D. W. MARGERUM AND B. A. ZABIN
2214
Vol. 66
TABLE I1
EFFECT OF VACUUMHEATTREATMENT ox CdSe STOICHIOMETRY Initial Cd/Se weighed molar ratio
Initial Cd Kp/Se Kp count/sec. ratioa
Heat treatment temp., *C.
Heat treatment, time, min. a t temp.
Wt. loss, %
Final Cd Kp/Se Kp count/seo. ratio
Final Cd/Se molar ratio from smooth curve of Fie;. 2
1.00000 0.826 f O . O O l b 1.00500 0.830 f .001 1.01000 0.834 & ,001 1.02000 0.843 31 ,002 1.00000 0.826 408 405 0.64 0.832f0.001 1.007 1.0000G 0.826 510 1425 1.05 .830& ,000 1.005 1.00000 0.826 515 1275 1.11 ,831 f ,001 1.006 1.00000 0.826 598 405 5.23 . 8 3 5 & ,001 1.011 1 ' 00000 0.826 599 105 . 8 3 5 & ,000 1.011 1.00000 0.826 602 225 3.53 . 8 3 6 f ,001 1.012 1.00000 0.826 676 15 2.69 ,827 & .000 1.013 1.00000 0,826 694 45 8.00 ,835 f ,001 1 ,U l l 1. 00000 0.826 950 60 -50 ,831 & ,001 1.006 Tungsten target, 50 kv. 26 ma. Arit,hmetic deviation based on 4 or more sets of counts (1.024 x 10: counts).
Acknowledgments.-The authors wish to express t'heir appreciat>iont'o R. Rohr for t,he design and incorporat,ion of mechanical modificat,ions in the vacuum spect'rograph and to Ail. Koblenz and 34. Yablon for the design and ii~corporationof
elect'rical modifications int>othe same equipment,. They also wish to thank G. Mandel for his many stimulating conversations and contributions to the clarifica,tionof ideas concerning incongruent vaporization.
COORDIXA4TIOXKINETICS BY I O S EXCHANGE BY D. W. MARGERWAND B. 4.ZABIN~ Department of" Chemistry, Purdue Universzty, Lafayette, Indaana Receraed .Mau 7, 1062
Cation-exchange resin is used as a metal ion buffer to give very lorn but constant concentrations of metal ions in order t o control the rate of fast coordination reactions in the solution phase. The rate of formation of nickeliI1)-EDTA is used t o test two variations of the system. Particle diffusion rates limit the magnitude of the coordination rate constants which can be measured. The fraction of resin in the hvdrogen ion form compared t o sodium ion form has an unexpectedly large effect on the diffusion of nickel ion under conditions of low nickel loading where the coupled resin diffusion process should depend largely on the self-diffusion constant of nickel ion.
Introduction I n this work an ion-exchange method designed to permit the study of some fast coordination reactions is tested. A strong acid cation-exchange resin (Dowex 50W) serves as a metal ion buffer giving extremely low but reproducible and constant concentrations of metal ion in the solution phase in equilibrium with the resin phase. The reacting ligand in the solution must be excluded from the resin so that its coordination rate depends on the equilibrium metal ion concentration. The system has the advantage of greatly slowing reactions but giving readily measurable concentrations of product. The reaction of nickel ion with ethylenediaminetetraacetic acid (EDTL4) served to calibrate the method because this formation rate can be calculated from its measured dissociation rate2 and the stability constant for nickelEDTA.3 The particle diffusion rate of nickel ion (1) Abstracted from the Ph.D. Thesis of B. A. Zabm, Purdue Uni1962 ( 2 ) C &I. Cook, Jr., and F. A. Long, J. Am. Cfiem Soc., 80, 33 (1958). (3) G. Schwarienbach, R. Gut, and C. Andelegg, H e l v . Chim. Acta,
1 ersity,
37,937 (1954).
limits the speed of the coordination reaction which can be studied. The resin in the sodium form is loaded with a few per cent of nickel ion and a low concentration of sodium ioii is maintained in the solution. A sufficient quantity of resin is used so that this loading does not change significantly during the reaction. Under these conditions the nickel ion concentration in the solution is expressed by eq. 1 and can be adjusted readily from lou7 to 10-j ~14and kept constant during a run. R n [ S i R 2 [IYa+l2 ] [Nit21 __ (1) [NaRI2 The reaction rate is second order d [NiYT]J'dt = kgIyT [UT] (2) where YT and XiTT refer to the total acid forms of the EDTA anion and the nickel complex, respectively. Combining eq. 1 and 2 gives a pseudo first-order reaction so that a plot of -log [YT] against time gives a slope equal to ~ N ~ Y T [ N ~ + ' ] / 2.303. The [Ni+2] is determined experimentally for different [Na+1.
