction between gaseous aJT111onia and sulfuric acid droplets in an aerosol. J. Phys. Chem. 62, 469-471. Robbins R.C., Cadle R.D. and Eckhardt D.L. (1959) The conversion of sodium chloride to hydrogen chloride in the atmosphere. J. Meteorology.!.§_, 53-56. Stelson A.W. and Seinfeld J.H. (1981) Chemical mass accounting of urban aerosol. Environ. Sci. Technol. 15, 671-679, 105 APPENDIX A ON THE DENSITIES OF AQUEOUS SULFATE SOLUTIONS Accepted for publication in Atmospheric Environment. 106 ON THE DENSITIES OF AQUEOUS SULFATE SOLUTIONS We have noted a disagreement among density data from different sources f~r NH 4Hso 4 solutions. The most recent source of data on NH 4HS0 4 solution densities is Tang (1980). Figure 1 is a reproduction of Figure 1 of that 1-1ork. Note the relative positions of the curves for (NH 4 ) 2so 4 • (NH 4 )3H(S0 4 )2 , NH 4HS0 4 , and H2so 4 . His cited source for (NH 4 )2so 4 and H2so 4 density data is International Critical Tables (1928). Tang (1980) states that the NH 4Hso 4 and (NH 4 ) H(S0 4 J2 density data were obtained experimentally and refers to Tang 3 and Munkelwitz (1977, 1978). From study of the latter reference, it appears that the NH 4Hso 4 density curve is, in fact, based on a single data point from the International Critical Tables (1928) together with the interpolation formula (Moelwyn-Hughes, 1961) pl (1) p = --'-- 1 - a\'1 2 1 1 where p =the solution density in gm ml- , pl= water density in gm mi- , w2 weight fraction of solute, and a is a constant determined from a given value of p at a known w2. Based on the International Critical Tables' NH 4Hso 4 solu- tion density at 25° and the solubility of NH 4HS0 4 i !lterpo lated from dat~ in Seidell and Linke (1965), a can be evaluated. The tlH 4Hso solution density values calculated from (1) are found to agree 4 closely with those in Table 1 of Tang and Munkelwitz (1977). The densities from Table 1 of that reference, together with those of (NH 4 J2so 4 and H2so 4 from International Critical Tables (1928) are shown in Figure 2. The (NH 4 J2so 4 and H2so 4 solution densities in Figures 1 and 2 are in excellent agreement as expected. Note the relative positions of the H2so 4 , (NH 4 J2so4 and NH 4Hso 4 curves in Figure 2, as compared with those in Figure 1. Tang (1980) does not state ~hy 107 1.30 E ....... E IC' >- I(f) z 1.20 w 0 0 10 20 30 40 50 60 w1 % SOLUTE Figure 1. Densities of aqueous sulfate and nitrate solutions 0 at 2s c [Figure 1 of Tang (1980)]. 108 1.9 o NH4 HS04 - Irish 8 Chen (1970) c H2 S04 - Chen 8 Irish ( 1971) • H2 S04 - Int. Crit. Tobi es (1928) 1.7 • NH4 HS04 - Perkin (1889) b. 1111 - (NH4 )2 S04 - Int. Crit. Tables(l928) NH4 HS04 - Tang 8 Munkelwitz ( 1977) ~ NH 4 HS04 -Tang E 1.5 E ' 0 I 0981) ->- 1111 OI t- (/) z w 1.3 D 1.1 0.9&...-~-1--~-A~---""-~--L.~--""-~-'-~.........i.-----....._~~ 0 0.3 WEIGHT Figure 2. 