Cation Errors of the Glass Electrode at High Temperatures Citation Smith, Max F. (1939) Cation Errors of the Glass Electrode at High Temperatures. Master's thesis, California Institute of Technology. doi:10.7907/af6j-8893. https://resolver.caltech.edu/CaltechTHESIS:01022025-222404716 Abstract No abstract. Item Type: Thesis (Master's thesis) 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): Beckman, Arnold O. Thesis Committee: Unknown, Unknown Defense Date: 30 May 1939 Record Number: CaltechTHESIS:01022025-222404716 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:01022025-222404716 DOI: 10.7907/af6j-8893 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16941 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 07 Jan 2025 22:30 Last Modified: 07 Jan 2025 22:38 Thesis Files PDF - Final Version See Usage Policy. 17MB Repository Staff Only: item control page

CATION ERRORS OF THE ou-·s ELECTRODE AT HIGH TEUP?;RATURES A THE':!JS StJ8!!ITTED IN PAH'T'IAL ?GLFIT_,LMfWf Of Tm.<: R.EQ,tHRE~MSWTS FOR 1'F E DEGREE MASTER OF' SCIKNCE May 30, 1939 Introduction Page l 5 Experimental Procedure 8 Experimental B~eults. 10 Theory of Glass Electrode summary 18 CA TION TDRR)RS OF' THH: GLA SS F.:LEC TRODE AT HIGH 'I'E&, p i:;;HATUHES INTRO DUC'l'! ,)N Cremer (1) c..in covered that a defi.nite potentia.l existed between an a cid and an alkaline solut1.on when the two solutions were separated by a th 1n gl ass membrane. He surmi eed tha t th e e;l a.se membrane was perrre &.ble only to hydro gen ions. from e a rlier work on ion mi gration throu 5h ; l a trn, but did not rea l ize that t he po tenti a l wa s a function of the hydrog,en ion concentra ti on in the two solutions. Haber and Klernensiewicz ( 2 ) were t h e first 1nveet,1 e;ators to show tha t the glass membrane functioned as a hy dro ,:5en electrode and th a t the ootential followed the Nernet equation E = 1J_T/11 ff,,,,,._ ,1 , where H1 an d H2 are the hydrogen ion concent ra tL; ns 1n the solutions on ei tl1f: r ai de of the me mbrane. Th e gl a s s membrane ue ,~d by these 1nveet1ga.tors was a s im ple thin-walled bulb blown on the end of a test tube. Th e tube was f11 ied w:1 t h u. solution of fixed hydro gen-ion concen '_.ration a nd wae immersed in other eolu t1 o ns of' various hydro gen ion eonoentrat.ions. Ca.lomel reference electrodes d1p c-ed into the internal and e xternal solutions. The potential develo pe d by the cell was measured by weane of a potentiometer .and quadrant electrometer. The bulb-type glae e membrane was subeequ- ently used by trany 1nveet1 ·,:::. at◊re for the measurement of hydro f. en 1on concentration and becaw.e known as the Haber Gla.se Electrode. The glass electrode is unique among hydrogen ion electrodes 1n that 1 t is uneffecte-d by the presence of oxi dizing or reducing r~ubs tances and 1e not. poisoned by substances whi ch often interfere with the use of other electrodes, such a s the hydrogen, qu1nhydrone, antimony, etc. The ,;_; la,se eleotrode may be used in the presence of colloids and sue pended solids and in various vjscous ma.ter1al s . Dec r i te t hese a dv ,:m tagee, the gl as s elect r ode wa s not widely used for many ye~rs because the ht gh electrical r esistance of the ~;.lass membrance necessitated the use of a quadrant electrometer for the potential mea surement. The develo pment of modern electronic circuits which could be u sed in place of the delicate quadrant electrometer has brought about a wide-spread uee of the glass electrode and today, the glasn electrode 1a one of the most commonly ueed means for the measurement of hydrogen•ion concentration. The glasf, electrode deviates in several respects from the behavior theoretically expected from a hydro fen-ion electrode. If 1dent1cal solutions are placed on the two sides of the glass membrane and identical reference electrode n dipped into the two solutions, t.he theoret:Ical poti,-m .tial between the two electrodes is zero. Act,;atly th!3 r e ie. usua .Lly a eli ..ht potential, known ,is the uAsymmetry Potentialtl. 