I. The Activity of Hydrochloric Acid in the Presence of a Unibivalent Salt. II. The Dissociation Constant of Bromide Chloride at Room Temperature. III. A Method for Deriving Photochemical Reaction Mechanisms of Certain Types from Observed Reaction Rates Citation Murdoch, Philip Griffis (1932) I. The Activity of Hydrochloric Acid in the Presence of a Unibivalent Salt. II. The Dissociation Constant of Bromide Chloride at Room Temperature. III. A Method for Deriving Photochemical Reaction Mechanisms of Certain Types from Observed Reaction Rates. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/aewy-z275. https://resolver.caltech.edu/CaltechTHESIS:09172024-180906590 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Bates, Stuart Jeffery (advisor) Dickinson, Roscoe Gilkey (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1 January 1932 Record Number: CaltechTHESIS:09172024-180906590 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09172024-180906590 DOI: 10.7907/aewy-z275 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16737 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 18 Sep 2024 17:46 Last Modified: 18 Sep 2024 18:20 Thesis Files PDF - Final Version See Usage Policy. 7MB Repository Staff Only: item control page

I THE ACTIVITY OF HYDROCHLORIC ACID IN THE PRESENCE OF' A UNIBIVALENT II SALT THE DISSOCIATION CONSTANT OF BROMINE CHLORIDE AT ROOM TEMPERATURE III A METHOD FOR DERIVING PHOTOCHEMICAL REACTION MECHANISMS OF CERTAIN TYPES FROM OBSERVED REACTION RATES Thesis by Philip Griffis Murdoch In partial fulfillment of the requirements for the degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1932 For advice and direction in these investigations the author is indebted to Professor S. J. Bates and to Professor R. G. Dickinson THE ACTIVITY OF HYDROCHLORIC ACID IN THE PRESENCE OF A UNIBIVALENT SALT The effect of added salts upon the activity of hydrochloric acid has been studied by a number of investigators. All of these, except Bates and Urmston have employed chlorides for the added salts. In this investi- gation the influence of the added electrolyte sodium dithionage , i.e., the effects of a negative bivalent ion, was determined. The added salt to be suitable for experiments of this nature must not react chemically with any of the essential constituents of the cell and must possess certain other properties. That is: (1) It should be the salt of a strong acid. (2) The silver salt of its acidic constituent should be soluble. (3) It should not be the salt of an acid such as nitric acid which acts as a (strong) oxidizing or reducing agent. (4) It should be quite soluble. These conditions greatly restrict the choice of salts. However, sodium dithionate appears to fulfil the conditions in a satisfactory manner. EXPERIMENTAL PART The cell used consisted of three silver-silver chloride half cells and two hydrogen half cells. each containing two hydrogen electrodes. connected to the silver-silver chloride half celh through two stopcocks. Hydro- gen, prepared by electrolysis of a sodium hydroxide solution, was passed through tubes containing glowing platinum wire, and admitted to the hydrogen cells by means of glass tube s which extended almost to the bottom of the electrode vessels, from which it escaped through bubblers. The elec- 2. trical contacts in the case of the silver-silver chloride electrodes were made by platinwn wires which extended through the bottom of the electrode vessel. The stoppers of the electrode vessel were made of glass, ground to fit tightly. The silver crystals for the silver-silver chloride electrodes were prepared by the electrolysis of 0.01 M silver nitrate solution, following the procedure of Randall and Young. 1 The hydrogen electrodes were of platinum foil. The foil was first covered electrolytically with a thin coating of gold and then with a coating of platinum black. The electrodes were washed first ~~th con- centrated nitric acid, in order to eliminate any lead from the small a.mounts of Pb(C2 H3 0z)2 in the platinizing solution, and then with many changes of water, in which they were allowed to stand until placed in the cell. Several variations of this method were tried, as a test of its efficacy, and were found to agree within one tenth of a millivolt among themselves. Thus the effect of the use of a thick coat of platinum black, or of the omission of the gold coat, or of the use of a rough but not black platinum coat was not to change the average electromotive force reading but merely to render it a little less steady. Variation of the rate of plating of the platinum had no measurable effect. The behaviour of the hydrogen electrodes prepared in the manner first described was quite satisfactory. 