0.6 FRACTION Calculated and measured sulfate solution densities at 25°c. 0.9 109 he has shifted the relative positions of the (NH 4 ) 2so 4 and NH 4Hso 4 density curves from those in his earlier paper. Also shown in Figure 2 is the point reported in the International Critical Tables (1928) for the density of 66.67 percent NH 4Hso 4 solution. It appears that Tang and Munkelwitz (1977) mistook the NH 4HS0 4 value from the International Critical Tables (1928) to be that for a saturated solution at 2s 0 c. The original reference, Perkin (1889), reports the specific gravity for a 66.67 percent NH 4Hso 4 solution. Thus, apparently the International Critical Tables (1928) misquoted Perkin (1889) and Tang and Munkelwitz (1977) further misconstrued the International Critical Tables (1928). The specific gravity has been converted to the density using the density of water from Weast (1973). The correction is small, about 0.3 percent. An additional calculation of H2so 4 and NH 4Hso 4 solution densities can be carried out. Irish and Chen (1970) and Chen and Irish (1971) report molar con- centrations for H20 and H2so 4 or NH 4Hso 4 from which solution densities can be calculated from _ M fS) + 18[H 0J 5 p - 1000 2 ( 2) where Ms is the molecular weight of the sulfate salt and [SJ and [H 20J are the molar concentrations of the sulfate salt and water. on this basis are shown in Figure 2. Densities calculated The sulfuric acid densities are in excel- lent agreement with those of the International Critical Tables (1928), whereas the densities of NH 4Hso 4 solutions differ with those reported by Tang and Munkelwitz (1977). It appears clear that an error exists in the NH 4HS0 4 data of Irish and Chen (1970). Although Mellor (1964) cites Postnikov et al. (1936) as a reference for NH 4Hso 4 solution density data, Postnikov et al. (1936) in fact studied NH4Hso3 . 110 As noted above, Tang (1980) disagrees with his own previous work (Tang and Munkelwitz, 1977) and with International Critical Tables (1928), and Irish and Chen (1970) disagree with all the other sources. The importance of knowing the correct density can be demonstrated by converting molality to molarity for a NH4Hso4 solution. [SJ The appropriate formula for conversion is p (3) Ms ms+lOOO 1 where ms = molality of sulfate salt. (8.687 molal), (3) becomes [SJ For a 50 weight percent NH 4Hso 4 solution = 4.344p. Using Figures 1 and 2, different values for the solution density are obtained, as indicated in Table 1. shows the discrepancy between the data sources is significant. Table 1 This disagree- ment is unfortunate since this mola11ty corresponds to a water acitivity of 0.69 and NH 4Hs0 4 deliquesces at 0.397 (Tang and Munkelwitz, 1977). Personal COITITlunication from Tang (1981) included NH 4Hso 4 solution density measurements which are shown in Figure 2. the point of Perkin (1889). These data smoothly extrapolate to At 50 weight percent NH 4Hso 4 , the calculated molarity based on this data is 5.675, which agrees well with Tang (1980) and Perkin (1889) in Table 1. Thus, the correct NH 4Hso 4 density concentration dependence is the NH 4Hso 4 curve in Figure 1 or the NH 4Hso 4 curve labelled Tang (1981) in Figure 2. A. W. Stelson J. H. Seinfeld Department of Chemical Engineering California Institute of Technology Pasadena, California 91125 111 Table 1. Densities and Molarities of a 50% NH 4Hso 4 Solution Data Source p, g ml -1 [SJ. moles i-l Tang (1980) 1.308 5.682 Tang and Munkelwitz (1977) 1.259 5.469 Irish and Chen (1970) 1.583 6.876 Perkin (1889)* 1. 293 5.615 *Calculated using Perkin's NH 4HS0 4 specific gravity datum and (1). 