JAXESN. BUTLER
1828
In the bonds to carbon.36 Again the large isotope effect may be due to the ability of the products to hydrogen bond to solvent more effectively than can the aquo acid. Considering the unusual isotope effects observed here, an application of the equilibrium isotope effect to the elucidation of reaction schemes would appear to require additional information on the effects with simple aquo acids. The five-parameter fit which leads to a negligible isotope effect for the dimerization of the conjugate base would seem to be more reasonable than the four-parameter fit which leads to a value log ( K B / K D )= -0.32. Finally a careful examination of the fit obtained for the [(CzHs)aSn]' data with a single equilibrium constant is informative. This can be done best by considering the least-squares residuals, and these are plotted vs. the pH or p D in Fig. 3. For the measurements in HzO, the residuals obtained for a given series of measurements are rather constant; therefore, the
errors are randomized effectively by the replication, of the experiments. I n the case of the measurements in DzO, the residuals tend to be more positive a t low and at high n values than they are in the intermediate a range. The effect is small, although it tends to indicate a slightly capricious behavior for the glass electrode in the p D range 5 to 9. Serious variations in the behavior of the glass electrode from the theoretical would seem to be ruled out, for these would lead to large deviations from the theoretical curve. Bell and Kuhn4 have recently noted that there are often significant differences in the dissociation constants of weak acids in DzO determined by spectrophotometric methods and by potentiometric methods with a glass electrode, and these differences are larger than one would expect to result from the variations in the electrode behavior observed here.
Acknowledgment. The authors wish to express their appreciation to Miss Ieva Ogrins, who synthesized the triethyltin bydroxide used in these experiments.
Activity Coefficients of Liquid Indium-Mercury Amalgams at 25
by James N. Butler Tyco Laboratories, Inc., Waltham 64,Massachusetts
(Received January 97,1964)
Activity coefficients for indium and mercury in their liquid amalgams a t 25 O have been calculated from measurements of e.m.f. in a cell without liquid junctions. Within experimental error, the results are described by the empirical equation log yrn = 1.54(1 - X H ~ ~ ) , where yrn is the activity coefficient of indium referred to infinite dilution, and X x g is the mole fraction of mercury. The activity of pure solid indium is 21.6 on the same scale. The excess entropy of the mixtures is nearly zero. The standard potential of the In+3-In couple is -0.337 v. at 25'. The results are compared with those obtained by other workers and with the predictions of the theory of regular solutions.
Introduction Although indium amalgams have been used in a number of electrochemical investigations, no accurate measurements of the activity coefficients in these liquid solutions are readily available. During the course of The Journal of Physical Chemietry
investigations a t this laboratory on electrocatalysis by indium amalgams, we had occasion to measure these activity coefficients. The results are summarized in this Paper. Richards and Wilson1 briefly investigated the rela-
Ac-rrvIw C~EFFICIESTS OF LIQVID INDIUM-NERCURY AMALGAMS
tivc potcntials of a series of very dilute indium amalgams i n thc course of verifying the applicability of the Sernst relation to amalgams. The large deviations obsrrvcd wcrc explained by Hildebrand2 as resulting from the formation of a compound such as InI-Ig4 in tho liquid mixture. Sund&i3measurcd the potentials of a series of indium amalgams in contact with indium perchlorate solutions using a ccll of the type
I
I
Hg Hg2CI2(s),0.1 m NaCl/IIn(C104)3In(Hg)
a t a temperature of 20’. Although activity coefficients can be obtained from such measurements, Sundkn did riot calculate them, but rather tabulated formal potcritials for indium amalgam electrodes of various concctitrations. Th(> use of sodium chloride in the calomel clcctrode instead of potassium chloride introduces an uncertainty of about 1 mv. in the liquid junction potential, so that it was thought best to repeat the measurements at 25’ using a cell without liquid junctions. Aftcr this work was complete, the author became aware of a parallel study by whose results agree qualitatively with ours, but whose treatment of the data and conclusions are different.