COORDINATION KIKETICS BY IONEXCHAKGE
Kov., 1982
I n an alternative method the same reaction is studied by loading the resin with low fractions of zinc and nickel and zinc-EDTA is used in place of free EDTA. The rapid equilibrium Zn3-T 1_ Zn+2 -k
(3) and the 45n+2equilibrium with the resin phase now J small but constant so that eq. 2 becomes makes [YT pseudo zero order. The coordination reaction is now so slow that diffusion in the resin phase does not interfere. The reactions in eq. 3 must be much faster than the coordination rate studied for the zero-order system to be applicable. Experimental YT
Apparatus and Reagents.--Reactions Were run in a 3necked 14. round-bottomed flask fitted with a paddle stirrer and immersed in a constant temperature bath a t 25.0'. One of the side necks of the flask contained a test tube which served as a baffle to help mixing, while the other neck contained a dip tube with a I-cm. diameter sintered glass disk. Samples free of resin could be drawn rapidly into this tube and accurate aliquots could be taken for analysis. Stirring rates were 400-500 r.p.m. (measured with a Strobovac) unless otherwise specified. Dowex 50W cation-exchange resins purified by Bio-Rad Laboratories were used. The capacity of the air-dried resins in the hydrogen € o m was determined by potentiometric titration with base in the presence of excess NaC1. The resins were treated with a sequence of HC1, water, EDTA, water, SaOH, water, EDTA, and water rinses to remove all traces of possible interfering metallic impurities. When m e t d ions were loaded on the resin, the slurry was stirred for 0.5 hr. to assure equal distribution of the metal. All water was first purified on mixed resin beds. Reagent grade EDTA, recrystallized twice from water and dried, checked satisfactorily as a primary standard when analyzed by dissolving it in base and titrating a standard copper solution using PAN i n d i ~ a t o r . ~ Solutions of NiCls and ZnSOJ were standardized with EDTA using murexide arid Eriochrome Black T indicators, respectively. Control of pH in the first-order nickel-EDTA reactions without upsetting the concentration of counterion was vital. The sodium ion contribution to the counterion concentration for these experiments was 0.020 M , 0.010 M in NaCI, and 0.010 M from the sodium salt of the buffer. The buffers used were: pH 2.5, sulfate-hydrogen sulfat,e; pII 3.2, chloroacetate-chloroacetic acid; pH 4.0, formate-formic acid; pH 1.5, acetate-acetie acid. At these concentrations, nickel complexes of the buffer salts are not important. The analysis for [Ni+2] in equilibrium with the resin and in the rate studies was based on the Ni(CN)4-2 absorption peak a t 267 mp with E = 1.16 X lo4. Aliquot&were added to NaCN solutions buffered a t pH 10 and the absorbance was measured on a Reckman DU spectrophotometer. Preliminary Studies .--The rates of elution of zinc, cadmium, nickel, and aluminum from 10 g. of nowex 50-X16, '200-400 mesh, 10% metal loading with 500 ml. of 0.005 Jf EDTA at p H 5 were compared. The zinc and cadmium were eluted rapidly, the nickel rather slowly, and the aluminum very slowly. The nickel rate showed diffusion interference (first-order plots of -log [YT] against time curved upward RS the coordination rate slowed with time and the diffusion rate caught up to build the [Ni+2] back up to its esuilibrium level). -Steps were taken to minimize both particle and film diffusion. A low cross-linked resin was used t o increase particle diRusion after it mas shown that EDTA did not enter the resin to react with the metals. A large quantity of resin of small particle size was used to give a large particle area near the surface and a large film area to mininiize both diffusion steps. Film thickness was minimized by using rapid stirring. The coordination rate was slowed by lower p l l , lower initial EDTA concentrations (10-8 to M ) , and lower loading.
-
(4) F. J. Welcher, "The Analytical Uses of Ethylenediamine Tetia-
acetic Acid," D. Van Nostrand Co., Inc.,Princeton, New Jersey, 1958.
