NOTES
April, 1956 Similarly, since the partition equilibrium of HY is described by equation 8 Ks(H+)w(Y-)w = (HY)o
(8)
and since (H+)wis controlled by the HX, we may write Ki = K6(H+),. Solving for (H+)o (9)
and substituting in (5) gives
which is of the form
where A = K1,
dz))
At the point of inflection, in the absence of Y-
The numerator describes the partition of HMX4, the denominator of HX. Both are moderately weak acids, hence the ratio and consequently the aqueous metal ion concentration a t the point of inflection should not vary much with changes of the organic solvent. The experimental findings of Irvine, et al., have shown that this is, indeed, descriptive of the behavior of these metals.8 KS, K 4 and K; are independent of the metal present, and equation 10 contains only two parameters which depend on the metal species present. For a given solvent, the ratio B/C is a function of H X concentration only. The ratio KL/K4 = (H+)o(Y-)~/(Y-)wwhich appears both in equation 10 describing the effect of (Y-), on E at constant Z(M)w and in equation 11 describing the effect of (Y-), on Z(M), a t the point of inflection may become accessible from data not involving metal extractions.9 Under certain conditions (e.g., lower HX concentration) it may be also necessary to consider the equilibrium (MXa)w J _ (MXs)o
and K:Z(M)w
in addition to eq. 1. This seems to be true in the case of thallium, l o for instance. Activity coefficients of ions in the organic phase are factors in Kt, K t and K4; these may not reasonably be expected to remain constant as the ionic strength of the organic phase changes. (The major contribution to the ionic strength in the organic phase comes from the H + and MX4- ions themselves in the absence of extractable HY). This effect may be expected to complicate quantitative application of equation 10, but is independent of solvent extraction processes and can in principle be understood. The treatment above formally ascribes the variation in E to changes in the acidity in the organic phase. A thermodynamically similar development formally based on the equilibrium (MX4-)0
= K2, B =
Equation 10a shows that Eo/, rises to a "high value" a t low metal and Y-, conof (K1 K1/(KP centrations, and decreases when these increase. The point of inflection in the graph of E vs. log I;(M)woccurs a t
+
501
(MXJIO
(8) J. W. Irvine. Jr., personal communication.
(9) Experiments performed by Dr. R. H. Herber ahow that the equivalent conductivity of HClO, extracted into ethers from aqueous rolutiona is distinctly higher than that of HCI.
+
(MXS)~ (x-10
and formally stressing the effect of halide ions in the organic phase, leads to an equation identical with (10). However, other evidence3-, indicates that HMX, and MX4- are the significant species in the organic phase. Acknowledgment.-The author wishes to thank Professor J. W. Irvine, Jr., for his cooperation in making the unpublished results of his group available and for helpful discussions, and Dr. R. W. Dodson for his encouragement and advice. (IO) R. W. Dodson and R. D. Stoenner, private communication.
A NOTE ON THE OSMOTIC COEFFICIENTS OF AQUEOUS POTASSIUM CHLORIDE SOLUTIONS AT 25' BY R. A. ROBINSON DepaTt?"
of Chemistry, University of Malaya, Singapore Received October 10, 1066
Brown and Delaneyl have recently described an ingenious method for measuring the vapor pressure lowering of an aqueous potassium chloride solution : the solution is maintained a t 25' whilst the temperature of a sample of the solvent is progressively lowered until it registers the same vapor pressure, the equality of vapor pressure being judged by means of a sensitive interconnecting bellows pressure gage. Their experimental measurements were therefore temperature differences which were then converted into terms of vapor pressures by means of one of two relations between the temperature and the vapor pressure of pure water. Brown and Delaney expressed their results as osmotic coefficients, cp = -(55.5062/2m) In PIP", and gave a set of such coefficients over the range 0.025 to 2.38 M calculated by each method. Thus a t 2.3783 M they found cp = 0.9205 or 0.9204 but at 0.02515 M ,0.9588 or 0.9659. This may suggest that the form of the relation between the vapor pressure of water and the temperature has great influence on the result. Nevertheless, because of the way in which the osmotic coefficient is defined, the effect of experimental error is considerably exaggerated for dilute solutions. Since an experi(1) 0.L. I. Brown lcnd C. M. Delaney, THISJOURNAL, 68, 255 (1954).