Experimental Potentiometric measurements were made using a Leeds and Northrup Model K potentiometer and the following cell5 In(Hg) 10.01 m ITC104, 0.01 m In2(S04)3 I Pt, H2(g) in an air thermostat maintained a t 25.0’. The amalgams were prepared from triple-distilled mercury (Doe & Ingalls) and 99.999% pure indium (American Smelting and Refining Co.) by weighing out the required quantities of mercury and indium and combining thcm under an atmosphere of nitrogen. Surface oxidation was not a problem in the more concentrated amalgams, but amalgams of concentration less than 10 mole yo In rapidly formed a gray film of indium oxide when exposed to air. The electrolyte was prepared from triple-distilled conductivity water, reagent grade perchloric acid (Raker), and indium sulfate (K and K Laboratories). Hydrogen was bubbled through the solution for several hours prior to the measurements to remove any dissolved air. I’re-electrolysis was not used because of thc possibility of setting up concentration gradients in the cell. The amalgam was introduced, under an atmosphere of nitrogen, through a capillary tube which extended to the bottom of thc ccll. Contact was made by means
1829
of a platinum wire, which was kept covered with amalgam during measurements. The pool of amalgam was approximately 10 in area. Several successive pools of the same amalgam were measured to minimize any “memory effect” due to the residue on the platinum lead. For amalgams containing from 1 to 30% indium, the potential could be reproduced to within 0.01 mv. under the best conditions. For more dilute and more concentrated amalgams, the errors were larger; but in all cases they were smaller than 0.1 mv. Measurement of the potential of a calomel electrode us. the hydrogen electrode gave a pH of 2.008 for the solution, a region where the formal potential of the In+3-In couple is independent of pH. 3,6 This, coupled with the buffering action of the sulfate ion, minimized any effects due to slight changes in pH during the course of measurements.
Results The measurements of cell potential under reversible conditions are listed in Table I as “cell e.m.f.” These values depend on the concentration of indium in the amalgam and the concentrations of indium ion and hydrogen ion in the electrolyte according to the Nernst relation
+
RT RT - In [In+31~+3 - In XInr 3F. 3F
(1)
where a H + is the mean activity of hydrogen ion in the electrolyte, E ’ I n + , , I n is the standard reduction potential of In+3to In, [In+3]is the molal concentration of indium ion in the electrolyte, y+3 is the mean activity coefficient of Inz(S04)3, XI, is the mole fraction of indium in the amalgam, and y is the activity coefficient of indium in the amalgam, with the reference state chosen so that y approaches unity for dilute amalgams (Henry’s law). So long as the composition of the electrolyte is constant, the first three terms of eq. 1 are constant, and (1) T. W. Richards and J. H . Wilson, 2. Physik. Chem., 72, 129 (1910); see also, Publication 118, Carnegie Institute of Washington, 1909, p. 25.
( 2 ) J. H . Hildebrand, J . A m . Chem. Soc., 35, 501 (1913). (3) N. SundBn, 2. Elektrochem., 57, 100 (1953). ( 4 ) L. F. Kozin, Tr.Inst. Khim. Nauk, Akad. A‘auk Kaz. S S R , 9, 71, 81 (1962); Chem. Abstr., 59, 6092h, 6093c (1963). ( 5 ) The IUPAC (Stockholm) convention for cell potentials is used throughout this paper. ( 6 ) W. Kangro and F . Weingkrtner, 2 . Elektrochem., 58, 505 (1954).
Volume 68, N u d e r 7
J u l y , lo64
JAMES N. BUTLER
1830
Table I : E.m.f. Measurements and Calculated Activity Coefficients, 25.0" Mole % ' indium
Cell e.m.f., mv.
100.0~ 70. Ob
266.7 266.8 264.30 263.03 258.95 258.31 251.80 245.50 245,35 237,06 234.70 226.46 223.31 217.90 214.40 201.44 200.68 179,O
64.41 63.60 52.22 50.00 39.98 30.40 30.00' 20.00" 16.26 10.ooc 8.41 5.00' 3.88 1.00" 0.920 0.0940 0
Activity baaed on Henry's law, mole fraction
Activity, coefficient
21.6 21.8 16.37 14.07 8.73 8.10 3.78 1,812 1.780 0.678 0.514 0.196 0.1358 0.0723 0.0480 0.01057 0.00968 0.000946 0
31.2 25.4 22.1 16.7 16.2 9.46 5.96 5.94 3.38 3.16 1.96 1.612 1.447 1.238 1.059 1,051 1.006 1,000
,...