0.03 millivolt. As a rule they checked to 0.02 or Although the three silver-silver chloride electrodes were not quite so satisfactory, the largest differences were seldom greater than 0.l millivolt. The average deviation of the final results at various series of concentrations from the smooth curve is less than 0.l millivolt. The cell was placed in an oil thermostat regulated to 25° ± 0.05°. The electromotive force was measured with a type K, Leeds and Northrup potentiometer using as standard a Weston cell that was frequently checked against a cell recently certified by the Bureau of Standards. The sodium dithionate was purchased CP from Eimer and .Amend, and purified by recrystallizing three times from water and drying at room temperature. It gave no turbidity with silver nitrate. as N¾S2 0 6 ,2!1£0, The salt crystallizes The proportion of water was determined at intervals and always checked closely with the calculated value, The hydrochloric acid was obtained by diluting the CP acid to a density of 1,1 and distilling in an all-glass still, the middle portion alone being retained, The distillate was then diluted to the desired con- centration and standardized by the silver chloride gravimetric method, Al l mixtures were made up by weight from stock solutions and from solid salt, All concentrations are expressed in mols per thousand grams of water. That dissolved air has an effect upon the potential of the calomel electrode in acid solution due to a reaction between mercury, chloride ion, hydrogen ion, and oxygen has been clearly demonstrated by Randall and Young. 1 The similar effect on the silver-silver chloride electrode is less serious. anntelberg2 found some influence and removed oxygen from his solutions by means of nitrogen. Randall and Young, however, discovered no measurable effect upon silver-silver chloride spiral electrodes in 0.1 M hydrochloric The change in the potential of the silver-silver chloride electrode *Spiral electrodes probably offer less silver surface and hence less opportunity for oxidation than do electrodes employing electrolytic silver crystals. The latter were used by GUntelberg and in this investigation. 4. results from the removal of chloride ion from the solution in contact with it by the reaction Ag+ 1/4 Oz+ H+ + Cl- = AgCl + ½~O. The change is synbat with the fractional change in chloride activity, and hence may be expected to be greatest at low chloride concentrations; likewise at high acid concentrations, as can be seen from an inspection of the equation. Thus with solutions of 0.01 M hydrochloric acid effects of the order of millivolts were observable, which were due to the effect of oxygen. With 0.05 Mand 0.1 M acid, however, no observable effect of this nature was found. The effect of possible adsorption on or reaction with the walls of the cell was tested for and proved to be inappreciable. The measured values of the electromotive forces at 25° and the computed activity coefficients are given in the Table. The former have been corrected to one atmosphere of hydrogen; the latter have been computed from the following relation, d. o<o logwith the aid of the values d.. 0 and E0 for pure hydrochloric acid at the same concentration. as given by Randall end Young. 1 DISCUSSION During the past few years many investigations and interpretations of the properties of solutions of strong electrolytes have demonstrated that in sufficiently dilute solutions the ion attraction theory quantitatively accounts for the activity of strong electrolytes as determined from measurements of the electromotive forces of appropriate cells~ of freezing point 5. lowerings, and of the effect&of added salts upon the solubility of relatively insoluble salts. In dilute solutions the physical basis for the ion attraction theory is relatively simple. The electrostatic forces acting between the ions are detennined by the magnitude of their charges, their distribution and distances from one another, and the dielectric constant of the medium. In a moderately concentrated solution a great many additional effects, many of them undoubtedly related to one another come into play to influence the activity coefficient. Thus the distribution of the ions will be modified in solutions in which the average effective diameter of the ions is comparable with the average distances of the ions from one another. Then at high concentrations ionization may no longer be complete. Hydration of the ions removes an appreciable part of the water from its normal state, thus changing the effective mol fraction of the ions and also the dielectric constant of the medium. In addition the dielectric constant is changed by the mere presence of a high ion concentration. 6. Electromotive Forces and Activity Coefficients of HCl HCl = 0.10 f {approx)* Added Naz Sz Of, Formality x 3 HCl formality E.M.F. 0 0.1036 0.1036 o. 3505 0.0500 0.1000 0.1035' 0.2000 o. 1034 , 0;4000 0.6000 0.8000 0.9000 1, 0600 1.0500 1.1000 0.1031 0.1029 0,1027 0,1026 0.1023 0.1023 0.1023 HCl = 0.05 f 0 0.0500 0.1500 o. 2500 0,4500 0.4500 0.6500 0.8500 1. 