,
NOTES
502
mental error in the measurement of the temperature difference is reflected in an almost directly proportional error in P/Po, it is better to compare PIPa rather than cp as calculated b y the two methods. I have therefore calculated P/Po from the cp values of Brown and Delaney and the results are given in Table I under the headings method I and method 11. From an examination of the deviations of individual runs from the averages given in their Table 11, it would seem that justice would be done to their work if we ascribed limits to their temperature measurements of i0.0002°. This would correspond to approximately f 0.00001 in PIPa whereas the average difference between Method I and Method I1 is 0.00004. Thus the method of calculation does introduce differences beyond the probable limits of experimental accuracy but not so very much greater. It seemed worth while trying a third method of calculation based upon the equation of Keyes2 for the vapor pressure of water
Vol. 60 PRESS URE-COMPOSITIONTEMPERATURE RELATIONS IN THE PALLADIUM-HYDROGEN SYSTEM BYKENNETH A. MOON
Contribution from Ordnance Materials Research Ofice, Watertown Araenal, Watertown, Maas. Received October 11, 1966
Passivity of palladium to hydrogen and hysteresis in the pressure-composition isotherms have been attributed by some' to the necessity of opening rifts in the metal in and along which dissolution of the hydrogen occurs. Others2-4 have believed that the palladium-hydrogen alloys are normal homogeneous solutions and passivity has been attributed6 to surface effects and hysteresises7 to sluggishness of recrystallization. I n view of the widespread current interest in metal-hydrogen systems and the continuing prevalence of the rift concept, it seems worthwhile to point out that the most reliable equilibrium pressure-compositionlog Po = -2892.3693/T - 2.892736 log T - 4.9369728 X temperature measurements in the palladiumhydrogen system are consistent with the belief 10-aT f 5.606905 X 10-6TTP- 4.645869 X 10-BTa + that the alloys are normal homogeneous solutions. 3.7874 X lO-'*T' $- 19.3011421 Figure 1 shows a projection of the pressurecomposition-temperature surface constructed from I n Table I the column headed method 111 gives data given in the literature.+" There is a critical the results calculated by this equation: i t will be point a t 295" and 20 atm., below which lies a uniseen that they are in good agreement with the in equilibrium, variant region where two phases are second method of Brown and Delaney. Under both with face-centered cubic arrangement of the earlier data (a) I give some values of PIPDintermetal atoms. Lacher2 has given a simple statistical poiated from the data of Gordon, et u Z . , ~ for concentrations below 0.1 M whilst those above 0.1 M mechanical interpretation of the equilibrium presare interpolated from a set of "best values" pre- sure-composition-temperature relationships, based viously advanced4 The final column contains on the assumptions t,hat hydrogen atoms can be values calculated from some more recent computa- accommodated in the lattice up to a limiting contions of Guggenheim and Turgeon.6 The maxi- centration of 0.59 atoms per palladium atom; mum difference in PIPois only 0.00006, the average that each pair of nearest neighbor hydrogen atoms is 0.00002, and it may be concluded that the contributes a fixed amount of interaction energy measurements of Brown and Delaney are in ex- regardless of the distribution of other hydrogen atoms; that the distribution of hydrogen atoms is cellent agreement with other data. random; and that the partition function of solute hydrogen atoms, relative to the lowest energy TABLE I dissolved state, is independent of concentration. P I P FOR POTASSIUM CHLORIDE SOLUTIONS AT 25' Rather good agreement between theory and experiment was obtained when the parameters in the Earlier data m Method I Method I1 Method I11 (a) (b) theory were evaluated a t the critical composi0.02515 0.99913 0.99912 0.99912 0.99914 0.99913 tion. .99847 .99848 .99847 .99847 .99849 .a445 The success of Lacher's treatment is strong ,99810 .99808 .99808 .99810 .99807 evidence against the rift concept, but this has been .05621 .99732 .99730 .99730 .99727 generally overlooked in the American literature. .OS020 .99598 ,99598 ,99600 ,1210 .99602 Lacher's approach can be supplemented with a ,99379 ,99376 .99384 .99379 ,1901 phenomenological treatment of the data for the .3180 ,98977 .98970 .99969 .99968 a alloys. The change of state is .4254 .M25 .7741 1.8631 2.3783
--
.98642 .98081 .97547 .94077 .92415
__
:98633 .98072 .97538 .94077 .92416
.98632 ,98070 ,97536 .94072 .92409
.98629 ,98070 ,97530 ,94078 ,92411
(2) F. F.Key,, J . Chem. Phys., 8 , 602 (1947). (3) W J. Hornibrook. C. J. Jan2 and A. R . Gordon, J . A m . Cham. Sot., 54. ti13 (1942). (4) R. A. Robinson, Trana. Roy. SOC.New Zealand, 76, 203 (1945): R. H. Stokee and B. J. Levien. J . Am. Chem. Soc.. 65, 333 (1946):
R. A. Robinson nnd R. H. Stokes, "Electrolyte Solutions," Butterwort& Scientific Publioations, London, 1955, P. 461.
(6) E. A. Guggenheim and J. C. Turgeon, Trana. Faradau SOC.,61, 747 (1965).
'/zHdg) f l l m Pd(e) = PdldUa,a),
(1)
(1) D. P. Smith, Phil. Mag., [7] 89, 477 (1948). (2) J. R. Lacher, Proc. Roy. SOC.(London). 1618, 525 (1937). (3) C. Wagner, 2.phyaik. Chem., 198, 407 (1944). (4) L. Pauliog and F. J. Ewing. J . Am. Chem. Soc., 70, 1680 (1948). (5) E. A. Gulbransen and K. F. Andrew, J , EEectrochem. Soc., 101, 348 ( 1954).
(6) E. A. Owen, Phil. Mag.,171 86, 50 (1944). (7) C. Wagner, 2. phyaik. Chem., 199, 386 (1944). (8) L. J. Gillespie and F. P. Hall, J . Am. Chem. Soc., 48, 1207 (1926). (9) L. J. Gillespie and L. 9. GaLtaun, ibid., 68, 2565 (1936). (10) A. Sieverts and G. Zapf, 2. phyeik. CAem., 174A,359 (1935). (11) P. 8. Perminov, A. A. Orlov and A. N. Frumkin, Doklady A k Nauk S.S.S.R.,84, 749 (1952); C. A.. 45, 107960 (1052).
d
