L. M. MUKHERJEE
974
equal. If the two quantities are greater by about 1% for DzO than for HzO then the heat of hydra’ tion of ferrous ion will be greater by about 6 kcal./ mole’’ in Dz0 than in HzO or by 1 kcal./mole for each water molecule if it is assumed that there are (17) W. M. Latimer, “Oxidation Potentials,” Prentice-Hall, Inc., New York, N. Y . , 1952, 2nd edition.
Vol. 60
six water molecules in the first hydration shell of ferrous ion. Thus the activation energy would be 1 kcal./mole greater in DzO than in HzO for the electron transfer mechanism. Unfortunately the observed increase of activation energy does not permit a choice to be KIade between the two POssible mechanisms.
THE STANDARD POTENTIAL OF THE SILVER-SILVER HALIDE ELECTRODES IS ETHANOL AND THE FREE ENERGY CHANGE IN THE TRANSFER OF HC1, HBr AND HI FROM ETHANOL TO WATER BY L. M. MUKHERJEE Department of Chemistry, University College of Science and Technology, Calcutta 9, India Received February 3,lQ66
I
According to the Born equation: A F = -a2/2r(l/Dz - l / D l ) the free energy change in the transfer of ions from one solvent to another should vary linearly with respect to the reciprocal of the radius of the ions. Previous observations with cells involving transfer of the chlorides of Li+, N a + and K f ions from methanol to water show that the free energy change decreases in the order KC1 > NaCl > LiCl contrary to the order expected from the radii of the ions, viz., Li+ < N a + < K+. It is suggested’ that the discrepancy may be due to some order/disorder changes associated with the process. The present communication is a report of the results derived regarding the free energy change in the transfer of electrolytes such as HCl, HBr and H I from ethanol to water, based on the difference in the corrected value of the standard potentials of the corresponding Ag/Ag halide electrodes in the two media. It is seen that the magnitudes of the free energy change are fairly linear with the reciprocal of the crystal radii of the anions and are in the order C1- > Br- > I-.
Introduction Direct measurement of e.m.f.’s of cells of the type M E M ; NIClnon-aq; AgCl/Ag
Ag/AgCl: MCl.,;
composed of 2 cells placed back to back gives, on extrapolation to cc dilution of both the solutions and reducing the difference in the “cratic” term t o zero by proper correction to equal mole-fraction, the free-energy change attending the transfer of ions of the electrolytes, from one medium to another. The theoretical estimate of this quantity, however, can be made from a knowledge of the extent of the shift in equilibrium constant for the cell process, viz. AgCl
+ hl
Ag
+ M + + C1-
with change in dielectric constant which is related by AInK =
- -2 z T
(& ‘6) A (b)
derived on the basis of the Born e q ~ a t i o nviz. ,~
the order KC1 > NaCl > LiC1, contrary to what is demanded by theory. A similar trend is also observed in the plot of AH against 1/D for these systems, where it is found that for a value of about 0.6 mole fraction of methanol the heat of solution of NaCl has the same value as in pure water; in other words, the heat of transferring the ion from water to the methanolwater mixture is zero. Thus, the simple electrostatic theory seems to be inadequate for explaining the observed facts and it is therefore suggested by Gurney‘ that probably the inequality of entropy of the ions transferred becomes so predominant that the final e.m.f. of the cells fails to correspond to the simple electrostatic rela tion. The present paper summarizes the results obtained with HC1, HBr and HI, a series in which the dimension of the anions increases in the order shown. I n these cases the more reliable hydrogen electrode can be used in combination with the corresponding Ag/Ag halide electrode as shown below Pt, Hz; HCl(Br or I)aq;Ag/AgCl(Br or I )
I
(Br or I) AgCl/Ag; HCl(Br or I)EPOH; H2,Pt
It appears that A In I< or AF will vary linearly with the reciprocal of the radius of the ions involved in the transfer. Thus, in the case of KC1, NaCl and LiC1, ie., a series of electrolytes with cations of varying radius, the expected relative magnitudes of the free energy change in transfer should decrease in order Li+, Na+, E(+. However, actual measurements with these electrolytes in methanol and methanol-water mixtures show that the relative magnitudes of the difference in free energy changes for the alkali chlorides are linear with l / D as expected, but that, the magnitudes of AF are in
Eo = EOH~O - E O E t o H , where Eo is’the e.m.f. of the whole cell a t 01 dilution of both the aqueous and ethanol solutions; EOH~O and EOE~OH represent the standard reduction potentials of the respective Ag/ Ag halide electrode relative to H-electrode as zero, in aqueous and ethanol solutions. Evaluation of Eo thus requires a knowledge of the standard potentials of the Ag/Ag halide electrodes in water and ethanol. Since sufficiently accurate data are available for the aqueous solutions, the main problem is to ascertain the standard po(1) R. w. Gurney, “Ionic Processes in Solution,” McGraw-Hill Book Co., New York, N. Y., 1953.