'fu (j potenti.al is presumably due to sli ,;.: ,ht d.ifferencee 1n the oomposi tic)ns of the two surfaces of t h e ;;, la.as membrane. The potential usvally do e s not exceed a few milli-vol ts and re~aine substantially eonet¼nt over lon s periods of time, at room tem pera.tures, eo that no error from this source ie ordinarily encountered in . practic:, l mea.Bu r·emento. The gl a si:1 electrode is usually standardized by means of buffer solutions of Jr.novm hydro 2,~en ion concentra t ion (pH) eo that the correction for asynmetry pot ,., ntis.1 is automatically included in the etanda.rdization. A mo1"e serious error of t.1.ie ?,lass electrode, from the standpoint of industrial pH measurements, 1.s the error ca.used by high alkal1•1on concentreitions in. the high pH region. Particularly 1n the pre sence of sodium ions, the glass electrode yields pH values which a.re str1allar than the tru.e pH valuee. The magn1 tude of the err Jr 1ncrea. ses with increasing pH, 1ncreae1ng slka l1•1on concentra tion and increaein g tem :;::i erature. }h1tall1c cations other than aod.1um produce simila.r errors but their effects a.re very much sJr.aller than that of sodium iOYlB. Dole (3) made an ext -:' naive study ion errors at 25° c. ;)f al ka.11 ... Dole and Wiener (4) measured sodium a.nd lithium-ion errors at 100, 25° and 50° C. Ga.rdn ,,r and Sanders (5) measured the sodium-ion errors of two commercial electrodes a.t 30°, 500 a.nd 60° O. Unfortunately theee 1nvestie: ators used ,.r leatrice.l me i:.ll.mrin ;s equipment wt l eb was not provided with temperature corrpensation ti o that the published value0 combine sod i um errors with an indefinite temperature error. There 1s cC; 'i idanoe that the ma.gn1 tude of t r:e al kal1-1on error de :/ends upon the composition of the glass from wh ich the membrane 1s made. Saol:r:alov a.nd Pa.eeynsky (6) sta ted that a 11 thium glass containing 80% s102, 10% cao and ·1e, L1.20 showed much smaller errors than the soda•lime Gian EledroJe Jleeve /ype Ca lornel Electroc{e Oosket Hydroq1?11 EIec /1-ocle Gasket (19 I flrra.n1emen t of Cell · glass usu ally used. Gabbard at:i.:i Dole ( 7) att.empted to make glass electrode s of' tb:i s composition but found them uneatisf't:i.cto:ry. At present, commercial glass electr-odes are made of a aocta... 11me-e111ca. glass known a s Corning 015, consi s ting of approximately 22% Na2'), 6% Cao and 72'!, 510 2 • De 8p1 te future impr ovements in E;la~'j s wbioh may provi de better 5laee electrodes, there j_e an immediate need for reliable and extensive measurements of al ka ' i-1on errors of electrodes ma.de from the 015 glas G. The recent extension of g lass electrode applic a tions 1,~ to hi e;h tem~:e r ature re g1ons rr- akee hi gh temperature values particularly desirable. Th e p:resent work war.;: undertake n f1:>r the purpose of supplyin g the needed data., APPAFiATUS Th e glaes elec t.rodes were supp l i e d by th.;~ Na.ti ·n a l Technica l Laboratories and we re made as follows: Cc, rn1 rig 015 gla s s was blown into a bulb on t >e :.md of a ten millimeter di ameter l e ad g,l a s s tube; tlrn le a d g laes be l n ? of very t1 1gb. re Pietivity, reduced t h e ele ctrical leakage to a minimum. The gla