..
a Pure solid indium. Saturated amalgam with excess solid indium present. Most precise measurements, f 0 . 0 1 mv.
the electrolyte for the three sets of measurements contained the same concentration of In*3 ion, it is possible to interpolate and extrapolate the measurements in the three sets and to place them all on a common scale of potential with an arbitrary zero. From these values of e.m.f., the activity coefficients were calculated. In the range where our measurements overlap, the results of Richards and Wilson are 20-50% larger than ours. An appreciable temperature dependence was observed only for the highest concentration amalgam (3.26 mole yo In). For this concentration, the activity coefficient is 1.42 a t 0" and 1.37 at 30'. Our measurements at 25' give an interpolated activity coefficient of 1.26 for a concentration of 3.26 mole % In. Sund6n3 measured a much more concentrated series of amalgams a t 20°, using the cell with liquid junction described in the Introduction. The activity coefficients calculated from Sund6n's measurements agree with ours within his experimental error. A further comparison of his results with ours will be made in the Discussion section. Kozin4 measured the e.m.f. of the cell used by Sund6n (part I), and also of the concentration cell
1
1
In(s) In(C10& In(Hg) their sum may be represented by E'. lated the function
E -
RT 3F
- In
XI,
=
E'
We then calcu-
+ RT In y 3F -
(2)
and plotted it as a function of the concentration of indium in the amalgam. Extrapolation to zero concentration gave a value of 240.4 mv. for E'. Then the activity of indium in the amalgam was calculated using the measured values of E and the extrapolated value of E'
E')}
(3)
These values for the activity and the corresponding values for the activity coefficient are listed in Table I. For comparison, we also calculated activity coefficients from other data in the literature. Richards and Wilson,' using a four-compartment cell, measured the potential differences between four amalgams of different concentration in contact with an electrolyte containing In+3ion. Three separate sets of amalgams, ranging in concentration from 0.01 to 3.26 mole % In, were measured a t 0 and 30'. Unfortunately, neither the values of the potentials with respect to a reference electrode nor the exact concentration of indium in the electroIyte were given. However, if one assumes that T h e Journal of Physical Chemistry
(part 11) a t temperatures from -1.5 to 80'. Kozin calculated activity coefficients only from the data in part 11, using the pure solid as standard state, which makes comparison difficult, Consequently, we calculated activity coefficients directly from his tabulated e.m.f. data given in both part I and part 11. Kozin's data a t 20" agreed with ours, although the accuracy of his data, as reflected by the agreement of results from parts I and 11, was considerably less than was implied in his discussion. The phase diagram for the indium-mercury system has been determined by a number of The composition of a saturated liquid amalgam is 69.2 mole % indium a t 20°, and 70.0 mole % indium a t 25°.7b~9311v1aAmalgams prepared with an indium content larger than this saturation value showed a constant activity of 21.6 + 0.8 in both our measurements (7) (a) H. Ito, E. Ogawa, and T. Yanagase, ,Vippon Kinzoku Gakkaishi, 15B, 382 (1951); (b) W. M. Spicer and C. J. Banick, J . Am. Chem. SOC.,75, 2268 (1953). (8) C. Tyrack and G. V. Raynor, Trans. Faradag Soc., 50,657 (1954). (9) L. F. Koain and N. N. Tananaeva, Z h . Neorgan. Khim., 6 , 909 (1961); Russ. J . Inorg. Chem.,6, 463 (1961). (10) G. L. Eggert, Trans. Am. SOC.Metals, 55, 891 (1962). (11) G. Jangg, 2. Metallk., 53, 612 (1962). (12) R. V. Chiarenrelli and 0. L. I. Brown, J . Chem. Eng. Data, 7 , 477 (1962). (13) B. R. Coles, M. F. Merriam, and Z. Fisk, J. Less-Common Metals, 5, 41 (1963).