4291 0,0500 0.04997 0.04991 0.04985 o. 04973 o. 04973 0,04963 0,04949 0,04914 0,3521 0.3531 o. 3544 o. 3557 o. 3564 0.3565 o. 3561 o. 3564 0.3560 o. 3559 Activity Coefficient o. 795 o. 771 o. 756 o. 738 o. 722 o. 714 o. 714 o. 720 (0.718) o. 723 0.725 (approx)* o. 3861 0,3886 0,3911 o. 3923 o. 3931 o. 3938 0,3944 0,3944 0.3934 0.830 o. 791 0.755 o. 738 (0.728) o. 718 o. 711 o. 713 o. 733 *The changes in HCl concentration result from the water of crystallization present in the sodium dithiona.te, 7. According to the simple ion attraction theory the activity coefficient of the ions should continue to decrease with increasing ionic strength. But some of the other influences noted above cause the coefficient to be greater than that predicted by the simple theory; this increase may be called the salting-out effect. To any given ion there may be ascribed certain salting-out effects at definite concentrations because this ion has at a definite concentration a direct influence on the properties of the solution; that is, it makes a definite contribution to the thermodynamic environment. On the other hand, the ion itself tends to be salted out. Certain ions, however, are undoubtedly salted out more readily from a solution of a given thermodynwnic environment than are others. The problem of the separation for analysis of these two salting-out influences (contribution and reaction to thermodynwnic environment) of a given ion constituent is one which may be attacked by investigation of activities in mixed electrolytes. Thus in the case of hydrochloric acid the activity ceefficient decreases in dilute solutions to a less extent than does that of almost any other electrolyte and at an ionic strength of four tenths passes through a minimum and then rapidly increases. Whether this is due chiefly to properties which the hydrogen and chloride ions impart to the solution as a whole or whether it it is because these ions are especially readily salted out is not clear from data on pure hydrochloric acid alone, but can be discovered from additional information of the type mentioned. In correlating the results of this investigation with those of others similar to it, use may be made of the following property of certain mixtures of electrolytes: tivity coefficient In mixtures of constant ionic strength_JA,the ac- oC of hydrochloric acid is related to the concentration Fisure 1 .,s r+-t-----L_J 1.0 8. m of the acid in the mixture and the a.cti vi ty coefficient ct.. o of: pure HCl at the same ionic strength by the equation log o<. This equation has been found to hold for all the mixtures containing only univalent ions for which it has been tried. (Harned3 has observed it to hold for mixtures, among others. of hydrochloric acid with lithium. sodium, or potassium chloride up to total ionic strengths of three, the highest measured.) Randall and Breckenridge, 4 however, found that it was not followed by mixtures containing barium chloride or lanthanum chloride. but that the similar relation in which m, the concentration of the hydrogen ion constituent, is replaced by the geometric mean molality of the hydrogen and chloride ion constituents did hold. This rule of Randall and Breckenridge (for which no derivation was given) and the one first stated are. of course, mutually exclusive except when the added electrolyte has no ion in common with those of hydrochloric acid, when the rules become identical. ~uch is the case with sodium dithiona.te; for this case plots of Cl. against mare shown in Figure 1 at various total ionic strengths. It will be seen that the above equation is closely followed. The comparative effects of increasing amounts of various salts upon the activity coefficient of hydrochloric acid is shown in Figure 2. Here the activity coefficient of the acid, of which the concentration is maintained constant at 0.1 f., is plotted against the ionic strength for the added salts lithium chloride. sodium chloride. potassium chloride. sodium perchlorate. barium chloride, sodium dithionate and perchloric acid. The figure shows that the minimum Fiaure 2 2 3 4 5 7 8 :7~-------------,,"="------------,.-----~---' 0.1 0.5 fl I 0 HCl in l,HCl04 ; 2 1 HCl ; 3 ,LiCl; 4,NaCl ; value for the activity coefficient occurs at approximately the same ionic strength for pure hydrochloric acid and for the acid in the presence of added uniunivalent salts except for potassium chloride. which is somewhat anomalous in this respect. but that the minimum is shifted to higher ionic strengths when bivalent ions are present. Of these salts the activity coefficients of lithium chloride. sodium chloride. potassium chloride, and barium chloride in solution alone are known. At a given ionic strength the activity coefficients decrease in the order given. l<'igure 2 shows that the effects of the salts on hydrochloric acid are in the same order, although no quantitative relation between the two sets of results has been discovered. This correspondence is to be expected from the ion attraction theory, or from others similar to it, since at the higher ionic strengths the properties of the solution are largely determined by the character of the added salt, and if it has a large salting-out effect on itself, i.e., if its activity coefficients are comparatively large, it would be expected to have a similar effect on others. Of course, in the mixtures which are not very dilute other influences come into play w~i.e,\\. cl.r¢ s~c.i.