s s membrane s tl1ern selves were about 0.0075 of an inch t h ick and ha.d resist ances at I I '' Lt ~ c::J 0 © 0-- 0 0 0 - ?oten t iomeler -lo -if 'o ; "'-------- p 0 - /17.5(1- um en t ~ - 0 ~ M II It I point h,7h re11sla11ce 5w1fch 0- --0 0 '-- f17 ff potn-C ') - -- ~ ,PII /vleter as n 11/I Cf) . ll ) - I Ltarls from Electrodes Ate17t1ometer Circuit 0 soo c from tcn,A c(/ t1y Ill Pre sa.tvrator liy dro9en Car va111 Cell B£Zse 250 o. or 100 to 150 megohms. Permanent internal solutions e,n.d e:l~ctrodes •were sealed in. Shielded leade extended into the electrode. to within an inch of the bottom so that electrostatic disturban.eee were completely avoided. The glass electr<!>dee were compared directly with hyQ.rogen electrodes in the cell illustrated in figure l, Thf.tre were t1f.:beE3n openings tor; six glass electrodes. three hy~ogen electrodes, one calomel electrode, a hydrogen inlet and outlet, a thermometer, a. glass · tube for adding and a. si phon tor removing solution. The cell was supported in an oil-filled thermostat. The c1rou1t used for me asurement of the potentials is shown in figure 11. The glass and hydrogen electrode leads were connected to a Beckman pH meter amplifier through a mult1-po1nt high resistance switch which made the comparison of many glass electrodes a simple matter. The potentiometer was a Leed s and Northrup student type, which could be read within ~ 0 .. l mv . Hydrogen electrodes made of plat1n1um wire were entirely satisfactory. The platinizing solution was prepared by dissolving cleaned waste plat1.n1um wire 1n a.qua r eg1 a, evaporating the solution t.o dryness, adding wat .e r and evaporating to dryness agair1" The residue wa.s d:i.e.1aolved in distilled wate:?:" and was used without further treatment suc:h as the ad.di t1on of l e si.d a cetate . It was fo:und that th~- pH of the pla.tin:i.zi:ng solution made very little difference in t he ac tion of the hydrogen electrodes as long as a s teady stream of hydrogen was us.a d. The ~lectrodes were cleaned. in a.qua :regia. and. then purged of oh lo:rine by electroliztn1~ in l.O N o1 H2 S.0 4 for :fifteen minutes or by di pp ing alt- ernately in boiling eoucentrated HN03 a.nd botling lO;t sodium acid sulphite.. The same effect wt.HJ produced by alloi.ving t h.em to sta nd in distilled water- for two or three days . A Beckman aleeve-..type satura ted KC l-calomel eleetrod~ wa.a used for the reference electr ode. This -e leotrop.e was checked a ga :1.nst two other saturated KCl•ealomel elee trodea a.nd tl1.ree o., l N. KC l - calomel electrodes. An experiment to determine t he leakage of KC l solution out of this type of elect:i:.,ode sh owed a maximum value of 0. 003 moles of KCl in twentyfour hours; this was not eno\.tgh to effect, t h e results of the experiments in any way~ The cell used for the eompa.riso n of the gl&ss and hydroe,;en electrodes was kept 1n a lihermostat filled with low conductivity transformer oil. The constant temperatures tha.t were required. were maintained by a 100 c.c. mercury regulator. conneC\$d through a vaeuwn tube relay to two knife bea.t-ers. An electric motor wa.e used tor ag1t.at.1ng the oil bath, but.it was disconnected while the readinge were being taken .. A seperate thermoata.