ACTIVITY COEFFICIER’TS OF LIQVIDINDIUM-MERCURY .AMALGAMS
and Sund6n’s.a Kozin’s measurements4 a t 20’ gave a value of 19.3 from part I and a value of 17.1 from part 11, which are somewhat lower, although not outside the possible experimental error. In our measurement,s, Sund6n’s measurements, a and Kozin’s measurernents,4 the e.m.f. of a saturated amalgam was within 0.1 mv. of the e.ni.f. for pure indium. This does not, however, iniply that indium and mercury form no solid solutions. In fact, the solid phase in equilibrium with the liquid a t 25’ contains about 15% mercury.gt13 A1thoug;h phase equilibrium may have been slow to be established and the solid phase in all three studies may have been pure indium, it i s more probable that the activity of indium in the solid solution is nearly identical with that of pure indium. From eq. 1, it is possible to calculate the standard potential of the In+3-In couple. However, it is conventional to assign unit activity (instead of 21.6) to pure solid indium. The measured value of pH was 2.008. The known concentration of In+a is 0.0200 mole/kg. The mean activity coefficient of indium sulfate a t an ionic strength of 0.160 m, interpolated from the results of Covington, Hakeem, and WynneJones,I4 is 0.163. Assuming that the activity of pure indium is 1.000, eq. 1 gives a value of -336.9 mv. for the standard potentiall. This agrees within experimental error with the measurements of previous workers.a,6,14-17The best value is -339 2 mv. a t Referring the activity of indium to infinite dilution in mercury (Henry’s law) the activity of pure indium at 25’ is 21.6 and the standard potential is -313 rt 4 mv .
*
Discussion The activity coefficients of binary nonelectrolyte mixtures can often be represented a,pproximately by the empirical equations due to Margule~1*~~9 log 71’ = -BXz2 log
”/’ =
(4)
-BX12
where the primed activity coefficients are referred to the pure liquid, and the negative signs are introduced because we are dealing with negative deviations from Raoult’s law. These equations are the simplest power series formulations for the activity coefficients which satisfy the Gibbs-Duhem relation over the entire range of composition. Regular solutions, l 9 for which the entropy of mixing is ideal, obey eq. 4 with B independent of composition and inversely proportional to the absolute temperature. Since we have referred the activity coefficient of indium to infinite dilution (instead of to pure super-
1831
cooled liquid indium), we must use the following modification of eq. 4 log
YIn
B(1 -
(5)
x~g’)
In Fig. 1, we have plotted, as a function of the mole fraction of indium, the coefficient B calculated from our data. Equation 5 is an adequate fit. By averaging our best points, a value of 1.54 0.05 was obtained for B.
*
0 THISWORK
+
~:~~ 1.1 o t
0.1
SUND~N
A KOZIN (PART I) KOZIN (PART
0.2
0.3
a4
0.5
0,s
0,7
n)
0.8
0.9
1.0
XIn
Figure 1. Fit of experimental activity coefficient data to the empirical equation log yrU = B( 1 - X a e 2 ) . The best value of B obtained from our data (circles) is 1.54, from SundBn’s data3 (crosses) is 1.46, from Kozin’s data4 (part I, triangles) is 1.64 and (part 11, squares) 1.53. The value of B calculated from the heat of fusion of indium and the activity coefficient of pure solid indium is 1.50.
An approximate value of the constant B can also be derived from our measured activity for pure solid indium, and the heat of fusion of indium, which has been measured to be 3.26 kjoules/mole.20 From this value, using the fact that the free energy of the liquid and solid are the same a t the melting point, 156.4’, the activity of supercooled liquid indium at 298’K. can be calculated. The heat capacities of the solid (24.35
+
(14) A. K. Covington, M. A. Hakeem, and W. F. K. Wynne-Jones, J . Chem. SOC.,4394 (1963). (15) S. Hakamori, J . Am. Chem. Soc., 52, 2372 (1930). (16) E. M. Hattox and T. deVries, ibid., 58, 2126 (1936). (17) M. H. Lietzke and R. W. Stoughton, ibid., 78,4520 (1956). (18) M. Margules, Stizber. A k a d . Wiss. Wien, 104, 1243 (1895). (19) J. H. Hildebrand and R. L. Scott, “The Solubility of Nonelectrolytes,” 3rd Ed., Reinhold Publishing Gorp., New York, N. Y . , 1950. (20) 0. Kubaschewski, 2. Elektrochem., 54, 275 (1950).