,
ti
tentials of the Ag/Ag halide electrodes in ethanol, for which the following cell was set up. Pt, Hz; HXEtOH; Ag/AgX (where x = Eobs = EO
-
2R T __ In F
cl, Br or I )
values of AFO for HC1 used in Fig. 2 have been derived from the difference in standard potential of Ag/AgCl electrode in water and ethanol as reported earlier.'
&EX
+ + a%Br
Experimental The ethanol used was of the same standard of purity and dryness, as characterized by ultraviolet spectrophotometry.2 The preparation of the Ag/AgCl electrode, together with details of its standardization in ethanol, has been discussed separately in a previous communication.S The hydrogen electrode assembly consisted of a freshly latinized Pt-foil in equilibrium with electrolytic Hz gas 1 atm.) purified through the usual train of purifiers, e.g., concd. HzS04,heated Cu gauze, lead acetate solution, concd. NaOH solution, concd. HzS04 and, lastly, ethanol. The Ag/AgBr electrode was of the thermal type, as was used by Keston4 in methanol. The Ag/AgI electrode was of the thermal electrolytic type, prepared by liberating iodine from aqueous K I solution in a separate anode compartment on a stout Pt helix fused a t the end of a Pyrex glass tube and previously coated with Ag by electrolysis of KAg( CN)2 and later, by decompositiy of a freshly prepared alkaliBefore and after experiment, free Ag20 paste at 450-500 the electrodes were checked in aqueous solutions of KBr and K I of known halide ion activity. Before use, the electrodes were washed thoroughly with ethanol. Dry gaseous HBr and H I were obtained by allowing pure, dry Hzand the halogens to react over heated pumice stone or platinum catalyst. Before absorption in ethanol the gases were led through a number of vessels containing red phosphorus and kept immersed in a freezing mixture, whereby the free halogen, if any, was completely removed. The stock solutions of HBr and H I in ethanol thus obtained were kept in a refrigerator in sealed black Jena glass containers to prevent possible decomposition of the acids and subsequent interaction with ethanol. The solution of HBr in ethanol was standardized by taking aliquot portions of the stock solution in an excess of aqueous K I solution and titrating the acid against standard KOH solution using phenolphthalein as indicator. The H I solution was taken in water to which a drop or two of very dilute Na2S203solution was added to discharge the color of the liberated iodine, if any, and then titrated against standard KOH as above. In view of the more or less unstable nature of the solutions, the preparation of the stock and the working solutions and the actual measurement of e.m.f. were completed within 24 hours. Compared to tho solution of HBr, the H I solution was very unstable and required caution and checking up. However, no appreciable change in concentration could be noted within 24 hours, before which time the entire measurements were completed. The concentration of the solutions has been calculated in terms of molarity. The e.m.f.'s were noted a t intervals of 30 minutes for about 3-4 hours a t 35 f 0.25' with the help of a Leeds & Northrup type-K potentiometer and a Hartmann-Braun galvanometer till the values were constant within =k0.0001 volt.
$;3
N
.
Results and Discussion The table below presents the e.m.f.'s observed for the above cells for different concentrations of HBr and HI solutions in ethanol and the extrapolated5s6values of the standard reduction potentials, Eo (relative to Hz electrode), of the Ag/AgBr and Ag/AgI electrodes, respectively. The values of the u0 parameter and other relevant quantities are also given in the table for reference. The AFO values indicate the amount of free energy change in the transfer of one mole of HBr or H I a t equal mole fraction from ethanol to water. The observed (2) L. M. Mukherjee, Science & Culture ( I n d z a ) , 19, 314 (1953). (3) L. M. Mukherjee, THISJOURNAL, 68, 1042 (1954). (4) A. S. ICeston, J. Am. Chem. Soc., 67, 1671 (1935). (5) H. 9. Harned, zbzd., 60, 336 (1938). (6) T. €1. Gronwall, V. K. LaMer and K. Sandved, Pkysak. Z . , 29, 358 (1928).