\ was kept at 25° o.; this thermostat contained two standard cells and the O.l N. KCl-ealomel half-eells. The hydrogen gas tra.1n is shown in t1gure lll. Thick-walled rubber tubing connetitio.n s were used where necessary; this tubing was first boiled in concentrated MaOH and th•n· impregn·a ted with paraffin. The hydrogen was saturated wit,b water vapor betor.e entering the cell in order to keep the concentration of the cell solution constant during e. run~ EXPERIMENTAL PROCEDURE The proe-edure was a. mod1fica.t1on of that used by Dole(8) in which the concentration of the ca.t1on 1s kept oaneta.nt during the experiment. ihe glass and hydrogen electrodes were compared 1n the ea.me solution a.e was first done by Hughes(9) .. A buffered solut,1on of the· acetate and phosphate of the oation under investigation wae placed 1n the cell; the electrodes were then placed 1n poe1t1on and the entire assembly lowered into the thermostat .. The hydrogen was started through the Qell and through the flask ~onts.in1ng the base , solution to be used for changing the pH of the eell solut1o-n. When the hydrogen ele-ctrodes gave c£.tnat... ant values, usually in two to two and one-halt hours. the potent,1'ale of the gla.sai and h,1dro9n electrodes ;· were recorded. The nH of the aolut1.onttn.,. the cell #,,, S'' • • "',. .•. was then chan5ed by elos1ng the st()pc.® k. ..on the hydrogen outlet tron :t.he flask and lEttl,t_in.g_ the pr$e.... S\U'e of the hydrogen force the base so,'lut1.on from the flask into the cell. When the stopcock was opened $he base ~olu,tion in the line to the cell ran baek 1ntd ;Ult flask, Since the bise add.e d had been aaturat•d with hydrogen and it. wis introduced without allowing oxygen to enter the cell, the hydro"" gen electrodes came to equil1br1um at once.. The potentials ·or the gla..ss electrodes beeame CO!nsta.nt in about ten m1nutes; ·t hey ..took somewlri_a.t longer ln potta.sa1um solutions below 40° C. Thirty to tor\y minutes were usually allowed to make certain that equilibrium wa~ reached. The potentiometer circuit was standardized against the two standard cells that were kept in the 25° C. thermostat.·. The st,andardiz~tion was done thro ... ugh the amplifier. The low input '¢\U"rent of the elect.ronic cm-cult. (2xl0 -l3A~mps. ) allowed the etand .. a.rd celle to be oonneoted wlthout polarization even though the circuit might be far out of balance. -10... EXPERIMENTAL RESULTS The cells which were considered in this 1nveat1gat1e>n were: l. Pt H2 2. Ag Isolutionx j (saturated KCl I Hg2c1 2 j Hg IAgCl j g:::;:~¼1 Glaee 1solution X 11 saturated Kell Hg2Cl2 I Hg If we subtract t he potentials of these two e4!llls we obtain the potential for the cell J. Pt H2 - Isolution X I g l ass I!~::;: ~¼ I AgOl IAg Using the ea.me terminology as Dole and Wiener (4 ) and calling this potential L1<l. then by definition LlG-= E 1 ... E 2 It haa been pointed out that at high pH LlG varies with the metal1c eation pre sent, 1te concentra tion and the pH of the solution. If the poten.t1a.l which would be obse-rved, 1r the glass electrode functioned as a. p$rfect hydrogen-ion electrode, ia called LlG 6 , then the error of the glass electrode ,t\E can be found. dE =- LlG .. AG0 ~G0 1e found by making measurements 1n the low pH range where t he gl ass electrode does a.ct a.a a perfect hydrogen-ion electrode. The preceding d1seuea1on will be illustrated later by the cor!a1derat1on of a specific case. The pH of the buffer solutions at the various e temperatures was determind by t he hydrogen electrode; I\ 1 ••• the potential or cell 1. Since the E. M. F.-temperature relations O.f the saturated KCl-calomel electrode are not well established. a.t the higher temper·a.tu.res used :ln this investigation, the pH values were reterred. to 0.05 N. potassium hydrogen phthalate with .t he assump- tion that th• pH of this solution does not change with tempfltrature. Clark (10) gives the pH of this solution · a.s 3.98. Recently Ma.einn~,, Belcher a.nd d. Shedlovsky ( 11) have reoomme1\ed the value e 4. 