+i.c:.. t-oY ea.c.k ..... ,.,."tA...r~, b.Y\6. M.t)..':f ~YeY\ \oe. i.n D. se.n&e on,osi:te -t::o "th.at which would be expected from a consideration of the properties of the unmixed component solutions. In the mixtures of tigure 2~ the activity coefficient of hydrochloric acid is in each case greater than that for the pure salt at the same ionic strength (where the latter is lmown). This indicates that other things being the same, the hydrogen ion is probably especially readily salted out. These results a.re also in accord with the fact that the activity coefficients of pure hydrochloric acid are greater than those 10. of other electrolytes at the same ionic strength. Hence hydrochlo- ric acid exerts upon itself an exceptionally large salting-out influence. Whether it would do so on other substances could be found out definitely only bY, measuring the activity of such substances in the acid. An inspection of Figure 2 shows that the shape of the curve with sodium dithiona.te is somewhat different from that with bariwn chloride (which is similar to the curves with calcium or strontium chloride). The former shows quite definitely a smoother, more gra- dually occurring rise than does the latter. Any attempt at an ex- planation of this phenomenon must be mere speculation; it may be surmised, however, tha.t this is connected with the very likely phenomenon of the occurrence of pronounced "specific interactions'' principally between ions having charges of opposite signs. 5 The influence of the bivalent ions heing greater than that of the univalent ions, in all probability, the dithionage curve may indicate primarily the saltingout effect of a negative (bivalent) ion upon hydrogen ion; the barium curve may correspondingly indicate primarily the siinilar effect of a pasitive (bivalent) ion upon chloride ion. REFERENCES 1. Randall and Young, J,Am.Chem, Soc,, 50, 989 (1928). 2. GUntelberg, Z.physik.Chem., ~ • 199 (1926). 3. Harned, J . .Am,Chem,Soc., 48, 326 (1926), 4. Randall and Breckenridge, J.Jun.Chem,Soc., 49, 1435 (1927). 5. Bronsted, J.Am,Ghem, Soc., 44, 877 (1922); ~• 2898 (1923). Le.Mer, ibid,, 51, 2622 (1929); GUntelberg, loc":-cit. Guggenheim, Skand,Naturf.Report, 18 (1929). THE DISSOCIATION CONSTANT OF BROMINE CHLORIDE AT ROOM TEMPERATURE The existence of a compound, or of compounds, between bromine and chlorine has long been suspected, 1 but it is only within the last few years that definite information concerning the formula and stability of such a compound has been obtained. 2 The evidence indicates that one, and only one, compound, of the formula BrCl, exists in appreciable proportions in the range of concentrations and temperatures studied. Barrat and Stein (loo.cit.) measured optically the conin carbon tetrachloride solution and found a mean value of about 0.28. Both Gray and Style (loo.cit.) and Jost (loo.cit.) have measured by essentially the same method the above K (as before, in terms of molal concentrations) in the gas phase. This method involves determining the concentration of bro- mine in the equilibrium mixture by measuring the light absorption of the mixture at a wave length (respectively A 5790 and A5750) such that C~ and, probably, BrCl do not appreciably absorb. These wave lengths, however, are in a discrete region of the bromine spectrum, which requires that corrections of uncertain magnitudes be applied for the effect on the extinction coefficient of bromine of the considerabl~ amounts of gases other than bromine itself which are present. This may lead to considerable uncertainty in K. (See Jost, loo.cit.) The present author became interested in bromine chloride when considering the photochemical properties of a gaseous mixture which was partially composed of bromine and chlorine. For the pur- poses of photochemistry it was desirable to know the equilibriwn constant K for the reaction, and also the extinction coefficients of bromine chloride; for the purpose in hand it was particularly desirable to know the former at room temperature and the latter at A 4358. Since the published values of the former are, as was pointed out above, open to some doubt, and the latter has not been determined at all, it was undertaken to measure them by a method whioh differs somewhat from the previous one in being free from the necessity for applying the foreign-gas correction and in making no assu.