975
POTENTIAL OF SILVER-SILVER HALIDEELECTRODE IN ETHANOL
July, 1956
AgBr '/z Hz & Ag H + E ~ O H BrTEtoH =
Concn. of HBr, M
6 A. E m . f .obsd (V.hOF
TABLE I AgI '/& @ Ag H + E ~ O HI--EtOB
to
1 atm. Hz press.
+
+ + A.
+
aon1 = G
Concn.
Em.f
.obsd
(v.).m
of HI,
to
1 atm. Hz
M
press.
0.011033 0.18285 0.020597 -0.50140 ,21400 ,010301 - ,53565 ,005516 .004597 ,22245 ,005463 ,04425 .002207 ,25805 ,001906 ,09365 .001204 ,28595 ,001565 ,10135 .001103 ,29010 ,001184 ,11475 .000602 ,31950 .000900 ,12890 ,000216 .37085 .000440 ,16395 ,000110 ,40600 EOA,,A,I = -0.25305 v. in EOA,IA,B, = -0.08155 v. in molar scale, i e . , molar scale, ie., -0.24047 v. in -0.06895 v. in molal scale molal scale AFOE~OH+E~O = -0.5232 X AFOE~OFI-H~O = -0.2146 X loz3e.v. 102a e.v.
0.570
E! 0.270
1.0 0.8
+
0.6 0.4
0.2
0
0.2
0.4 0.6 0.8
-
Log. salt/acid. Fig. l,--,~, 0.0103 N &/EtOH titrated with 0.1040 N NaOEt/EtOH by quinhydrone electrode; O, 0.01104 N HBr/EtOH titrated with 0.08387 N NaOEt/EtOH by Helectrode.
The plots of E against log x/(l - x) (Fig. 1) where x = fraction of the acid neutralized do not exhibit linearity. This failure of the Henderson equation was considered as the basis for regarding HBr and H I as completely dissociated. Deyrup,8 from a study of the kinetics of acetal formation, also concluded that HCl, HBr and H I behave as strong acids in ethanol. The magnitudes of the free energy change (see Fig. 2) associated with the transfer of the ions of (7) L. M. Mukherjee, Naturwissensehajlen, 41, 228 (1954). (8)A. ,J. Deyriip, J. Am. Chem. ~ o c . ,66, GO (1934).
AI.
976 g-
1.2r
I
I
.‘-
0I 0.46
I
1
0.48
0.50
I
I
0.52
0.54
Vol. 60
SPlRO
0.56
(I/?) X 10-8, em.-’. Fig. 2.
HCI, HBr and HI are in the order HC1> HBr > HI which is also the increasing order of the dimensions of the halide ions. Moreover, the free energy changes when plotted against the reciprocal of the crystal radius of the corresponding ions, viz., C1-, Br- and I- ions, give a straight line. Although no
quantitative agreement was sought for, it is suggestive that these results are in conformity with the viewQthat in the field of a small ion in vacuo there is initially more energy to lose and consequently when the ion is plunged into a solvent, more energy is lost and the energy loss is greater the smaller the size of the ion. Acknowledgment.-My grateful thanks are due to Dr. S. K. Mukherjee, D.Sc., Department of Applied Chemistry, University College of Science & Technology, Calcutta, and to Dr. A. K. Ganguly, D.Sc., for their valuable suggestions and helpful criticism of the work. (9) M. Born, 2. Physik., 1, 45 (1920).
THE TRANSFERENCE NUMBERS OF IODIC ACID AND THE LIMITING MOBILITY OF THE IODATE ION IN AQUEOUS SOLUTION AT 25’ BY M. SPIRO‘ Department of Chemistry, University of Toronto, Toronlo 6, Ontario, Canada Received February 8 , 1066
The transference numbers of iodic acid in aqueous solution at 25’ have been determined for concentrations from 0.01 to 0.08 N by the direct moving boundary method. Both the hydrogen and the iodate ion constituent transference numbers were measured and their sum was unity to within a few units in the fourth decimal place. Above a certain low current range the iodate transference numbers increased with increasing current. The Longsworth function t i ’ varied linearly with concentration and an extrapolation gave a value of 40.54 for the limiting mobility of the iodate ion. A re-examination of recent conductance data on KIOs indicated that the conductances below 0.0015 N were not reliable but that the values above this concentration were in good agreement with the present work and led to a dissociation constant for KIOs of 1-76 mol. I.-’.