00 a. t 12°0; 4.oo at 25°c and 4.015 at 38°0. D1sp1te the probable greater accuracy of this work, the value 3.98 wa:s used in the following computations beoauee the other "V'alues have :not been widely accepted. srhe un ... cert,a1nty in the pH valuee of the potassium hydrogen phtha.lat& bu:ffer at the vario\J.s tempera.ture.s is only of seeondary importance in this 1nvest1gat1on for it. does not enter direotly into the alkali-ion errors. It ap ... pears.only in the 1nd1eated pH values or the solutions. A large change in the pH values of these solution.s- would cause only a slight shift in the error curV'·e e shown 1n the following figures. At ea.ch temperature the hydrogen and calomel electrodes were immersed in 0.05 ?'l potassium hydrogen phthalate solution a.nd the eell potential (E} determined. From the equation E ... E ' tihe .quantity Et was found tor ea.ch temperature. This quantity 1:ncludee the E. M.1. or the ea.lomel reference eell, the liquid Junction pQtent1al and t.he correction for t,be reduced partial pt-essure of 'hhe hydrogen gas a.t $he hydrogen electrode. ":'he exp•rimental values are shown 1n the following ta.'ble TABLE l I&', (vo,ts2 Temuer.a t~t 30<) 0 -0.2420 400 -0.2338 5,00 -0.2255 so0 -0.2174 10° -0.2093 The experiments included. 1n this 1nvest1ga.t1on a.rethe measurements ot cation errors of the glass electrode at the following temperatures and eonoEmtra.t1one. Tem,eera. ture. et O 0 300, 40() , 500 . • oO • 70 C c 0 o t:. o 30, 40 • ,50, o 0 , 70 o qation .concegt.t-atiQn 0,,1, 1.0, 2.5 M sodium-ion 0.1, 1.0 N potase1um-ion 30(/)' 50°' 60° 2.5 N potassium-ion 30°, 40°, so0 , 60° 1.0 N l1th1um-1o:n. 30°, 40° 2.0 N lithium-ion 40°, 50°, 60°, 10° 30° 0.1 N 11th1um ... 1on 0.01 N caleium•ion 60° Typical experimental data. an.d computed results are given in table II,. eodiwn-ion at 50Q C., The values a.re for H1, H2 and H3 a.re 2.5 N the measured potentials (1n volte) or the cells composed or a calomel reference electrode and three 1nd2.d1dua l hydrogen electrodes. Thia 1s the potential of cell l given above,. o1 , o- 2 •--G are the correspondj,rtg 7 potent,iala of the aame ealomel electrode and seven 1ndiv1dual glass electrod~s. Thia eomprises cell 2 given above .~ The measurements were made on n1n$ different solution.a. The pH values shown w--ere obtained by the use of e1ua.tion 2, the value of E' for- the temp- erature in question and the average value of H1 , H2 and H3• 1101 --- LJ.G are the algebraic d1fferenees between 7 G1 ............ G and the average value of H1 , H2 and H3 • This 7 of course is the potential of cell 3. LI E1 --- llE7 are the sodium-ion errors of the respective glass electrodes; t .e., the differences 'between the measured glass elec- trode-calomel electrode potential s and. the correeponding potenti a l s which would have been obtained if the glass electrode functi oned as an ideal hydrogen-ion electrode. The latter ootenti a.ls were obt_:~.ined fro m the values of AG 1n the low pH reg ion, where the alkali-ion error s are negl1 g 1 ble. This proc edure will a lso eliml nat,e the asym- metry potential. If there were no alkali-ion error; the values of 4G, for a. given electrode, would remain constant with increa sing pH. If t h e a verage va lue of .1 (} ii1 the region of ne gli gible cation error is called dG0 , then the cation errors are o·b ta.ined by subtracting .AG0 from the measured value s of i1 0 . 