112 References Chen H. and Irish D. E. (1971) A Raman spectral study of bisulfate-sulfate systems. II. Constitution, equilibria, and ultrafast proton transfer in sulfuric acid. J. Phys. Chem. 75 (17), 2672-2681. International Critical Tables (1928). New York. Volume III, p. 56-60. McGraw-Hill, Irish D.E. and Chen H.(1970) Equilibria and proton transfer in the bisulfate-sulfate system. J. Phys. Chem. 74 (21), 3796-3801. Mellor J.W. (1964) Mellor's Comprehensive Treatise on Inorganic and Theoretical Chemistry, Volume VIII, Supplement I, N(Part I), p. 503, John Wiley & Sons, New York. Moelwyn-Hughes E.A. (1961) Press, Oxford. Physical Chemistry, 2nd ed., p. 808, Pergamon Perkin W.H. (1889) LXVIII. - The magnetic rotatory power of nitrogen compounds, also of hydrochloric, hydrobromic, and hydriodic acids, and of some of the salts of a111T1onia and the compound anrnonias. J. Chem. Soc. 55, 680-749. Postnikov V.F., Kirillov I.P., Nabiev M. and Khaidarov V {1936) The viscosity of single salt aqueous solutions. J. Appl. Chem. (USSR)~. 1926-1928. Seidell A. and Linke W. F. (1965) Solubilities of Inorganic and Metal Organic Compounds, 4th ed., American Chemical Society, Washington. Tang I.N. (1981) Personal Corrrnunication. Tang I.N. (1980) On the equilibrium partial pressures of nitric acid and arrmonia in the atJllQsphere. Atmos. Environ. li· 819 - 828. Tang I.N. and Munkelwitz H. R. (1978) The optical and thenoodynamic properties of (NH4)3H(S0 4 J2 (Letovicite) aerosols, Presented at the May 1978 Industrial Hygiene Conference, Los Angeles. Tang I.N. and Munkelwitz H. R.(1977) Aerosol growth studies - III. Armlonium bisulfate aerosols in a moist atmosphere. J. Aer. Sci. §_, 321-330. Weast R.C. (1973) Press, Cleveland. Handbook of Chemistry and Physics, 54th. Edn. CRC 113 APPENDIX B PREDICTION OF THE DENSITY OF AMMONIUM BISULFATE SOLUTIONS Accepted for publication in the Journal of Physical Chemistry. 114 PREDICTION OF THE DENSITY OF AMMONIUM BISULFATE SOLUTIONS A. W. Stelson and J. H. Seinfeld Department of Chemical Engineering California Institute of Technology Pasadena, California 91125 ABSTRACT The densities of arrmonium bi sulfate solutions are predicted from molal volume and bisulfate dissociation data. Good agreement is shown between measured arrmonium bisulfate solution densities and the predictions. A dis- crepancy between densities predicted using tabulated data from Irish and Chen and measured aTmlonium bisulfate solution densities is resolved (1,2). 115 The concentration dependence of the density of arrrnonium bisulfate solutions has recently been studied (1). It was found that the NH 4Hso 4 solution densities calculated from the data for the molarities of NH 4Hso 4 , [NH 4Hs0 4 J, and water, [H 20J, in Table I of Irish and Chen (2) differed substantially from available data. The objective of this cormiunication is twofold: (a) to determine the source of this discrepancy, and (b) to ascertain whether the extent of bisulfate dissociation in NH 4Hso 4 solutions is accurately represented by the data in Irish and Chen (2). The validity of the NH 4HS0 4 molarity and extent of bisulfate dissociation data in that table will be determined by comparing predicted and measured NH 4Hso 4 solution densities. Although we focus on resolving the NH 4Hso4 solution density discrepancy, we also illustrate a general technique by which the densities of aqueous arrrnonium sulfate-sulfuric acid solutions can be calculated from dissociation data. The molal volume of an electrolyte, ¢i' can be calculated by ¢. = - 1000 ( 9-. 