~ption as to the magnitude of the extinction coefficient of BrCl. In outline, the method was as follows. The transmissions of various mixtures containing different knovm total amounts of bromine and chlorine were measured. Each of these transmissions gave a relationship between Kand e , the extinction coefficient of bromine chloride (making the well supported assumption that BrCl was the only compound present), as follows: (1 - 4K)(log r )2 = (2~) lBr20 + c~J log , - (2Fi') (Br )(C~ 2 2 0 where -r is the ratio of the transmission which the mixture actually has to that (calculated) which it would have if no reaction had occurred. 0 ) 1 is the length of the light path through the mixture and V the volume of the reacti on vessel. Br20 and C¾ 0 are the known total amounts of bromine and chlorine present. The experiments made divide themselves into tvfo groups, those with about equivalent amounts of bromine and chlorine present. and those with large excesses of chlorine. Theoretically, any pair of runs could yield equations capable of solution for the two unknowns, Kand €. Practically, however, the above equation is of such a nature that significance could be attached only to the solutions for pairs of runs of which one was from each of the groups mentioned above. There were thus obtained two sets of three solu- tions for K and € . Experiments. The transmissions were measured using a mer- cury arc with a filter transmitting A 4368 only, and a photoelectric cell in series with a sensitive galvanometer. Bulbs containing known amounts of bromine and chlorine were admitted successively, by cracking with a glass-enclosed magnetic hammer, into a previously evacuated spherical liter flask of known transmission for A 4358., The transmission was measured after each admission, so that eaoh run gave a value for the extinction coefficient of bromine, as well as the other data required. (In ene run the chlorine was admitted first so that its extinction coefficient was measured. The value found checked that of von Halban and Siedentopf within the experimental error.) Numerous readings were taken for each transmission obtained, so as to eliminate in the average the fluctuations (whichware not large) of the mercury arc. 0,220 o.479 0.308 0,471 0.468 0,218 0.475 0,302 0,466 0,464 o. 221 o. 487 o. 342 0.498 0,494 of the empty cell, The "observed" transmissions have been corrected for the transmission 0.219 0,512 - 10,65 l,63xlo-2 4,88xlQ-4 5 0,477 - o. 308 10,67 4. 42xlo•3 3,11 X lQ-4 4 0.317 - 0.168 10.57 6,05xlo- 4 4,79xlo- 4 3 0.469 o. 339 - 10,20 i.77xlo-4 2. 97xio- 4 0,469 2 10.60 c~ alone 0.248 0.515 0,332 0.491 0.485 Transmissions Calculated for Br2 + Cl2 , for Br2 +Cl2 K=0,12 K=0.135 K=0,05 K=0,12 € = 36 €. = 36 € = 36 €. = 31 - 0.346 2,5xlo- 4 2,85xlo-4 1 i,. ¢..wt. ./tit:er Vo\ ... ts-sa;.... Br2 alone ~~jlli e&.tn Mols c~ Mols Br2 Run I Observed T.ABLE ."'" 5. The weighted mean of six determinations of E~r~ 3 A 4358 was 154. Gray and Style found 160. Riba.ud found 149. 5. Results. at The results of five experiments give K = (Br2 )(Clg) = 0.115 (BrC1) 2 ' = CBr2 + Cc¾l - 41. 9 = 35. 9 a.t 20° to 23 °c. The data for 2 Kand €BrCl are shown in the Table, from which it can be seen that although the concentrations of bromine vary only by a factor of about 1.7. the ratios of chlorine to bromine vary from .0.9 to 33.4. The Table includes values of the transmissions calculated from the mean values of K and CBrCl' given above, and also, for comparison., from values differing somewhat from the means. Discussion. It thus appears that the measured transmissions can be accounted for within the limits of experimental error by assuming first that bromine and chlorine combine to form the single compound BrCl, second that the BrCl exists in equilibrium proportions. and third that Br2 , C~, and BrCl.respectively obey Lambert's and Beer's laws in the gaseous mixtures, at the temperatures and pressures used. The second assumption is well justified since measurements on the rate of BrCl forma.tion4 indicate that it talces place within a few minutes . .Ample time for reaction and diffusion was allowed in the experiments. (Runs sometimes lasted over a week.) The third assumption has been justified insofar as gaseous C¾l and Br2 alone are concerned by various experimenters. 6 There seems to be no reason for expecting appreciable deviations in mixtures of the two, for a wave lensth ( i14358) which is in the region of con- 6. tinuous spectrum for each of the three components. (For justifica- tion of this as regards BrCl see Jost, reference 2-, above.) Granting the second and third, the first assumption is then justified_!: posteriori by the experimental results. Gray and Style (lac.cit.) and Jost (ref.1 above) found K to be about 0.13. The present result is essentially in agreement, the difference being within the experimental error. 