2215
First-Order Formation of NiYT (Nif2 in Resin and YT in Solution).-Two hundred meq. of resin (about ,200 g. of wet Dowex 50W-X2,200-400 mesh), loaded 2% wlth nickel, was placed with 500 mi. of solution containing [Na+] = 0.020 M and the desired buffer in the %necked flask and after 30 min. fractions were taken for analysis of the equilibrium nickel. The resin was filtered, washed with water, and the process repeated to check reproducibility of values obtained for the equilibrium nickel. Then a solution of EDTA containing the same counterion concentration was added and 5-ml. fractions were taken a t time intervals for analyais. The [XYT] is the nickel found less the equilibrium nickel. Plots of -log [YT] against time were linear and did not show the diffusion interference observed previously. Zero-Order Formation of NiYT ( N P and ZnT2 in Resin and ZnYT in Solution).-The same resin conditions for the first-order runs were used except that the resin was loaded 4% with zinc as well as 2% with nickel. The solution was 0.10 M in sodium ion and was varied in chloride and acetate ion. The resin (100 meq.) was added to 500 m1. of the sodium salt solutions and samples were withdrawn after 30 min. for nickel and zinc analysis. The zinc was determined using Zincon6 a t pH 9 with correction made for the nickel interference. The solution then was made M in ZnYT and the reaction was followed by the determination of nickel as before. Only a few per cent of ZnYT reacted during the rate study and the reaction plots of [N~YT]against time were linear in accordance with a zeroorder rate. Dissociation of NiYT (Resin in H f and Na+ Form).The rate of dissociation of XiYT was measured using 200 g. of the X-2 resin without metal loading to displace the reaction. The reaction volume was 500 ml., the [Na+] n-as 0.10 M, the initial [N~YT] was about 5 X 10-6 M , and the pH varied between 1 and 2 . Plots of log [ N ~ Y T ] against time were linear.
Results The rate constants for the dissociation of nickelEDTA using the resin to displace the equilibrium are compared in Table I with values calculated from the radionickel exchange2a t the same ionic strength. In general, the agreement is excellent and where the deviation occurs, the resin experiment gives the TARLE I FIRST-ORDER h T E CONST4STS FOR THE DIbSO( I A T I O N O F
NiYT [Na+] = 0.10, 25.0" p1I
1 (32 1 63 1 40
[NIYT]initial x 10.
4 if3 5 34 2 72
This work icd, min.
-1
2 8 x 10-2 0 19 0 81
Cook and Lon@ kd. inin.-'
4 5 x 10-2 0 20 0 74
constaiit by a far more direct route. In ally casc, thc resin certainly does not catalyze the reaction despite the fact that the resin phase acidity is 14 and NiYT dissociation in 1 114 greater than 1 1 H + is almost instantaneous. Thus, NiYT does not enter the resin phase i n its dissociation and by the principle of microscopic reversibility, the formation of SiYT should not occur in the resin phase. Further evidence that EDTA reaction in the resin phase is not appreciable is seen in Fig. 1, where increased concentrations of EDTA in the solution phase do not result in increased rate constants. The second-order rate constants calculated from the observed first-order formation of nickelEDTA are shown in Fig. 1as a function of the initial EDTA concentration and pH. Despite the fact that the individual rate plots did not show sig(5)
R.M. Rush and J. H. Yoe, A n d . Chem., 26, 1345 (1954).
D. W. MARGERUM AND B. A. ZABIN
2216
c
1
I1 .$ 10
0
4 [YTli
2
6
8
10
x lo4.
Fig. 1.-Apparent second-order rate constants for the formation of n'i(I1)-EDTA from free EDTA and Ni(I1) from cation-exchange resin: 200 meq. Dowex 50W-X2, 200-400 mesh; 2% Ni+2loading; [Naf] = 0.020 M ; total volume, 500 ml.; 25.0'; stirring rate, 400-500 r.p.m.
.$ -60
a
I
/
0
1
,
I
,
/
2 3 Rate of mass transfer X lo', mole Ni meq. resin-1 min.-l.