1 [E; J do i) (1) where d0 =density of water, [Eil =the electrolyte molarity, d =the solution density, and ME. =electrolyte molecular weight (3). , For a mixture of electro- lytes the mean molal volume, ~. can be predicted by Young's rule, l: [E; 1¢; l:[E; l (2) where¢. for each electrolyte is taken at the same molar ionic strength (4). 1 116 From Equation (2), a generalized expression can be derived for predicting the molal volume of an arrmoniated sulfate salt, ~((NH )x(H)Y(S0 ~, 4 4 2 ) (H) (SO ) ) = 25 x ¢(NH+) + 2y(l-y) ¢(HSO-) ~r(NH 4 x+y 4 x+y \ 4 x y 4~ 2 + ( 2f'x+2yy _ x+y (NH SO-) i) ¢(S0-2)4 + x+y2yy ¢(H+) + 2x(l-S) 4 4 x+y ¢ (3) where x, y = the ammonium and hydrogen stoichiometric coefficients of the sul+) . The +]/([HS0 - J + [H] -) + fate salt, B = [NH + 4 4 J/([NH 4 J + [NH 4S0 4 J , and Y = [H total sulfate salt concentration conveniently cancels out of the numerator and denominator in Equation (3). The ionic strength, I v , of the sulfate solu- tion is given by (4) Typically, ionic molal volume data are not available except for very dilute solutions so the molal volumes of electrolytic salts must be used. Equation (3) can be rewritten as +NH4)x(H)/S04)~) = al<P(NH;,NH;.so~) +( 2 s~:;vy - 1 - al) ¢(H+,H+,so;) 2 +(ill- 2a - a )¢(NH+4' HSO-) + (2v-2n-2ex + 2a +a 2 ) ¢(H+ ' HSO-) 4 2 1 x+y 4 1 x+y , +,NH so -) + (2x-2~~ H ,NH 4S0 4- ) x+y- - a 2 ) ¢ (+ + a 2¢\NH 4 4 4 where a 1 and a 2 are constants. NH4so4 ion-pairs. (5) Equation (5) was written including terms for The thennodynamic literature disagrees over the presence 117 of NH so4 ion-pairing. The Raman spectroscopy work of Irish and Chen (2), 4 Chen and Irish (5) and Young et al. (6) indicates the amount of NH so4 4 ion-pairs is sma11 via their internal consistency checks. (7) Indirectly, Reardon infers a significant amount of NH 4 so4 ion-pairing exists. In agreement with the Raman data, we will assume the amount of NH 4 so4 ion-pairs is sma11. Thus, B = l and a 2 = O. Equation (5) simplifies to 2y-2yy-2x + ( 2x+ 2·,·y - 1 - a ~(H+ H+ SO=) +( ) x+y ' ' 4 1 "" x+y +2a ) 1 ~(H+,HS0 -) 4 (6) With sulfuric acid solution densities, sulfuric acid dissociation data + + - and an expression for the hydrogen-sulfate molal volume, ¢(H ,H ,so4), the hydrogen-bisulfate molal volume, ¢(H + ,HS0 4-) , can be calculated by where ~(H so ) =the sulfuric acid molal volume. 2 4 Equation (7) is derivable from Equation (6) with a = 0, x = 0 and y = 2. 1 The hydrogen-sulfate molal volume can be determined by an approach analogous to that of Lindstrom and Wirth (8), (8) 118 where the molal volumes,¢( ), are determined at constant ionic strength, ~(X+,X+,SO~). ¢(X+,Ct-), ¢(H+,C£-) =the molal volumes of x2so 4 , Xet and HC£, respectively and x+ =the Na+, NH~ or K+ cation. (It is assumed that NH 4C£, NaC£, KC£, HC£, (NH 4 ) 2so4 , Na 2so4 and K2so 4 totally dissociate within the concentration range of interest.) The (NH 4 )2so 4 and H2so4 molal volumes can be calculated with density data from Beattie et al. (9), the K2so4 molal volume from Dunn (10) and Wirth (11) and the Na 2so 4 molal volume from Dunn (10), Geffcken and Price (12), Beattie