of accuracy. For the chloride and iodide, the error was negative in all six annlyscs performed, the mean error being of the order of -22, whereas for the bromide the error was positive ( E -1- 0.774). For the estimation of the other constituent (sodium or lithium), however, the method is not very suitable; high results (even up to 7 x ) are sometimes obtained, because of the leakage of lithium chloride from the calomel electrode. As the amounts involved in the analyses are relatively small (0.1-0.2 mmole), even slight leakage tends to vitiate the results, so that only potassium can be accurately estimated even for chloride, bromide, and iodide. For the sulfate, potassium in the presence of sodium and lithium can be estimated with a mean error of - 2 x . F o r the fluoride, only two sets of analyses were performed, the error being - 1.S and $0.8 respectively. The method is not suitable for estimating larger amounts, because it would require inconveniently large volumes of solvent to
z,
keep the acetates in solution. The titration medium should contain acetic acid and chloroform in the ratio 1:20. A smaller proportion of chloroform impairs the sharpness of the first inflection. The method affords a rapid and reasonably accurate means for analyzing binary mixtures of potassium with sodium or lithium. After determining the total alkali metals by the usual methods--e.g., as sulfate or chloride-the potassium content may conveniently be determined by differential titration as described, the other constituent being obtained by difference.
RECEIVED for review January 30, 1967. Accepted May 10, 1967. Work supported by a fellowship awarded under the Colombo plan by the Ministry of Education, Government of India t o I. L. Shresta. Necessary facilities for him were provided by the Government of Nepal.
Concentration Gradients in Film and Spherical Mercury Electrodes under Variable-Flux Plating Conditions Sidney L. Phillips and Lawrence F. Karr International Business Mucliines Corp., Systetns Decelopment Division, Box 390, Poughkeepsie, N . Y . I2602
THETHEORY of plating amalgam-forming metals a t film and spherical mercury electrodes has been treated by many workers (1-5). Amalgamation is invariably carried out under constant flux conditions, either from a stirred solution as in the pre-electrolysis step in anodic stripping analysis (2), o r from a n unstirred solution as in chronopotentiometric plating (4). In both cases, the equations describing the concentration gradients existing within both film and spherical electrodes permit predictions to be made concerning the effects of such parameters as plating time, electrode radius, and diffusion coefficient. Thus, the effect of finite electrode size can be characterized reasonably well when metal deposition takes place under conditions of constant flux a t the electrode surface. On the other hand, the case in which the flux of the amalgamforming metal ion is a function of time has only been considered in regard to the effect of curvature of a spherical electrode o n the magnitude of the plating current (6). Here, extension of the theoretical treatment to include a description of the concentration gradients within the electrode is desirable because important experiments such as cyclic stationary electrode polarography often involve formation of amalgams under variable-flux plating conditions. As in the stirred solution case, knowledge of the concentration gradients would then permit estimates to be made of the effect of finite electrode volume o n cyclic polarography, square-wave voltammetry, and alternating-current polarography. In the present work, the theory of amalgam formation is extended t o include time-dependent plating conditions. I n particular, emphasis is placed on the flux of the metal ion being (1) (2) (3) (4) (5) (6)
W. H. Reinmutli, ANAL.CHEW,33, 185 (1961). I. Shah and J. Leninson, Zbid.,p. 187. W. 7.DeVries, J . Elrctroariul. Cliern., 9, 448 (1965). S. P. Perone and A. Brumfield, Zbid.,13, 124 (1967). D. K. Roe and J. E. A. Toni, ANAL.CHEM., 37, 1503 (1965). W. G. Stevens and I. Shain, Zbid.,38, 865 (1966).
proportional t o t-1Iz: the case corresponding to chronoamperometric deposition. The calculated concentration gradients also describe the amalgam distribution during the cathodic portion of a cyclic experiment, so that an estimate of the effect of finite electrode volume on the anodic portion of this experiment can be made. The film electrode is considered first. CONCENTRATION-TIME RELATION
Planar Film Electrode. The initial-boundary value problem for the film electrode may be formulated in terms of the usual Fick's law equation for diffusion between two parallel planes :
Here, CR is the concentration of amalgam-forming substance within the film; t i s the time; DE is the diffusion coeficient; and x is the linear distance within the electrode. F o r the planar mercury film electrode, the bounds o n x are the solidmercury interface defined by x = 0, and the mercury-solution interface a t x = 8. The electrode then has a finite film thickness, P. Initially, we assume the mercury film is free of amalgamforming substances so that t = 0,0