I
4
5
Fig. 2.-Effect of pH and cross-linking on the error in the second-order rate constant due to particle diffusion: 200 meq. Dowex 50W-X2, 200400 mesh; 2% Niez loading; [Nail = 0.020 M ; total volume, 500 ml.; 25.0'; stirring rate, 400-500 r.p.m.
nificant diffusion interference, Fig. 1 indicates that the diffusion problem still persists a t higher p H and higher initial EDTA concentrations where the diffusion rate cannot quite maintain the equilibrium nickel ion concentration because of the increased coordination rate. The correct value for IGN,\'Tis taken as the extrapolation to zero initial EDTA. Decreasing the quantity of resin also decreased the apparent rate constant. The stirring rate of 400-500 r.p.m. should result in a film of constant thickness surrounding the resin beads and minimize film diffusion.6 Reducing the stirring rate to only 75 r.p.m. would have increased greatly any contribution of film diffusion, but as seen in Fig. 1, this had no effect. Increasing the resin cross-linking did cause considerable reduction of the apparent rate constants, so particle diffusion appears to be the source of interference in the kiqetic studies. It is convenient to define the inilia! rate qf mass transfer in terms of the moles of nickel transferred per meq. resin phase per min. to the solution phase. In Fig. 2 the per cent deviation of the apparent rate constant from the extrapolated value is plotted against the initial rate of mass transfer. The X8 resin shows much more deviation than the X2 resin at the same pH, illustrating the crosslinking effect on particle diffusion. At pH 4.0 and 4.5, the limitation of particle diffusion in maintaining the desired equi(6) M. Tetelbaum and H. P. Gregor, J . Phys. Chem., 58, 1166 (1964).
Vol. 66
librium nickel concentration is the same. However, a t lower pH, as the fraction of resin in the hydrogen form begins to be appreciable, the particle diffusion rate of nickel appears to increase and causes less deviation in the kinetic study for the same mass transfer rate. A rate of mass transfer at pH 3 was estimated for copper ion. The copper coordination reaction Ivith EDTA is much faster than the nickel reaction and the rate of transfer from the resin phase probably is not coordination controlled. Using the same resin and solution conditions copper ion reM EDTA in 30 see., giving ail acted with 2 X average rate of mass transfer of 1 X mole Cuf2 per meq. resin per min. This is greater than the initial rate of mass transfer for nickel, which is controlled by both diffusion and coordination, but if it represents the limitiug rate for nickel diffusion it could cause the deviations observed at low pH. The extrapolated values for JCN~YTare plotted in Fig. 3 as the measured constants and are compared to those calculated from the dissociation rate constants and the stability constant for nickel-EDTA. The agreement is within the accuracy of the calculated constants except a t higher pH, where in one case diffusion limits the accuracy of the ionexchange method and in the other case the contribution of other terms in the radionickel exchange2 could easily lead to high values for the formation rate constant. The comparison is made for ionic strengths of 0.02 to 0.03 in both cases. The results of the zero-order ion-exchange system for the same reaction but at a higher ionic strength (0.10) are shown in Fig. 4. In this system, diffusion is not a problem because the coordination rate is much slower and the larger rate constants a t higher pH values can be measured accurately. The relative change of the rate constant with pH follows the results found for the first-order exchange system given in the lower curve in Fig. 3. The constants used for the calculations include the values for the stability constant' of ZnY-2, the acid dissociation constant3 for ZnHY-, and the acid dissociation constants3 of EDTA corrected for temperature.* The equilibrium [Zn+2]and [Ni+21 tyere greater than 10 times that used for the firstorder runs and therefore were determined with greater precision. The curve in Fig. 4 can be resolved into the inaividual rate constants for Ni+' with HzY-2 and HY-3 in the same manner used by Taiiaka and Sakuma.9 Table I1 compares their data a t 0' and their treatment of the data of Cook and Long?at 25.0' with our data. The agreement is satisfactory, considering the accuracy of the various stability constants that must be used in the calculations. The curve in Fig. 4 has several points for reactions run in 0.10 M NaOAc using the observed equilibrium nickel and correcting for zinc acetate. The NiOAc+ ion appears to react at the same rate as the aquo Ni+2 ion. This is in disagreement with the results of Tanaka and (7) C . N. Reilley, J . Am. Chem. SOC., 78,5513 (1956). ( 8 ) M. J. L. Tillotsom and L. A. K. Staveley, J . Chsm. Soc., 3613 (1958). (9) N. Tanaka and Y. Sakuma, Bull. Cham. SOC.Japan, 82, 578 (1969).
