COMMUNICATIONS T o THEEDITOR
June, 1958
THE VALIDITY OF ONSAGER’S
767
(O.25)-HzO,’ (h) NaCl (0.25)-KCl (0.5)-K,0,’ and (i) NaCl(0.5)-KCl (0.5) HzO.’
RECIPROCAL RELATIONS I N TERNARY DIFFUSION1
TABLE I
Sir : An outstanding case for which the Onsager reciprocal relations (ORR) have not yet been verified experimentally is in isothermal diffusion.2 Since there is no ORR in binary diffusion, ternary or more complex systems must be considered. Recently, diffusion coefficients of relatively good precision have become available for several ternary systems. 3,4,6~6,7 These coefficients are based on equations involving concentration gradients. The corresponding expressions for which the ORR should be valid involve chemical potential gradients-and consequently require a knowledge of activity coefficients in these ternary systems. Transformation of the thermodynamic expressions into concentration gradient forin, assuming no volume flow,8 leads to the following necessary and sufficient condition for the ORR t o be satisfied in ternary systems: aDlz
+ bD2z = CDLI+ dDs1 ad
- bc
(1)
= 0
where
LHSa
RHS3
3.73 3.50 1.55 1.53 0.40 3.12 2.24 2.25 1.76
3.80 3.71 1.16 1.53 0.31 3.24 2.26 2.30 1.80
Difference
0.07 .21 .39 0 .09 .12 .02 .05 .04
Est. exp. error
0.14 .17 .08 .18
.08 .09 .06
.06 .04
The estimated error here is attributed solely t o uncertainties in the D i j . Since there is unquestionably some error in the activity coefficient assignments, it is felt that this evidence supports the validity of the ORR in cases (a), (b), (d), (e), (f), (g), (h), and (i>.1° The details of the calculations and activity coefficient approximations as well as the derivation of equation (1) will be given in a paper about to be submitted for publication. UNIVERSITY OF CALIFORNIA RADIATION LABORATORY DONALD G. MILLER LIVERMORE, CALIFORNIA RECEIVED MARCH24. 1958
a = [l
(10) Cases (e) and (d) are apparently inconsistent. In (d), working backwards indicates that raffinose is salted out by KCl, with a reasonable salting o u t coefficient. I n (c), raffinose would appear to be salted in.
c2 VI + 3 1p = & -
c1 Vz
Y = Ca - 6v3
= [1+
-1
c2 v z c3 v3
Here c i are concentrations in m_oles per liter, ~i are chemical potentials per mole, Vi are partial molal volumes, and D i j are the reported diffusion coefficients based on concentration gradients. Since no experimental data are available, it was necessary to estimate the required activity coefficient~.~ In Table I are the results for the systems: (a) LiC1-KC1-H20,4 (b) LiC1-NaC1-H,0,4 (e) rslffinose-KC1 (0.5d4)-Hz0,6 (d) raffinose-KC1 (0.1M)-HzO,~ (e) raffinose-urea-Hz0,6 (f) NaCl (0.25)-KC1 (0.25)-H20,’ (g) NaCl (0.5)-KCl (1) This work was performed under the auspices of the U. S.Atomic Energy Commission. (2) Some verified cases have been discussed in D. G . Miller, Am. J . PILUS., 24, 433 (1956). (3) P. J. Dunlop and L. J. Gosting, J . Am. Chem. Soc., 77, 5238 (1955). (4) H. Fuiita and L. J. Gosting, ibid., 78, 1099 (19513). (5) P. J. Dunlop, THISJOURNAL, 61, 994 (1957). (6) P. J. Dunlop, ibid., 61, 1619 (1957). (7) I. J. O’Donnell and L. J. Gosting, “Enlarged Abstracts of Papers Including the Syniposiuin on the Structure of Electrolytic Solutions,” Electrochemical Society, May, 1957. (8) If the condition is one of no mass flow, substitute M I the niolecular weight for 71. (9) The activity coefficient derivatives were computed as follows: in (a), (b), ( f ) , (g), (h), and (i) from Harned’s rule with a 1 2 = ($1” 9z0)/2.3m (Harned and Owen, “Electrolytic Solutions,” 3rd Edition, 1958, Reinhold Publishing Co., eqn. 14-4-3); in (c), (d), and (e) by assuming Henry’s law for raffinose and t h a t D In yl/bml are the same as in binary solutions. I n (0) and (d), D In y ~ / D c zwas computed from a representative saltine o u t coefficient for ICCl solutions. I n (e), b In y d h z was taken as I / z ( D In y ~ / D m lf D In y z / D m z ) .