et al. (9), and Gibson (13). The NH 4Ct molal volume can be calculated with density data from Beattie et al. (9), Pearce and Pumplin (14) and Stokes (15), the NaC£ molal volume from Millero (16), Wirth (17), Dunn (18), Kruis (19) and Beattie et al. (9), the KCt rrolal volume from Wirth (11), Geffcken and Price (12), Dunn (18), Kruis (19) and Beattie et al. (9) and the HCt molal volume from Beattie et al. (9), Wirth (17), Millero et al. (20) and Dunn (10). The ionic strength dependences of the molal volumes can be obtained by fitting polynomials to the data. The ionic strength dependences . . data are shown 1n of¢ ( H+,H +,so4=) calculated from the NH 4+, K+ and Na + cation Figure 1 in addition to the tabulated values taken from Lindstrom and Wirth (B) and Klotz and Eckert (21). The K+ and Na+ data agree quite well whereas the NH; data disagree with.the others at low ionic strengths. + + The three different = ¢(H ,H ,so 4 l expressions will be used to calculate the sensitivity of ¢(H+,Hso4) to ¢(H+,H+,SO~). With the sulfuric acid dissociation data of Chen and Irish (5) and Young et al. (6), ¢(H+,Hso4) can be calculated from Equation (7). The ¢(H+,Hso4) ionic strength dependences from Lindstrom and Wirth (8) and Klotz and Eckert (21) are shown in Figure 2 in addition to the ¢(H+,Hso4) ionic strength 20 22 :I: - 0 ,,. ,,,,,,,,- ,,.,"' o~·~...~ ....... Figure 1. 14t ___ j = Iv ¢(H ,H ,so ) ionic strength dependence. 4 + + 0.QI 0.1 .-·......J-" o (j) .9-. Klotz 51 Ec!lcert ( K 2 S04 - KCI - HCI ) t o i I linds1rom G1 Wirth ( Na 2 S04 - NaCl- HCI) j o Na 2 S04 - NaCl - HCI K2 S04 - KCI - HCI (NH 4 ) 2 S0 4 - NH 4 CI -HCI j :=·-·--·-·- ... ---0.001 ,- --i------~--------- 16 - i I ----------------~~-­ /·<:··' --a.. 18t + .. :I: en ... 0 II .,. - 24 26 28 I 1.0 I i I i I IO.O I '° ...... ...... 42 I -&- :I: - Figure 2. I I I A A I I 0.1 A I Iv I 1111 I ... T 1.0 • 111 • A • ... ' The solid line is the least • &/ Ill ,,. 6 square fit to the data of Klotz and Eckert (20), I < 0.14, and v Chen and Irish (2). ~(H + ,Hso - ) 4 ionic strength dependenc e. I .. / ' I _/. I • KLOTZ & ECKERT o KLOTZ o ECKERT (Recalcula ted) t CHEN & !RISH YOUNG ET AL. • LINDSTROM & WIRTH 11 34 ~I 0.01 36 381- - 4+ ..... I 0 en • "II' 441- 461- 40 10.0 I 0 I-' N 121 dependences calculated from the data of Chen and Irish (5) and Young et al. (6). The individual data sources shown distinctively different Q>(H+,Hso4J ionic strength trends. The error bars in Figure 2 represent the standard deviation + + + of Q>(H + ,HS0 4- ) evaluated from the K , Na and NH 4 data and the points are the mean values. Below an ionic strength of 0.14, the results of Klotz and Eckert + + - (21) were recalculated using the expressions for ¢(H ,H ,so4l in this paper. The data in Figure 2 were evaluated in order to ascertain the best representation for ¢(H+,Hso4). The data of Chen and Irish (5), Young et al. (6) and Klotz and Eckert (21), Iv.:_ 0.14, are thought to be the best quality. Above an ionic strength of 0.14, the Klotz and Eckert (21) data are poorer since they assumed the classical ionization constant to be invariant. Lindstrom and Wirth (8) assumed ;·(H+ ,Hso4) = ¢(H+ ,HzP04) +an adjustment factor and thus, ¢(H+ ,Hso4) shown in Figure 2 is actually ~(H+,H 2 Po4) modified. The best representation for ¢(H+,Hso4) i5 obtainedfromthedataof Chenandlrish (5)andKlotzandEckert (21), I v-<0.14, since these data smoothly extrapolate to each other, whereas, the data of Young et al. (6) and Klotz and Eckert (21), Iv.:_ 0.14, are discontinuous. The data of Chen and Irish (5) and the recalculated results of Klotz and Eckert (21) were fit via a least squares technique to a polynomial, ¢(H+,Hso4) = 33.25 + 9.03 Iv 112 - 2.773 Iv+ 0.4134 Iv where the standard deviation is:_ 0.12. 