Within the last 30 years, the conductances of many strong and weak electrolytes, and the transference numbers of several strong electrolytes, have been measured in aqueous solution with a precision of a few hundredths of 1%. No accurate transference determinations have been made on any simple, incompletely dissociated electrolyte, despite the fact that such information would be helpful in interpreting moving boundary work with buffer as well as the transference data of salts in non-aqueous of solvents low dielectric constant. Moving boundary transference measurements were therefore done on iodic acid, the latter being chosen because it is monobasic, its dissociation constant is known (0.167 mole l.-1),3 and it is stable and easily purified. KIO, and H3P04 were suitable indicators for the determination of the hydrogen and the iodate ion constituent transference numbers, respectively, both giving stable, falling boundaries. Experimental The tube in the falling boundary cell had an internal diameter of 2.4 mm., and was calibrated with the KCI/LiCl system, taking tzCi = 0.49000 a t 0.04 N.416 The current, (1) Chemistry Department, University of Melbourne, Carlton, N.3, Viotoria. Australia. (2) E. B. Dismukes and R . A. Alberty. J. A m . Chem. Soc., 7 6 , 191 (19541,and earlier papers: I. Brattsten and H. Svensson, Acta Chem. Sound., 3,359 (1949),and earlier papers. (3) 0.Redlich, Chem. Reus., 39, 333 (1946); N. C. C. Li and Y i n g Tu Lo, J . A m . Chem. Soc., 6 8 , 397 (1941). (4) R. W.Allgood, D. J. Le Roy and A. R . Gordon, J. Cken. Phya., 8 , 418 (1940). (5) L. G. Longsworth, J . A m . Chem. Soc., 6 4 , 2741 (1932).
controlled by a semi-constant current device,e was measured in absolute amperes by means of calibrated resistances and a Rubicon precision potentiometer. Time readings were made to the nearest half-second with a metronome clicking a t 2 beats a second in conjunction with a Hamilton chronometer watch, which was checked periodically against the Dominion Observatory official time signal. The faraday was taken as 96500 absolute coulombs. The average reproducibility of the runs, in terms of the average deviation from the mean, was 1 in 6000 for the calibration runs, 1 in 5400 for the HI03/KIOs runs, and 1 in 2600 for the HIO3/ HsPO4 runs. The boundaries in the HIOs/H3POd system looked much “thicker” than those in the HIOa/KIOs system. Chemicals.-The “equilibrium” conductivity water used for all solutions and purifications had a specific conductance ohm-‘ cm.-land a pH of 6.0. For the solvent of 0.8 X corrections in the HI03 solutions, the contribution to the conductance due to the ionization of carbonic acid (0.40 X ohm-’ cm.-l) was subtracted and 0 . r ~X ohm-’ cm.-l added’ to take account of contamination in the cell. A strong, aqueous solution of Merck reagent iodic anhydride was filtered through a sintered glass frit, and the iodic acid twice recrystallized by slow evaporation in a vacuum desiccator. A stock solution was made up and analy?ed in an atmosphere of purified nitrogen by weight titration with NaOH solution, using either brom thymol blue or B.D.H. universal indicator. The NaOH solution was prepared by diluting a saturated solution of Merck reagent NaOH, and the carbonate remaining was decomposed by boiling the titrated solution twice just before the end-point. A reproducibility of 1 in 8000 was attained. The primary standard was constant boiling HC1.8 Mallinckrodt analytical reagent 85% orthophosphoric acid was twice recrystallized as HIPOIJ/~H~O.Seed crys( 6 ) D. J. Le Rog and A. R. Gordon, J. Chern. Phys., 6 , 398 (1938).
(7) D . R. Muir, J. R. Graham and A. R. Gordon, J . A m . Chem. Soc., 76,2157 (1944).
( 8 ) A. I. Vogel. “Quantitative Inorganic Analysis,” Longmans, Green end Co.,London, 1939,p. 279.