7. SUMMARY The dissociation constant K = (Br2 )(Cl.z) of bromine • (Brc1)2 chloride at room temperature was measured and found to be 0.12 (molal concentrations used). Under like conditions the extinc- tion coefficient of BrCl for ~ 4358 was found to be 36. - c (B1'Ct)l (I = I 0 10 ) • REFERENCES 1. See Gillam and Morton, Proo.Roy.Soc., 124, 604 (1929) for a bibliography on this subject. - 2. H.Lux, Ber,, 63, 1156 (1930). Forbes and Fuoss, J . .Am.Uhem.Soc., 49, 142 (1927). Butler and MacIntosh, Trans.Roy,So'c:-Canada (3) 21, sect, 3, 19 (1927) Barrat and Stein, Proo.Roy.Soc., 122, 582 (1929). Gillam and Morton, loo.cit. -Gray and Style, Proo.Roy.Soc., 126, 603 (1930). Jost, Z.phys.Chem., (A) 153, l43°Tl931). Yost and Brass, unpublished data from This Laboratory. 3. Ribaud, Ann.de Phys.,.!!,_, 107 (1919). 4. Jost, Z.phys.Chem., (B) 14, 413 (1931). 5. von Halbran and Siedentopf, Z.phys,Chem., .!,9!, 71 (1922). Ribaud, loo.cit. A METHOD FOR DERIVING PHOTOCHEMICAL REACTION MECHANISMS OF CERTAIN TYPES FROM OBSERVED REACTION RATES The rates of photochemical reactionscan be accounted for by postulating that in addition to such reaction as is caused directly or by light absorption, the products of the latter initiate one~more purely thermal reactions. All of these reactions constitute the mechanism of the overall chemical change. In order to see clearly the implications of any empirical rate investigation as regards the mechanism., it is desirable to express the observed rate as some function of the absorbed light energy and of the concentrations of the reactants. The finding of the most suitable function is often dif- ficult, however, and one of the aims of this paper is to exhibit certain type forms of this function which may be of use for this purpose. Suppose that the observed rate is expressed as a function of the absorbed light energy and the reactant concentrations. The problem is no,,v to find those mechanisms for the reaction for which the calculated rate is of the same functional form as that actually found. In the past this problem has nearly always been solved by a process of trial and error, the observed rate having been compared with that calculated from different assumed mechanisms until a mechanism had been found which gave the observed rate and also satisfied any other conditions imposed upon it by the experimental results, such as might relate to temperature coefficient, etc. 2. Since this procedure is tedious and uncertain, it was thought de~~~~ sirable to~ilnprove itt ~uch an attempt was made previously by Schwab• 1 who was able to derive uniquely the mechanism corresponding to a given photochemical rate, provided that reactions of the following type were responsible: Each reaction of the series must involve one inter- mediate present at small concentration, and one reactant present at large concentration, only. Schwab applied his method to the case or the chlorination of chloroform. ~uch mechanisms are very scarce, however, so that a means of treating a wider variety of reactions becomes necessary. It would of course be desirable to obtain a method of general applicability, but unfortunately the result would be prohibitively complicated; hence the results we can obtain cannot be completely general. The easiest way in which to effect the necessary lilnitation is to select the types of mechanisms with which to deal, picking if possible those not only of simple form but of frequent occurrence. ~his criterion may be satisfied, since, of the photo- chemical mechanisms which are now regarded as being the best known, a considerable number are of types which can be included in the following scheme: I Here E 1 and E 2 are the intermediate substances which are present during the course of the reaction only at very small concentrations, and A, • • • A a. are the reactants the concentrations of which are not 3. subject to this limitation. the reactions. reactions. The A's may thus include products of The R's, as used above, are simply symbols for the e, and e~ are defined by R0 • R0 may involve any one of the A's without affecting the following formulas at all. simply for definiteness. A, is taken Imt«te.cl , R0 may include other A's or pro- ducts, and even other intermediates than E1 and Ea, provided the added intermediates do not form or use up product. If, however, these intermediates can subsequently react in only one way, i.e., to form a product, the expression for the overall rate derived below is unchanged except for an additive term Niabs• where N is an integer. In the scheme above, E, and E.a occur only where shown. E, and E.a must reach steady state concentrations, so that when the overall rate is measured, d(E 1 ) =0 and d(f.e) =O. ( 2 ) dt dt We have, then (1) (2) Where Iabs is the number of quanta of radiation, which is of such wave length that it produces the reaction Ro, absorbed per unit time per unit volwne; the k's are the respective reaction rate constants. ± i.""I S2 = ~ ~ ki,_ (A,.,). °'-"' But, the abserved rate is given by R = Po labs + (EI )s; + (Ez )s! (3) 4. ~ where S I = Po• Pij • and P are the net numbers of mols of product appearing in the reactions R 0 • Rii • and R, respectively. (The "product11 is the substance the rate of the appearance of which we are measuring. above may be one of the A's it would not always Since this as noted be correct to write in additional terms on the right-hand side of I of the form Pil P.) We can solve (1) and (2) for (E,) and (Ez); substituting the values, so obtained. in (3) and then collecting terms we obtain as the finalexpression for the overall rate, ~ = [ t'o + t -,~e;a, + cz.;sf] 11.kls Jz t + {si••~ r;2, •:I<.r:1M f =-, .,,.