COORDINATION KINETICSBY ION EXCHANGE
Nov., 1962
2217
Sakuma,g who find that the acetate species reacts somewhait faster. TABLEI1 SECOND-OElDER RATE CONST.4NTS FOR THE REACTION OF :Ni+2WITH EDTA, L. MOLE-^ MIN.-’ kNiH2-f
This work Tanaka ,and Sakunia
x
12.
1.1
:::
Temp.,
kNiHY
x 10-4
10”
0.06 1.82
P
OC.
0.10 .10
25.0 25.0
20
0.0
*
Discussion The dissociation study of metal complexes using ion exchange resin should prove to be a valuable approach. to the measurement of the dissociation rates of :EDTA. and other co8:rdination complexes where so frequently the equilibrium cannot be shifted b;y other means without catalyzing the rate. The first-order and zero-order ion-exchange formation rate studies of nickel-EDTA are shown to give accurate rate constants within the limitations set by particle diffusion. The first-order ion exchange method can readily measure rate constants ablout 100 times larger than can be measured by direct conventional mixing techniques. The ion-exchange method is limited to negatively charged complexes of moderate stability. The zero-order ion exchange method should be capable of extending this by another :factor of 10 to 100. The greatest source of error in the first-order system is obtainimg an accurate and reproducible measurement of the equilibrium metal. concentration. I n this case 10-20% error was encountered for the very low nickel concentrations. This was reduced to about 5% error in the zero-order system, which had a higher nickel concentration. The main source of error for the absolute values obtained in the latter system is the accuracy of the several stability constants which must be used in the calculations. Cumulative errors of 0.1 p K unit are possible, giving 25% error in the rate constant. The general applicability of the zero-order system is limited by the requirements of the second coordinatio’n system relative to the desired reaction rate. The diffusion interference should be reduced by operating a t lower temperatures. The activation energy for the diffusion of small ions through the resin is about the same as that through water.1° On the other hand, the activation energy for many coordination reactions is much higher. Thus, a t lower temperatures the coordination rate would be decreased relative to the diffusion rate. The elTect of the solution pH on the particle diffusion of nickel ion in the resin is seen in Fig. 1 and 2. ‘Table 111 summarizes this effect in terms of the per cent resin in the hydrogen form and the slight swelling of the resin which can be expected.11 The diseociation rate data in Table I and the formation rate data in Fig. 3 show no contribution of EDTA reaction within the resin, so this cannot account :For the particle diffusion p H dependence. (10) G . E. Boyd and B. A. Soldano, J . A m . Chem. Soc., 76, 6091 (1953). (11) 0. D. Bonner, J . Phys. Chem., 69, 719 (1955).
3.0
2.0
0
4.0
5.0
6” Fig. 3.-Agreement of first-order ion-exchange kinetic method with calculated rate constants for the formation of Ni(I1)-EDTA: 25.0’; p = 0.020. The calculated values are from the dissociation rate constants reported from radionickel exchange2 and the equilibrium constants.3
x 0,lOM NaOAc
4.5
4.0
3.5
5.0
PH.
Fig. 4.-Variation of rate constants with pH for the form;tion of Ni(I1)-EDTA using zero-order conditions: 25.0 ; y = 0.10.
TABLE I11 pH ON PARTICLE DIFFUStON Dowex 50W-X2, 0.02 M N a +
THEEFFECT
Y €1
% RH
OF
Swelling, % ’
Initial rate of mass transfera
4.5 0.1 ... 1.1 x 10-7 3.2 2.6 +0.5 1 . 8 X 10-7 2.5 13 +3 4 . 6 X 10-7 a With 10% or less deviation of codrdination rate constant.
Table I11 indicates that relatively small percentages of hydrogen ion in the resin can double and quadruple the diffusion rate of nickel ion even when there is only 2% nickel loading in the resin. This is given in terrns of the initia! rate of mass transfer which essentially normalizes the differences in coordination rate as the pH changes. The slight swelling of resin cannot account for these large changes. The mobility of hydrogen ion in solution is six times that of sodium ion and this factor may carry over to the resin phase. However, Helff erich’s calculationsI2 indicate that the rate of particle diffusion in a divalent-monovalent coupled diffusion a t low divalent metal ion loading is due largely to the divalent metal ion diffusion rate and is almost independent of the monovalent counterion diffusion. I n the present case the (12) M. S. Plasset, F. Helfferioh, and J. N. Franklin, J . Chem. Phys. 29, 1064 (1958).