-
THE STABILITY CONSTANT OF T H E FERRIC GLYCINE COMPLEX
Sir: The recently reported1 value of 20 f 2 l./mole for the stability constant of the 1.1 ferric glycine complex differs considerably from the value of log K = 10.0 at 20” and p = 1 obtained in this laboratory from both spectrophotometric and oxidationreduction potential measurements.2 Values of log K ranging from 8.8 to 10.5 also have been found for a number of other simple a-amino acids.2 Such values are consistent with the published3 stability constants of amino acid complexes with ferrous, cupric and other transition metal ions. That ferric complexes with anions should be more stable than the corresponding ferrous complexes would be expected from considerations of entropy effects4 and of electronegativity differences; no exceptions appear to be known. . Glycine, like most a-amino acids, exists in aqueous solution almost entirely as the with pK1 = 2.31, p K z = 9.72, at 25°,5 for (1) C. R. Maxwell, D. C. Peterson and P. W. Watlington, THIS
JOURNAL, 62, 92 (1958). ( 2 ) D. D. Perrin, J . Chem. Soc., in press.
(3) A. Albert, Biochem. J . , 47, 531 (1950); 60, 690 (1952); 64, 646 (1953). (4) R. 6. P. Williams, in “Special Lectures in Biochemistry, 19541955,” University College, London, p. 43. (5) J. T. Edsall and M. H. Blanchard, J . A m . Chem. Soc., 56, 2337 (1933).
COMMUNICATIONS T o THEEDITOR
768
Vol. 62
e+NH&HzCOO- + H +
Correction for hydrolysis using equation (11) leads to values for this reaction of log K = 1.3 to 1.7 and over the pH range 1.51 t o 2.95. The earlier esti+NHsCHzCOONH2CHzCOOH+ mate,’ from kinetic measurements, of 10 l./mole respectively. Under the experimental conditions (taking total ferric and glycine concentrations) ([HG]o>>[li’e+++]o, where [HG]o is the total initial would become log K = 3.0 a t pH 3.5. This value glycine concentration), the concentration of gly- may be a little low because of competitive complex formation with sulfate ion. cine anion at any pH is given by On the other hand, if the equilibrium conIG-l(1 [H+l/h [H+]’/kikz) = [HGlo (1) stants are expressed in terms of ferric ion and To correct for hydrolysis the relative proportion, glycine anion concentrations, using equations (I) 2, of the ion Fe+++ in the mixture, Fe+++, Feand (11))Maxwell and Peterson’s result’ gives log OH++, Fe(OH)z+ and Fe2(0H)2++++, must be K = 9.1, while the figures of Maxwell, et known. From the published data,B an estimate a t lead to values of log K which increase from 8.5 to 22°C and = 0 would be 9.6 in passing from pH 2.95 t o pH 1.51. These estimates, although subject t o rather large un1 x = certainty, agree more closely than do the calcu1 5 X 10-a/[H+l 7 X 10-B/[H+12 2 X 10-a[Fe+++]l[H+12 lations postulating reaction with the zwitterion. They are also comparable with the figure of log (11) Both Maxwell, et ~ l . and , ~ the present writer Ii: = 10.0, obtained under somewhat different express the constant for the ferric glycine complex experimental conditions from an extensive series in the same way, that is, for equilibrium with of measurements.2 These measurements, made ferric ion and glycine anion. However, Maxwell, over the pH range 1.0 to 4.1, indicate strongly that et al., incorrectly identify the value pK1 = 2.31, the glycine anion, and not the zwitterion, is the with the reaction NHZCH2COOH NH2CH2- complex forming species. OF MEDICAL RESEARCH COOH+, so that their results are actually in JOHNCURTINSCHOOL NATIONAL UNIVERSITY terms of ion pair or complex formation between AUSTRALIAN CANBERRA, A.C.T. D. D. PERRIN ferric ion and the zwitterion form of glycine. AUSTRALIA +NHaCHzCOOH
+
+
+
+
+
+
+
(6) A. R. Olson and T. R. Simonson, J. Chem. Phys., 17, 1322 (1949); T. H. Siddall and W. C. Vosburgh, J . Am. Chew. Soc., 18, 4270 (1951); R. M. Milburn, J . A m . Chsm. Soc., 79, 537 (1957); B. 0.A. Hedstrom, Arloiu Kemi, 5, 457; 6, 1 (1953).
RECEIVED MARCH26, 1958 (7) C. R. Maxwell and D. C. Peterson, J . Am. Chem. SOC.,79, 5110 (1957).
rI
ll