~ f's,•N(AJ+!:,}=-'[,<,, Ki• I.I'• .. ~,,)+·•· K(,_(pJ·1+ r-12! kl., -l(A .VA.\l ( 4) 2, W.Vf i.~j This equation can be used in two ways: Starting with an empirical rate expression,the conditions which the K's and p's of the mechanism in any particular case must satisfy can be deduced from it. and consequently such mechanisms of type I as ar e suitable (if aey) can be selected; or on the other hand (4) can be used to write down immediately the rate corresponding to any assumed mechanism of of ~ i:l\g !lol'Y\.c.wk~~ C:.on'\pH. e~-t ~d., ID,a:t th. ll.d.VArita.g-e type I. The former of these ways has the disadvantage ~that it may point out more mechanisms from which to choose than are directly obvious for use with the latter. Thus in the case of the photochemical decomposition of HI, for which the rate is RHI = -2 labs• the deductive method indicates the following possibilities: 5. RO : HI + hY - H + I R,2, : HI+ H I + R.a R:z.,: Hz + I R M + 2I - H + HI M+:t,a and also a mechanism with the third reaction eliminated, as well as shnilar mechanisms with H interchanged with I, and 1f:a with :t,a. From quite separate information as regards the energetics of the reactions involved, the second of the mechanisms mentioned is chosen as that actually occurring. Likewise in the case of the photochemical bromination of cinnamic acid (or of stilbene), for whith the rate is RB r 2 = -K-rr:;:;,b a s (Br2 ), the deductive method indicates that the mechan- ism responsible for this reaction may be either of the follow£ng(in which C represents cinna:mic acid): Ro Br2 + hv R,, .. Br + Br 2 ~ - 2 Br Br 3 R,~: Br2 + Br 3 ~ Br + 2 Br2 R:z.1.: C + Br 3 - Br + CBr2 R M + 2 Br - M + Br2 Ro Br2 + hV - 2 Br R II Br2 + CBr - B r + CBr2 R,., : C + CBr - Br + 2 C or c~ Rzz. : C + Br - CBr ( 5) or, R . M + 2 CBr - - M + Br + 2 C or C:a -2 (6) 6. Since, from the chemical nature of the substances, it may be supposed that CBr is more likely to exist than is Br 3 , (6) is perhaps preferable. In (6), the derivation does not limit kz,, so that it may be taken as zero if desired. by Berthoud; 3 The mechanism is then identical with that proposed there is not, however, any obvious reason for completell excluding R2, 1 • The procedure used in deri-lri.ng the above mechanisms is, in outline, the following: The R of equation (4) must be equal identi- cally to the empirical rate expression, so that the coefficients of the various I ab s terms and also those of the various individual terms in powers of the reactant concentrations may be equated term by term. This procedure constitutes the introduction of the empirical observations into the calculation; the result is a set of equations among the as yet undetermined constants of the type scheme, which serves partially or completely to determine them. A single example is pre- sented in some detail, as illustration, taking the somewhat complicated case of the photochemical formation of HBr, for which the rate is = K,(liz )(Br 2 )~ (B~ + ~ (HBr) ( 7) Before proceding further with this example it is advisable to develop a general method for dealing with problems of this kind. Consider the second term of (4). Suppose that the rate is found empirically to be (8) 7. Equating coefficients ( ll.) CY~= ki.2. (9) i ~~- '( ki, (Pi:, + r~4) (b) L i\ = (C) L \~= v~•~:l. [ 'Yi ki,(Pi,+~aj +v t kj, (Pi2+ r j,~ .: %.i where C is an undetermined constant. Return now to the formation of HBr. Here, as in maey other cases, the nature of the products of light absorption m.a.y be regarded as known from independent spectroscopic data. It is not necessary to make use of this information in order to derive results of interest from the formula, but its use simplifies the treatment and makes the results more specific. In the present case R0 is Br2 + hl>~ 2 Br. We follow a precedent found usually to be valid in neglecting the effect of the excitation energy of one of the Br atoms on the reaction rate. Hence Let Es= Br, s = 1 or 2. es= 2, et= o. A, = Br2 , A.a = ~. A3 = BBr. Then., from ( 7) and (8), 1,2. = K, , the other L's = o. Let us apply (9): (a) (b) t = 2 or 1. 