Volume 68, Number 7
J u l g , 1966
JAMES N. BUTLER
1832
10.5 X lO+T joule/deg.) and the liquid (31.4 joules/ deg.)zl were used to obtain the variation of the heat of fusion with temperature. Upon integrating the GibbsHelmholtz equation, the free energy change on fusion was obtained as a function of temperature AGr
=
1.201 X lo3
+ 37.771T + 0.00525T2 16.24T log T joules
(6)
The activity of pure supercooled liquid indium a t 25’ is given in terms of the activity of the pure solid by
(7)
In (al/a,) = A G f / R T
Since we have shown that the activity of pure solid indium is 21.6, referred to infinite dilution, we find on evaluating eq. 6 and 7 a t 298’K. that the activity of pure supercooled liquid indium is 31.4. Since XI, = 1, this is also the activity coefficient, and we find from eq. 5 that B = 1.50. This result is independent of all the activity coefficient measurements except that for pure solid indium, and yet it agrees very closely with the average value of 1.54 for B, obtained from the other activity coefficient measurements. Such consistency argues strongly for the validity of eq. 5 in describing the data. In Fig. 1, we have also plotted the values of B calculated from the data of other workers. The values of B calculated from the data of Richards and Wilson’ vary between 0.9 and 6.7, with no apparent trend, and were not included in Fig. 1. Although the scatter is larger, SundBn’s data3agree with ours over most of the concentration range. The measurements of Kozin4 a t 20°, from both parts I and 11, are also plotted of Fig. 1. Although his values of B are generally higher, they agree with ours, within the experimental error. It is interesting to note that Kozin bases a large part of his discussion on discontinuities which he observes in the slope of the e.m.f.-concentration curve. These breaks show up as sharp minima on the plot of Fig. 1. In every case, however, the extreme variation between minima and maxima is within the experimental error estimated by comparison of data from part I and part 11. Thus, the conclusions which Kozin draws from these breaks in the e.m.f. curves are probably unjustified. The excess molal free energy of a binary mixture1g (over the ideal free energy of a mixture of two liquid components) is given by AGE
=
RT(X1n In 7’1,
+ X H In~
where both the activity coefficients are referred to the pure liquid (Raoult’s law). From eq. 4, we have
The Journal of Physical Chemistru
AGE = -8.76X1,XHg
(8)
kjoules
(9)
Calorimetric measurements of the molal heat of mixing of indium and mercury have been made by Kleppa and Kaplan,22~23 whose data can be described by the empirical relation
AH^
=
-9.15xInxHg
kjoules
(10)
This gives us directly a value for the excess molal entropy of the mixture
ALP= -1.3xInxHg
joules/deg.
(11)
which is very close to the zero excess entropy predicted by the theory of regular solutions. Kozin4 gives data over the temperature range from -1.5 to 80’, which can be compared with thermodynamic predictions. From each of the fourteen sets of Kozin’s data, an average value of B was calculated, and’ these are plotted as a function of temperature in Fig. 2 , along with the average values from our data and from SundBn’s data. On the same figure is plotted a curve showing the theoretical temperature dependence of B , assuming that AH”: is given by eq. 10 independent of the temperature and that ASE = 0 log
YIn =
(480/T)(l - X,gz)
(12)
where T is the absolute temperature. Although our data and SundBn’s data fall below the curve, most of Kozin’s data falls above the curve. The results of all the studies indicate that the excess entropy is within ~1 joule/deg. of zero. Kleppa and Kaplan,22using SundBn’s3data, also concluded that the excess entropy of indium-mercury solutions was zero within =t1 joule/ deg. Thus, within the uncertainty of these measurements, the theory of regular solutions seems to describe adequately the behavior of the indium-mercury system. The dependence of the activity coefficient of indium (referred to infinite dilution) on composition and temperature is adequately represented by eq. 12, plotted in Fig. 2, which was obtained assuming zero excess entropy. Similarly, the activity coefficients referred to pure supercooled liquid (Raoult’s law) are given by log 7’1, log
Y’H~)
AGE = - ~ . ~ O ~ B R T X I , X H ~
Using our average value of B, 1.54, we obtain a t 25’
=
Y ’ H ~=
-( 4 8 0 / T ) X ~ ~ ~
(13)
-(480/T)X1n2
(14)
(21) H. Moser, Physik. Z.,37, 737 (1936). (22) 0. J. Kleppa and M . Kaplan, J . Phys. Chem., 61, 1120 (1967). (23) 0. J. Kleppa, Acta Met., 8, 435 (1960).
