On Ion-Specific Membranes as Electrodes in the Determination of Activity of Calcium An Exchange of Comments SIR: I wish to call your attention to a fundamental error in the paper by Shatkay entitled Ion Specific Membranes as Electrodes in the Determination of Activity of Calcium ( I ) . The author has assumed in virtually all of his figures and discussion involving calcium chloride solutions that the activity of calcium (the single ion activity) is directly proportional to the mean ionic activity of calcium chloride. There is ample data in the literature to show that this ratio for a mixed uni-divalent salt is, in fact, far from constant (26). Consider, for example, the data in the recent paper by Kohn and Furda. Using their data (5,p. 1931), I have calculated the ratio of the mean ionic activity coefficient for CaCl, to the average value of the single ion activity coefficient for Ca2+ in calcium chloride solutions. Even within the limited range of 0.01-0.15 molal, the ratio is far from constant. Garrels (6) has calculated the single ion activity coefficient for C a Z +in CaClz both from the mean activity coefficients of CaC12and KCl, and from the mean activity coefficients of CaBrZ,KBr, and KCl. With his data, it would appear that the ratio of mean ionic acitivity coefficient to single ion activity coefficient at 1M is about 1.7; at infinite dilution it must be 1.0. Thus, between 10-5Mand 1Mtheratio changes by about 7 0 z . Yet Shatkay has assumed that the calcium single ion activity and the mean ionic activity are directly proportional over the entire range from 10-5M to 1 M (see Figures 2 and 6, Ref. 1). The large difference between the calcium single ion activity and calcium chloride mean ionic activity makes the “theoretical’’ curves of Figures 9-1 1 virtually meaningless at high ionic strengths. Even below 10-’M, if Shatkay’s data are recalculated using extended Debye-Hiickel values for the single ion activity coefficients, serious discrepancies appear. For example, the electrode slopes of 27-28 mV. in Figure 6 (curves 1 and 2) apparently are actually greater than the theoretical Nernst value. The proper procedure for evaluating specific ion electrodes using mean ionic activity is to use an electrode pair in which the second electrode responds to the counterion. This procedure was followed by Eisenman (7) in establishing that the glass sodium electrode had a theoretical response, by Schonhorn and Gregor (8) for the multilayer membrane calcium electrode, and, most recently by Ross (9), who showed a theo-
(1) A. Shatkay, ANAL.CHEM., 39, 1056(1967). (2) J. Kielland, J . Amer. Chem. Soc., 59, 1675 (1937). (3) R. P. Frankenthal and L. Meites in “Handbook of Analytical Chemistry,” L. Meites, ed., McGraw-Hill, N. Y., 1963. (4) G. Nehara and M. M. Mortland, Soil Science SOC. Amer. Proc., 24, 261 (1960). (5) R. Kohn and I. Furda, Coil. Czech. Chem. Communic., 32, 1925 (1967). (6) R. M. Garrels in “Glass Electrodes for Hydrogen and Other Cations,” G. Eisenman, ed., M. Dekker, Inc., New York, 1967; p. 349. (7) G. Eisenrnan, D. 0. Rudin and J. U. Casby, Science, 126, 831 (1957). (8) H. Schonhorn and H. P. Gregor, J . Amer. Chem. SOC.,83, 3576 (1961). (9) J. W. Ross, Science, 156,1378 (1967).
Table 1. Change in Ratio of y f CaClz/yCa2+ with Ionic Strength Ionic strength, molarity Ratio of y i CaCl,/y Cat+ 0.01 0.02 0.05 0.10 0.15
1.22 1.28 1.40 1.51 1.60
retical Nernst response over a four-decade range for his calcium electrode. In all cases a silver-silver chloride wire was used as the second electrode in chloride solutions. This has the additional advantage of eliminating liquid junction potentials from the data (10). MARTINS. FRANT Orion Research Inc. Cambridge, Mass. 02139
SIR: In my paper Ion Specific Membranes as Electrodes in Determination of Calcium (1) I attempted to present a convenient method for the assessment of the specificity of membranes. The method was based on three assumptions, all stated explicitly: first, that the membrane is discussed as if it was completely specific; next, that the activity of calcium in a mixture is affected by ionic strength only; and finally that acai2is directly proportional to 7*cac12. With the above method, some conclusions were reached regarding paraffin and other membranes, conclusions which differed significantly from those advanced before. All the three assumptions mentioned above are merely approximations, and the method may be refined by altering any or all of them. In such an exchange two points should be considered : the gain of accuracy and the loss of convenience. Dr. Frant considers that the final assumption is incorrect, and that ycS+2for pure solutions of CaCL can be derived more exactly by other methods. The concept of single ion activities is still debated. The arguments for and against have been ably summarized from the viewpoint of pure thermodynamics (11) and of membrane chemistry (12). For the purpose of the method described above, the common practice was adopted to use the well defined y* instead of the possibly more accurate y ~ ~ Thus, + ~ . in all Ref 1, only CC. or C C ~ ~is *used, ~ ~and C Y ~C ~~+does ~ not appear at all. One of the advantages of this approach is that T* of any salt can be easily obtained from handbooks and reference books, while single ion activity coefficients are still being discussed (13). Use of any of the values of 7 c a + 2 as calculated by four dif(10) L. W. Marple, J . Chem. Eng. Datu, 12, 437 (1967). (11) E. A. Guggenheim, Phil. Mug., 19,588 (1935). McGraw-Hill, New York, (12) F. Helfferich, “Ion Exchange,” i962 p. 140. 1131 R . Kohn and I. Furda. Coli. Czech. Chem. Communic.. 32. i925 (1967). ~
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