8. Consequently, from (c)12 , k2.,~ 0, and hence., from (c)23 , Likewise, from ( c )12 , P,2. + p 21 ) 0 O. = (K:zku - k 3 , H-P,2. + P32) ii K1 = Hence K:;ak 11 k .2., (P,2. - - P32) from (b) and (c), 3 from ( c ) 12 and ( c }~3 k 1z. It is very unlikely that =-p 32 • Therefore, combining equations, But also I from ( 9 :Xe), K:a = k 3 :a ~ k ~1 = O. P2., .2. ~ o. 0 the ratio of two velocity constants should have exactly the same value as the ratio of two others. The equation above ca.n be satisfied, however, if k 11 and k 31 a.re vanishingly small. Hence, k 31 = O, kll = O. Now,our reaction sche~e does not include such a reaction as Br2 +Br --+ Et+ wish from ehemical considerations to try to exclude this case we must set k 15 = o. But, k,z. = C ~ 0., so that S must be 1. Hence~= O, and we see immediately that the requirement of our mechanism that p be zero satisfies also the condition that the first term of (4) be zero. The mechanism is Ro Rn Ra., R '31 R , 2. R.z 2 now Br2 + h~ --. 2 Br 0 a.a + Br -+ Ez + P 2.1 HBr 0 Br2 + Ez __.. Br + P11. HBr 0 R32 EBr + Ez ..:..+ Br + • • • R M + 2Br -+ M + Br2 9. It appears immediately from an inspection of these equations that they can satisfy the conditions derived above on the p's if Ez is H and P2., p 32 = O. = 1, P,2., = 1, p = -1, or if E:z is ~Br and P2., = O., P,2. = 2, 32 If on the other hand, the reaction Br + Br2 ~ Br 3 is al- lowed, the above scheme cannot be satisfied. is that with E:z The austomary mechanism = H. Examples of the second method mentioned above for the use of (4) are hardly necessary since the procedure is one of simple substitution in the formula directly. Since mechanisms of type I are known, it might be supposed that meBhanisms of the following type would occur: Ro . A, + h"i --,. e,E + ~Ez Ri., . A · + E, - 1 \ R'-1. . Ai,+ E:z R E:a + • •• } 1 = 1,2 ,- • · d. E II + • •• . M + E, + E:z--+ ••• Follo~ring the same procedure as for type I, the overall rate is found to be D [',, :: Lfe + e ,+ e.t. -p + 2. ~p I" ..,,-Sz- ~s , (e - Q "\1 1 4 S I • S .l.. ' :2.)j c\. AS (10). where the symbols have the same meaning as before. (See under equations (2) and (3)) 10. Equation (10) is too complicated for convenient direct use, but is considerably simplified in two special cases. (11) If on the other hand e 1 -=/= ~ , while E,a reacts only by R O and R, '° e, - ¾ . ~ ] I 2 sI (12) abs A simil ar rate expression evidently obtains if we change the condition to apply to E I instead of ~. A 1 + h -., ~ e 1 E 1 + ~~, El Sometimes when R O is and ~ are simple substances which can re- combine in only one way, i.e.~ to form A 1 again. Moreover, it is usually the case that if e 1 = e2 = e, then e = 1. This gives p 0 = -p. In this case the first term of (11) disappears, so that the rate is proportional to '{ Iabs• Examples of types (11) and (12) are not given. It seems likely that they occur, particularly (11), but that this form of rate expression because of its unf'a.miliarity has not been used to express the empirical results in some cases where it would apply. 11. SUMMARY By postulating one of two types of mechanism (i.e. I or II) expressions for the corresponding reaction rates are derived. These may be written (giving I and the simple cases of II) as: = (N, + :!..)I + ,&_~ labs type I ( 4') Q, labs R = ~labs+~ (M) i Type Ila (11') = (N, + ~)labs type llb (12') R R P2 abs P2 (M) P2 The N's are integers, the P's are homogeneous linear polynomials in the concentrations of the reactants (the A's), the Q's are homogeneous quadratic polynomials in these same concentrations. The equations (4), (11), end (12),corresponding to those just given, can be used to calculate directly the rate corresponding to mechanisms of type I, type Ila or type IIb, respectively. Examples of the converse pro- cess, the derivation of mechanisms from given empirical rate expressions, are given for type I;-in detail f'or the photochemical formation of HBr. Similar procedures could of course be used for rate expressions having the form (11') or (12'). N0 te, however, that if the rate expression has the fonn ( 12' ) , which is a s peoial case of ( 4').. the mechanism my be of either type and both should be tried. Likewise if R = N Iabs all three should be tried. (For the sake of completeness it may be mentioned that if' we start with a scheme like I except that the reactions Ri, and the reactions Ri.1.. may be of the respective types Ri. 1 : Ai.+ E 1 ---:➔ gi,E2.+··· J 12. R i.2. : Ai + &a ----+- gi.:z. E, + • • • • we find that The second term of (13) is proportional to labs for relatively very small labs• while it is proportional to ~ labs• for relatively very large Rates depending upon mechanisms of type II. however, show exact- ly the opposite change in fotm with labs• as can be seen from an inspection of the second term of (10).) REFERENCES 1. G. M. Schwab, Zeit.phys.Chem., B !_, 147 (1930). 2. Bodenstein, Ann. Physik, ~, 138 (1927). 3. Berthoud, Trans . Faraday Soc,,_£, 560 (1926).