ACTIVITYCOEFFICIENTS OF LIQLIDINDIUM-MERCURY AMALGAMS
0 THIS WORK
+
SUND~N
A K O Z l N (PART I ) 0 KOZlN (PARTE)
2.0 19
-10
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
TEMPERATURE ‘C
Figure 2. Temperature dependence of the coefficient 13. The curve (eq. 12) was cdculated from the known heat of mixing of indium and rncrcury, w i t h the assumpt,ion that the excess entropy of the solution w a zero. ~
In both the dependence of the activity coefficient on composition, and in the ideal entropy of mixing, rnercury-indium mixtures behave approximately like regular solutions. In one respect, however, they are not completely regular. A large negative volume change (1 ~ m . ~ / m o l eis) observed on mixing mercury and indium,22 and its magnitude suggests that a negative excess entropy of approximately 5 joules/deg. should be observed. I t is possible that the conipensating positive entropy arises from repulsive interactions betweeri partially shielded I n + ions in thca metal. The large activity coefficients (indicating large ncgative deviations from Raoult’s law), as well as the large negative heat of mixing, indicate that indium-mercury interactions are much stronger than niercurymercury or indium-indium interactions. Whether or not an actual compound species such as InHg exists in the liqnid phase cannot be unambiguously decided from thermodynamic measurements alone, l9 but such a compound certainly exists in the solid phase. Phase diagram s t i i d i e ~ ~show - ~ ~ that in the cornposition range where liquid amalgams can be obtained a t room
1833
temperature, two compounds, InHg and InHg6, are probably formed9~12~13; but only InHg, melting a t - 18.5’, is agreed upon by all investigators. The solid solution of InHg is only about 2 mole o/o, which indicates the possibility of ,specific bond forniation between In and Hg in the liquid. Kozin4 observed discontinuities in the slope of his e.ni.f.-concentration curves a t compositions corresponding to InHg, and InHg, which he int,erpreted as evidence for the forination of stoichiometric compounds in the liquid phase. Such discontinuities are possible, and when observed have been interpreted as indicating strong ordering in the liquid phase. 2 4 , 2 6 However, only Kozin’s data of part I shows the breaks prominently. His data of part 11 shows them to a much smaller extent, and a t compositions considerably different from InHg, and InHg. Seither our data nor SundEn’s data show any such breaks. Since we have already pointed out that the variations which are interpreted as breaks in the slope of the e.m.f.-concentration curve are probably within experimental errors, they cannot be considered adequate evidence for the formation of compounds in the liquid phase. The consistent description of the thermodynamic properties of these solutions by the theory of regular solutions argues against the formation of any specific compound othcr than InHg. According to statistical mechanical theory, 26 zero excess entropy is obtained with a single potential of interaction with nearest nt4ghbors of a given kind, and compound formation as such need not be postulated.
Acknowledgments. The author gratefully acknowledges the very competent assistance of Miss lfary A. Loud in perforniing the experiniental work, and thanks Dr. A. C. JIakridcs and Dr. A. *J. Rosenberg for many helpful and stimulating discussions. This work was supported by thc Office of Kava1 Research, 3Iaterials Sciences Divishn, Contract No. SOnr-376,5(00), ARPA order No. 302-62. (24) hl. B. Rever and C. F. Floe, T r a m . A . I . M . E . , 156, 149 (1944). (25) H. Liang, AI, B. Bever, and C. F. I’loe. ibid., 167, 895 (1946). (26) R. 11. Fowler and E. A. Guggenheim, “Statistical Thermodynamics,” Cambridge Lniversity Press, London, 1960, pp. 316-366.
Volumc 68,Sumber 7
J u l y , 1964