'I'he age of the glass electrode appear s to have very little effect u pon the cation errors e xcept 1n the -14- ease of ,e od1.um•ions. There is some evidence th a t freshly blown glass electrodea show eom.awhat smaller sodium-ion errors than are 1illbown by old electrodes. In Table II, electrodee n4 and Cry were freshly blown electrodes. The effeot of age, however. appears to be le~e than the var1at1one normally found among 1nd1v1dual electrodes. All experiment1il results are summarized 1n Figures 4 to 17. The points shown on the graphs :represent. the average values obta.1nad for at le a at five glass electrodes 1n e a ch case. In Table III alkal1-1on errors published by other workers are compared with the corresponding values obtained in this 1nveet1 gat1on. In general the agreernent is satisfactory for most practical measurements . For ref.ined pH determ1.nat1ons where large sod1um ... 1on errors are involved and where the age of the glaas electrode may be an im portant factor, direct determination of the aodium-1on error should be wade under the actual o per ctting cond1 tions. Rounded off value s of g lass elect.rode errors at 300 - c. l .Q ~ ~ :2.:.1 Na 9 0 (2 ) 9.5 l ( 4) 10 2 ( 6. 4) 1 ,.,.., (11.5) 10 .5 7 (9 .. 4) 21 (18.5} 11 '\ {14 ~h,) l -· 34 ( 30 • 3) 11.5 23 (21.3) 52 ( 45. 2 ) 12 3 /4 { ..-~J t.·~, •. c; ) 75 (63.1) mv. ..., ~ ✓ Values in parenthe sia Bre tho ~e of T V T • mv. 2 J.·..J • (5.5) Gabbard. ~:n d Dole ( '7). TABLE ~ - - ITJb ~ Hounded off values of :31asa electrode error.s at 50° C. mi 2.:.1 11 rnv . - - 0 (3) 0,.1 Na ·mv. ? ( 21) !..& Na mv. 14 (7.1) 1.:.9. 11 9 3 9.5 5 (l) 1 0 (8) 7 ( 4. 3) 25 (12.9) 10 7 ( .);! 'I 20 (17) 1'1 (10) .,-. 40 (25.4) 10.~ 13 (7.5) 34 ( 30) 27 (18) 59 (39. 0 ) 1.1 19 (14.2 ) 51 ( 46 } 41 (27) 83 (58.5) 11.5 2"{ (25.5) 71 (68) 12 108 (75.5) 94 {98) Value s in parent,hee1s are those of Dole and Wiener (4). mv. TA.BLE 2.5N ira l. 2. ;. 4. 5. 6. 7. 8. 9. H1 fl2 H3 .5630 .6312 . 5630 .5630 .6312 .. 7167 .7915 .9561 . 7168 .7914 .9562 .8410 • R4ln'.J .,,t . 81tlO .8998 .8998 .8998 .9562 .9560 .9561 .999'.:; 1.0115 1.Cll5 l. ,; .1708 .1787 .1842 f1 pH .• "'14o7 , 3. 7.665 4. 8.832 5. ll.4o2 6. 9.602 1. 10.527 8. 11.402 9. 1 2. c.'?02 H1 '-..Tl .6767 .6784 .6823 .7051 .8206 .7306 .6312 .7166 .7915 .9561 .8410 .8998 .9561 l.Cll5 3. 4. 5. 6. 7. 8. 9. .1268 .1342 .1355 ~ .5630 ,:;. . 21.2 127.6 44.6 50° C G-3 ,}4 Gi.:: ,;,) (t6 G7 :0820 :0321 .0621 -:1518 -:0959 -: 0013 .0582 -:-0178 .0482 -:0148 .0694 .1277 .1832 .1556 tflG3 L1G4 .4GL-:) .al6 /JG7 .6450 .5951 .5967 .5982 .6251 .6275 .7148 • T363 .7189 .5830 .c1G2 . 64ltl4 . 5460 .6479 . 6660 ~6472 . 6638 •77C:. . • J°'7' . 7729 1 .6972 r,· A-· 5 .. 0010 .0016 . 0031 .0171 . 0043 .0249 .0025 182. 4- .1.993 .. .0846 .0198 51279 .0404 .0804 .l j)O .1~290 .1829 .1888 .1153 .0379 . c6Jr9 .1190 .1681 volts three hydrogen - 3 The potential inin volts of six glass ;1otenti.al Gl ... 6 1:'r1e of .65co AS4 . '"o~-,s· • 0 02~} .0539 .0963 .1452 .7104 .6330 .6600 .7141 . 5294 .,1"E3 .0027 .0216 .1 315 .0528 • ~)12 ~~ • 7592 .AE2 \_, . 2420 .6728 .7137 .7607 .8085 . Lf\:;l • '{"('"(I.; .1524 .19 22 .2578 .2483 .8233 83. 3 129.2 .1782 .1861 .1877 .8720 .1439 .2080 .1415 .1954 .1991 .18 ::-1 .71290 • 028.l~ .0872 .2308 .6469 ";0037 .1184 .1793 .2457 .J.744 • .0056 .0345 .1153 .0862 .1C46 .1130 .1191 .6854 • '7°5' . (_. .. •,i. -7740 . 8298 '7'7 ,)V 7. ,.., .8219 Ave. L> E mv. 2.1 3.8 G2 -;1137 t0814 -:0475 . 7(:)1 '57 .0343 .0687 .0864 .1255 .1R03 • 1 .355 .1104 .1538 (average) H 2. .6312 .7166 .7915 .9561 G1 ll • ()O~?t• .2582 .. 5808 .5842 .5993 .6983 .7950 .8386 .8884 .6578 ~E,. 0 1)1t7 .C215 • (J ()~?. 2 .0041 .OC: 34 .8408 • '7548 .0185 .1260 .0400 .1356 .1238 .1776 .1874 .2420 .2518 .7333 .0477 . 0896 .2208 .0802 .6202 .6998 .. 7493 .0185 .1175 ,.0394 .0670 .1190 .1725 electrodes. electrodes. d Gl .,. 