3/2 (9) The solid curve in Figure 2 is Equa- tion (8) and will be used to represent the ionic strength dependence of Q>(H+ ,Hso4J. To calculate the NH 4Hso 4 molal volume, the arrmonium-bisulfate molal volume, ¢(NH +4 ,Hso4- ), must be known. calculated from The arrrnonium-bisulfate molal volume can be 122 (lO) The ionic strength dependence of ¢(NH;,Hso4) can be detennined with the ¢(H+,Hso4) ionic strength dependence calculated from the sulfuric acid dissociation data of Chen and Irish (5) and Klotz and Eckert (21). + + = Analogous to the approach of Lindstrom and Wirth (8), ¢(NH 4 ,NH 4 ,so4 ) and + + - ¢(H ,H ,so4) can be replaced by - 1("''NU+ NH+ c:o=, + .+.IH+ 1-1+ so=)\ ,._,N,,+ H+ ' so=, 4 1 - 2 '+'I' "4' "4'¥ 4' " "''' ,.. ' 4'/ '!'\I n4' ( 11) By substitution of Equation (11) into Equation (6) and solving for a1 , one obtains ~((NH 4 )x(H)y(S0 4 )·~)= (2::;XY - 1) ¢(NH;,H+,SO~) +( fu - 1) ¢(H+ ,Hso4i + ( 1 - m-} ¢(NH:.Hso4) . (12) From the ionic strength dependences of ¢(NH:,H+,so;). ¢(H+,Hso4) and ¢(NH:.Hso4) and bisulfate dissociation data for NH 4Hso 4 solutions, the molar volume of NH 4Hso 4 , ~(NH 4 Hso 4 ), and the density of NH 4Hso 4 solutions can be calculated. From Equation (12), ~(NH4HS04) = y¢(NH;,H+,SO~) + (l-y)¢(NH;,Hso4) . (13) With the dissociation data of bilsulfate in arrrnonium bisulfate solutions of Young et al. (6) and Irish and Chen (2), the molal volume of arrrnonium bisulfate can be calculated using Equation (13) (22). After the arrrnonium bisulfate molal volume has been calculated, the density can be detennined from 123 where M(NH ) (H) (SO ) 4x y = the molecular weight of (NH 4)x{H) (S04 )x+ . 4~ 2 Y ~ 2 The density has been calculated for 0.206 to 6.571 molar or 0.39 to 9.76 ionic strength arrrnonium bisulfate solutions. The solubility of arrrnonium chloride is 5.70 molar. and thus, the molal volume data of armionium chloride had to be smoothly extrapolated to 9.76 molar (14). The calculated solution densities are compared to the densities calculated from the [NH 4HS04 J and [H 20J data in Table I of Irish and Chen (2) and the measurements of Tang (23) and Beattie et al. (9) in Figure 3. The agreement between the predicted NH 4Hso 4 solution den- sities from molal volume and dissociation data and the data of Tang (23) and Beattie et al. (9) is good, whereas the solution densities calculated from the [NH 4HS0 4 J and [H 0J data in Table I of Irish and Chen (2) disagree with the 2 theoretical predictions and the experimental measurements. Thus, the water molalities in the paper of Irish and Chen (2) must be in error, since the solution densities calculated from the ammonium bisulfate molarities, [NH 4Hs04 J, agree well with the theoretical predictions from the data of Young et al. (6) and the data of Tang (23) and Beattie et al. (9). Recent