J. GREYSON
2218
coupled diffusion constants for Nif2-Na+ and Nif2Hf will be essentially identical because of the low nickel concentration in the resin. Thus, there should be little difference between the rates of mass transfer for hydrogen or sodium forms, but a large effect is observed. Hydrolysis of nickel ion is not important in solution at these pH values and the resin phase has a much higher acidity than the solution phase, so this cannot be the cause of the diffusion effect. These data suggest that nickel ion transfer is not a simple diffusion controlled process but that the nickel at the sulfonic acid sites may be activated by hydrogen ion. It has been well established that the transfer of other cations in the sulfonate resin phase is diffusion contr01led.l~ However, nickel might be an exception because of its sluggish reaction. For (13) G . E. Boyd and B. A. Soldano, J . A m . Chem. SOC.,7 5 , 6107 (1953).
Vol. 66
example, nickel ion is slower to react with sulfate ion than many other metals, but this would mean that the hydrated ion must lose coordinated water at some resin sites.14 If this is the case similar effects might be found with other metal ions which have sluggish coordination reactions and this deserves further investigation. Coordination control in the elution of metal ions from resins can be an asset in the separation of metal ions in ion exchange processes, giving a kinetic separation factor in addition to an equilibrium factor. Acknowledgment.-The authors wish to thank the Air Force Office of Scientific Research and the Monsanto Chemical Co. for support of this research. (14) M. Eigen, in S. Kirschner, Ed., “Advances in the Chemistry of Coordination Compounds,” The Macmillan Co., New York, N. Y.. 1961, pp. 371-378.
TRANSFER FREE ESERGIES FOR SOME UNIVALENT CHLORIDES FROM HtO TO D2O FRO31 RlEASURENEI?;TS OF ION EXCHANGE PIIEMBRANE POTENTIALS BY J. GREYSOS~ International Buszness Machines Corporation, Thoinas J . Watson Research Center, Yo7 ktown Heights, New York Received M a y 18, 1989
I representing a cation exchange membrane and ill: representing the ions Li+, Na’, K+, Csf, SH4+, and (CH3)4Ni have been investigated. The e.m.f. values show a spontaneous transfer of salt from DzO to HzO. The measurements, combined with published enthalpy data and with additional measurements of systems of HzO-DzO mixtures, yield entropy values which are interpreted according to Frank’s “iceberg” theory.
Because of the property of permselectivity which ion exchange membranes possess they may be used as reversible electrode^^-^ in systems for which no other reversible electrodes can be prepared or in systems in which the reactivity of ordinary electrodes may interfere with the measurement. They are therefore suited to investigations of cells of the type
E
=
AET f
RT F
-
SA B
tidlnai i
where the leading term is the free energy of transfer of the salt from A to B and the integral, which extends over the composition range from A to B, expresses the contributions of the transport of ionic species and of solvents that are coupled to the flow of current through the cell.3 For the amalgain all these transport processes certainly are negligible. They also would be negligible in cell I with an ideal where / I is a cation exchange membrane, h1 is ion exchange membrane and may be assumed to any cation of interest and solvents A and B are any be negligible for cell I with a real membrane iu solvents of interest. Such membrane cells are certain limiting cases. Such a limiting case assumption can be made for similar to the amalgam cells cell I if 4 , is HzO and B is DzO because proton exAg’AgC1MCl (al)’HgMCl (al)lAgCl$g (11) change is rapid. The solvation sheath of the dif/olv. A (11/golv. B j 1 fusing species can exchange within the membrane making the coupled mass transport of solvent which have been studied by Akerlof and others to negligible, We therefore have undertaken to inobtain information about the process of transfer of vestigate the potentials of a series of membrane salt from solvent A to B. In both types of cells cells in which the half cells were, respectively, the potential is given by H2O and DzO solutions of the salts LiCl, KaCl, (1) Research Center, Stauffer Chemical Company, Richmond, KC1, CsC1, ITH4C1, and (CH8)&C1. It would be California. interesting to verify our assumptions or at least (2) Discusszons Faraday SOC.,No. 21 (195G). determine the extent of error due to them by (3) G . Scatchard, J. Am. Chem. Soe., 76, 2883 (1953). undertaking a similar series of measurements using (4) G . Akerlof, {bid., 62, 2353 (1930).
1