6 The difference 1n volts of the potential of the average hydl. . ogen electrode and the potential of the individual glass electrodes. E1 _ 6 '1G ... G0 or the increase of G ca.used by the presence of sodium ions. /6 I . J ... . . 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I:.. -~ +- - -<~ -:-· - •• • • -~~-~-~---+-~-+--+~:- -+t+f- >---:.~:+'- : _ _;__ 1 - •: -l ------· -- I .• ~ ----c- -- ·_:_: , _ , - - , f - - - - - - + ---+ - - - 4 r ,•-• • •-•: ·••-• •· I r~~...:....:......:. .:....:..:. __i. _;_ - ~ =-+ --_...:_ ._-: :.. ~ 2 -+ , > > i: . . .. . . .; ... ..:.. :... : . ':; .. :... :. ;.:: :. : ' ··•- -- : --~--~ 1-- · -- -- . --~ ~ 20 -- / ,__ __ ... !_• • - -~----- - +---+----<- -,_ ___ __ _ _ _... __ _ _,________,_+--- 4 -- - ___ ~ -- ___ i -t-----+-- - r - - - + -----+ - + - - - + - - - --- - -- ·i. - --+---<- . , . ; ~ .( 7.. :· ,; ., . ,, . 6 7 a 9 pll 10 I/ 12 13 1. • • • '/I : . : (/) ~ LI o THEORY OF THE GLAS S ELEC'I1WDE There are three general theories for glass electrode 'behs.v1or: the phase boundary potential theory, the membrane-diffusion potential theory. and the 1on adsorption theory. M. Cremer {l), as etated before, assumed the gla.s e wae permeable only to hydrogen ions. He arr1ved at this conclusion because the work of E. wa~burg showed that the electrical conductivity of glass was of electrolytic-type. M1cha.e11e : (1 9 ) extended this theory by considering t,he diffusion of other cations a.thi gh pH. Dole ( 3) showed this idea to be erroneous by doing two parallel experiment s 1~ which he measured the potentials between o.lN NaOH solution and (a) p \.We O,lN HCl solution and (b) O.lN HCl so- lution which wa s O.lN with respect to sodium-ion; the t wo potenti als were fo und to be the same. If the sodium error was due to the diff usion of sodium-ion, the pot~mt,ial would be a function of the sodium-ion concentration on both sides of the gl a ss membrane. Horovitz (12) assumed an ion ad sorption on the glass surface. He l ater modified this theory to include an ion interchange between the glass surface and solution; he again changed his theory to take 1nto account the ionic mobility of t he i ons (13) and the heat of the mixture on the surfa ce of the gl ass. Schiller {14) and Lengyel (15) also advanced ion adsor ption theories. Leng.yel used quartz for his work; it 1.e doubtful if the action of quartz and glass membranes are similar since the quartz a.eta eeeent1ally as a condenser while the low ... resista.nce glass does not. Haber (2), a.a already mentioned, advanced the f1ret phase boundary theory. He neglected the action of metallic cations at high pH values. Hughes (16) stated that the buffer action of eod1um silicate kept constant the hydrogen ... 1on coneen1;,rat1on within t.he glass. While he mentions alkali-ion errors, he makes no attempt to explain them. Gross and Hal pern (17) attempted to account for the alkali-ion errors by assuming a dissolving of t,he glass 1n the water and the water 1n the glacs. They poBtula.te that 1n low pH regions the 1on1e concentration 1n the glass 1e due to hydrogen and hydroxol 1one but a.t h1.gher pH the metal 1on also has an effect on the 1on1e concentration. In order to make these a.seumptione, it was necessary to assume a region of mutual solub111ty; it 1a difficult to visuali ze this film as exi sting 1n view of the slowness with which glass d1Bsolves and the rapidity with which glass electrodes come to equilibrium. Dole (3) used the Henderson and Planck formulas for liquid Junction potenti als to derive an equation whioh fitted t,he measured alkali-ion errors up to a. pH value or 12. The equation q~:>nta.1ne,d several constants that were neither constant nor theoretically det.erminable. Dole (18) later applied stati&tiee.l mech ... antes to the problem and obtained an equation that. predios 1noreaeed eation .error a.t higher temperatures. The eqw,.1,ion 18: !!"'