corrrnunication from D. E. Irish (24) included a polynomial fit to the NH 4Hso density data used in Irish and Chen (2), 4 (15) Equation (15) agrees with the data of Tang (23) and Beattie et al. (9), in support with our observation that the water molarities in Table I of Irish and Chen (2) must have been calculated incorrectly. The NH 4HS04 solution 124 1.7 DATA •IRISH Ea CHEN 1.6 • TANG ~BEATTIE 1.5 ET AL TH£0R£TICAL PR£DICTIONS o IRISH b CHEN Cl YOUNG /" // . / ET AL 'E 1.4 .. ..,, Cl' >t- 8• .;) //~ y- U> z w 0 1.2 t9 u 1.0 Q91..-~.J-~...L....--....L.~.......1.~.......1----1..............-............-........... 0.0 LO 2.0 3.0 4.0 NH 4 HS04 Figure 3. 5.0 6.0 7.0 8.0 9.0 MOLARITY Density of NH Hso solutions. The lines are the 4 4 authors' representation of the data of Tang (22) and Beattie et al. (8) and Irish and Chen (2). 125 densities predicted from Equation (15) agree with the theoretical predictions based on dissociation and molar volume data within 0.40% for Irish and Chen (2) and 0.65% for Young et al. (6). In addition to isolating the error source in the paper of Irish and Chen (2), we have illustrated a technique by which the densities of ammoniated sulfate solutions can be calculated from dissociation data or vice versa. Spe- cifically, this work discussed arrrnonium bisulfate solutions but Equation (12) can be applied to any aqueous ammonium sulfate-sulfuric acid solution. 126 literature Cited 1. Stelson, A.W.; Seinfeld, J.H. Atmos. Environ., 1981, .!§_, XXX. 2. Irish, D.E.; Chen, H. 3. Millero, F.J. Chem. Rev., 1971, Zl· 147. 4. Young, T.F.; Smith, M.B. J. Phys. Chem. ~~~~· 58, 716. 5. Chen, H.; Irish, D.E. J. Phys. Chem. 1971, Ii· 2671. 6. Young, T.F.; Maranville, L.F.; Smith, H.M. In "The Structure of Electrolytic Solutions," Hamer, W.J., Ed.; Wiley: New York, 1959; Chapter 4. 7. Reardon, E.J. J. Phys. Chem. 1975, Li• 422. 8. Lindstrom, R.E.; Wirth, H.E. J. Phys. Chem. !~~~· 73, 218. 9. Beattie, J.S.; Brooks, B.T.; Gillespie, L.J.; Scatchard, G; Schumb, W.C.; Tefft, R.F. In "International Critical Tables of Numerical Data, Physics, Chemistry and Technology," Washburn, E.W., Ed; McGraw-Hill: New York, 1933; Vol. III, p. 51. 10. Dunn, L.A. Trans. Faraday Soc. ~~~~· 62, 2348. 11. Wirth, H.E. J. Am. Chem. Soc. 1937, 59, 2549. 12. Geffcken, W.; Price, D. Z. Phys. Chem. ~~~~· B26, 81. 13. Gibson, R.E. J. Phys. Chem. 1927, l!:_, 496. 14. Pearce, J.N.; Pumplin, G.G. J. Am. Chern. Soc. 1937, 59, 1221. 15. Stokes, R.H. Aust. J. Chem. 1975, 28, 2109. 16. Millero, F.J. J. Phys. Chem. ~~Z~· 74, 356. 17. Wirth, H.E. J. Am. Chem. Soc., 1940, 62, 1128. 18. Dunn, L.A. Trans. Faraday Soc. 1968, 64, 1898. 19. Kruis, A. Z. Phys. Chem. ~~~~· 834, 1. 20. Millero, F.J.; Hoff, E.V.; Kahn, L. J. Solution Chem. 1972, l• 309. 21. Klotz, J.M.; Eckert, C.F. J. Arn. Chem. Soc. 1942, 64, 1878. J. Phys. Chem. ~~Z~· 74, 3796. 127 23. For Irish and Chen (2), the dissociation data of bisulfate in arrrnonium bisulfate solutions were taken directly from Table I. The polynomial presented in Chen and Irish (5) was not used since it inaccurately represents the data of Irish and Chen (2) at high NH 4Hso 4 molarities. Tang, I.N., Brookhaven National Laboratory, personal comnunication, 1981. 24. Irish, D.E., University of Waterloo, personal cormnunication, 1981. 22.