Comments on Chronopotentiometric and Electrode Potential Investigations in Molten Equimolar Sodium and Potassium Metaphosphates SIR: In reading the recent paper by Wolfe and Caton ( I ) on chronopotentiometry and potentiometry in molten equimolar NaP03 and KP03, it seemed that unusually long transition times were being used to obtain information concerning diffusion processes. Laitinen and Ferguson ( 2 ) have shown that in fused (Li,K)Cl eutectic at 450 “C, a semiinfinite linear diffusion model applies only for transition times shorter than about five seconds. It occurred to us to test the validity of the diffusion model in the highly viscous metaphosphate system. As pointed out by the authors ( I ) , a linear relationship between i o ~ l and / ~ C (definitions are the same as those used in Ref. I ) is a necessary condition for a reversible diffusion controlled process. However, necessary and sufficient conditions to establish that a given process is reversible and diffusion controlled, within the limits of chronopotentiometry, are (a) ioT1’z is a linear function of C with zero intercept, and (b) ioT1lz is independent of io. Unfortunately, insufficient data are presented to test condition (b), but a check of (a) is possible using the available data. We have taken the data from Table I1 in Ref. I and computed the “least squares” best fit to a linear model of ioT1’z us. C. The results are presented in Table I. While it certainly takes some imagination to glean a statistically significant answer from three or four data points, we feel that the analysis can be used to arrive at some useful conclusions. For U(IV), U(VI), and Cu(I), we feel that the analysis indicates that the reversible, diffusion controlled model as put forth by the authors does not apply. The magnitude of the intercepts for these three cases varies between 6 and 42% of the measured values and they are significant at the 95% confidence level. For the remaining three cases the significance of the intercept is not nearly so well defined. This is probably due to a breakdown of the statistical treatment caused by the small number of points rather than a second “class” of data. In any case there doesn’t appear to be any simple explanation of the results. If the reaction were highly irreversible, one would expect a negative deviation in the plot of iO7’iz us. C at constant io. (1) C. R. Wolfe and R. D. Caton, Jr., ANAL.CHEM.,43, 663 (1971). (2) H. A. Laitinen and W. S..Ferguson, ibid.,29,4 (1957).
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ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
Table I. Least Squares Best Fit of Data (Ref. I ) Slope in Number crnmA Metal of data secl/a/rnole Intercept in ion points, n X mA secl/a/cmz so. -0.5 f 3.2b 0,176 CU(I1) 3 5.8 f 1.4b + 3 . 3 f 1.8 0,313 cum 5 22.6 f 1.1 3 28.2 f 2.5 +0.3 f 3.7 0.075 AN) +1.0 f 1.9 0.354 4 11.1 31 1 . 3 V(V) U(V1) 5 6.10 f 0.27 -0.76 f 0.45 0.136 U(1V) 5 3.03 & 0.09 +0.26 f 0.04 0.005 s is an estimate of the standard error of the fit. confidence at (n - 2) degrees b The indicated interval is for 95 of freedom.
An impurity discharged at a potential prior to or during the main process would produce a positive intercept. If convection were t.he only interfering process, one would expect positive deviations from the Sand equation which would approach zero as the transition time decreased. Possibly some of the observed deviation is due to the technique used to measure the transition times. This is not likely to account for the total discrepancy since this technique has been shown to be satisfactory (2). Furthermore, the cases which show the most significant deviations from theory are those having the most ideally shaped curves for which any reasonable transition time measuring techniques would be suitable. In conclusion we would like to simply restate the obvious pitfalls of calculating such parameters as diffusion coefficients from any experimental technique without first taking as many precautions as possible to ensure that the fundamental assumptions implicit in the theory are upheld.
L. R. LIETO‘ JR. R. 0. JOHNSTON, Department of Chemistry and Chemical Engineering University of Illinois Urbana, Ill. 61701 RECEIVED for review July 9, 1971. Accepted October 29, 1971. 1 Present address, Department of Chemistry, Illinois State University, Normal, Ill. 61761.