~ A _.,. A(ClHle- OH+ e,.. Nr!fftt_-""Afe ¼e C ~ . AE= 7 . cH -F, . • • iNJ7 '!/ '/,I 6E is the error of the glass electrode. R, T, and F have their usual significance. B is the ratio of the proba.b111 ty of a tranei,. ,.on t.o the glass eurfaoe t..o the reverse transition at equilibrium. (Dole takes these as unity ) c 1e the concentration in moles per liter . . f is the activity ooeff1cient. Q is the d1f'ference between the energy of a.n ion in the interior of the solution and the energy ot an ion on the glass surface. The subscript Me refers to any cation other than H Do-l e calculated values of measured errors and found them to be around 13 to 15 k. cal . per mole. The values in.creased with increasing pH, but a.t 50° C they became more constant. The many constants in this equation can only be evaluated by experimental measurement and the experi- ment rem.o ves tbe need for the equation. It is, therefore~ of no value from ahe standpoint of providing a meaner by which glass electrode errors may be eo:mputed.. lt: ven though the constants could be evaluated, the equation fails t.o explatn either the 1ndivtdual action of glaas electrodes or the increasing reproduc1b111ty of the potaas1um-1on errors aa the temperature 1s increa sed. The mod.1fied ionic exchange theory or Horovitz might, offer a better explanation, but 1t would be of no greater value in predicting the gl ass electrode errors. SUMMARY l. The cation errors of Corning 615 glass eleotr-odes were determined tor various ooneentrat1ons 0 of lithium, potassium and sodium ions at 30, 400 & 500 • 60° and 70° C a.nd for calcium ion at 30°and 60° C. The errors were found to increase with increasing temperat-ure . 2. F'reeh glass eleotrodee showed slightly ·· :smaller errore than those which had been uesd for some time. 3. Pota.esium-ion errors, which were vari able a.t low temperatures, became def1nate a t temperatures above 40° c. ACKNO WLEDGMENT The writer wishes to ts,ke t,hts opportunity to acknowledge his indebtedness to Dr. A. o. Beekman for his helpful suggestions a.nd. to the National Technical Laboratories for aupplyi.ng the glass electrodes and much of the equipment used in this investie;a.t1on. B!BLIOGRA PHY 1- :M. Cremer, zutaehe F. Biol. !fl.; 1 (1906) 2- Haber and Klemensiewicz, Ann~ D. Physik. ( 4) ~. 927 (1908) 3- :M . Dole, J. Am. Chem. Soc. 22.l. 4260 (1931) 4- M. Dole and B. z. Wiener, Trana. Eleetrochem. Soc. li, 107 (1937) 5- Gardner and H. w. Sanders, Anal. Ed. Ind. Eng. Chem. 9, 274 (1937) 6~ Seokalov and Paesynsky, z. Phyeik. Chem. A 160~ 366 (1932) 7- J. L. Gabbard a r1d lL Dole, Trnne. EleetrQchem. 8... M. Dole, .1. Am Chem. Soc. 9- W. S. Hughes, J. Am . Chem. Soc. Soc. ll, 129 (1937) u, 4260 , _, ,· 31) !!1, 2860 (1922) 10... 11 11- D. A. M&cinnee, D. Belcher and Shedloval{y, ,J. Am . Chem. So c. §Q_, 1094-9 (19 38 ) 12- Y. . Horovitz• Z. Phy s1 k. 12,, 369 ( 192.3 ) 13- z. Physi x . 1115, 42Jt (1925) H. Schiller, Ann . Phy s i k . ll, 105, (1924 ) 15 ... Lene;yel, Z • Physi k, Chem. 16- W. 17 .. The Determ1nat1on of Hydrot~en Ione", W. 1: . Clark i{ . Horovitz, 1.2~• 371 ( 19 31 ) s. Hughes, ,T. Chem. P.oc. 491 (1928) P. Gross and O. Ha l ~;ern, z. Phy e i k. Ch em. 11r.; ,. 5 4 (1925) iIS. 255 <1925) g. 862 (1934) 18- M. 19- L. !a chael1 s • D1e i'Ja turw1 ea .• 1 4 . 33 ( 1926) Dole. J. Chem. Phys.