both the barium sulfate and the Cab-0-Si1 slowly settle out, leaving a clear solution of scintillator at the top of the vial. This results in a change in the counting rate similar to that shown in Figure 1. The addition of sufficient sodium hydroxide to render the suspension slightly alkaline causes the suspension to set to a thixatropic gel that remains firm for at least several weeks. As shown in curves 2 and 4 of Figure 1,
no decrease beyond that due to radiological decay occurs from
a rigid gel. An over-all recovery of 93 with this procedure.
or better is obtained routinely
RECEIVED for review September 15, 1969. Accepted October 30,1969.
Second Harmonic Alternating Current Polarography. Some Experimental Observations with Zinc Ion-Zinc Amalgam System in Chloride Media Thomas G. McCord‘ and Donald E. Smith2 Department of Chemistry, Northwestern University, Euanston, Ill. 60201
RECENTLY, second harmonic ac polarographic studies of processes following the simple quasi-reversible electrode reaction mechanism ka,u
O+ne+R
have yielded excellent agreement between theory and experiment ( I , 2). Rate parameters obtained ( k , and a) were consistent with results of other methods. Measurements under conditions of the classical faradiac impedance experiment (without dc polarization) ( I ) and under ac polarographic conditions (with dc polarization) ( 2 ) were represented in these recent data. The most difficult aspect associated with developing a rigorous formulation of the second harmonic response involves predicting effects of spherical diffusion which originate in the dc polarization process (3-6). This is particularly true in the case of amalgam-forming processes where such effects are relatively large (5). The aforementioned agreement between theory and experiment under ac polarographic conditions ( 2 ) was observed for systems characterized by nernstian (diffusion-controlled) dc processes, a situation in which theoretical accommodation of the spherical diffusion effect is not particularly difficult. These studies did not encompass the more severe situation which arises when charge transfer kinetics are sufficiently slow that the dc process is controlled by charge transfer kinetics and diffusion (non-nernstian or quasireversible dc processes) (3, 4 ) . In this particular case the spherical diffusion correction provided by existing second harmonic theory ( 2 ) is expected to be rather inexact because it is based on the assumption of nernstian behavior in the dc 1
sense. Thus, the possibility exists that its use in analysis of second harmonic data might yield inaccurate charge transfer rate parameters whenever the dc process is quasi-reversible. In order to assess the seriousness of the foregoing problem, we carried out a comparison of existing second harmonic theory with experimental results obtained with one example of the “worst case” in which both amalgam formation and a quasi-reversible dc polarization step are operative. The system selected was Zn2+/Zn(Hg)in 1 M KCl, HCl. A detailed fundamental harmonic investigation of this process has been effected by Sluyters and coworkers ((7-10) whose data indicated that the kinetic parameters, k, 3.8 X cm sec-l, 01 G 0.30 (9) [ain this work is equivalent to in References (8) and (9)], were appropriate for our purposes. The results of our second harmonic ac polarographic investigation are presented here. EXPERIMENTAL
The experimental procedures are identical to those described previously (2). Polarograms were examined at the frequencies; 23, 332, and 1110 Hz. The polarographic solution, 2.0 x 10-3M Zn2+ in 1.OM KCl, 1.0 X 10-3M HCI matches one of those reported by Timmer, SluytersReybach, and Sluyters (9). Theoretical equations and data treatment procedures employed in this work are given in Reference (2). Explicit comparison of theoretical and experimental polarograms involved rate parameters in the ranges, 5 k , 5 1.2 X 10-2 cm sec-1 and 0.2 5 a _< 0.5. Other parameters used in theoretical calculations were: IZ = 2, C,* = 2.0 X 10-3M, Do = 0.7 x 10-5 cm2 sec-’ ( I I ) , D R = 2.0 X cm2 sec-1 (12), and A = 0.035 cm2.
Present address, General Electric Corp., Materials and Pro-
cesses Laboratory, Schenectady, N. Y . , 12305 2
To whom correspondence should be addressed.
(1) J. E. B. Randles and D. R. Whitehouse, Trans. Faraday Soc., 64, 1376 (1968). (2) T. G. McCord and D. E. Smith, ANAL.CHEM., 41,131 (1969). (3) J. R. Delmastro and D. E. Smith. J. Electroanal. Chem.,. 9,. 192 (1965). (4) J. R. Delmastro and D. E. Smith. ANAL.CHEM.. 38. 169 (1966). { 5 j T . G. McCord, E. R. Brown, and D. E. Smith,.ibid., p 1615. (6) T. G. McCord and D. E. Smith, ibid., 40, 289 (1968). \-,
126
a
(7) M. Sluyters-Rehbach, A. B. Ijzermans, B. Timmer, J. B. Griffioen, and J. H. Sluyters, Electrochim. Acta, 11, 483 (1966). (8) B. Timmer, M. Sluyters-Rehbach, and J. H. Sluyters, J. Electroanal. Chem., 14, 169 (1967). (9) Ibid.,p 181. (10) Zbid., 19, 85 (1968). (11) I. M. Kolthoff and J. J. Lingane, “Polarography,” Vol. 1, 2nd Ed., Interscience Publishers, New York, 1952, pp 52, 95. (12) W. C. Cooper and N. H. Furman, J. Amer. Clzem. SOC.,74, 6183 (1952).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
Table I. Comparison of Second Harmonic Data for Zn2+/Zn(Hg)in 1M KCI, 10-3M HCI with Theoretical Predictions Theoretical value for k , = 4 X 10-3cm Second harmonic characteristic Drop life, sec Frequency, Hz Experimental value sec-I, CY = 0.30 Peak separation (in mV) 4.4 23 46 44 4.4 332 57 56 4.4 1110 62 65 14 23 48 48 14 332 60 62 14 1110 66 74 Peak height ratio 4.4 23 1.57 1.57 cathodic peak height 4.4 332 4.10 3.15 4.4 1110 4.28 4.27 = anodic peak height 14 23 2.16 1.98 14 332 6.39 3.75 14 1110 5.44 5.04 Cathodic peak time... 23 1.37 1.28 dependence ... 332 1.27 1.20 height at 14 sec ... 1110 1.17 1.18 = height at 4.4 sec Cathodic peak magnitude, pA 4.4 23 0.244” 0.244 4.4 332 0.298 0.310 4.4 1110 0.339 0.328 14 23 0.335 0.313 14 332 0.381 0.373 14 1110 0.398 0.388 Cathodic peak frequency 4.4 23 1 1 dependence relative to 23 4.4 332 1.22 1.27 Hz 4.4 1110 1.39 1.35 14 23 1 1 14 332 1.13 1.19 14 1110 1.19 1.24 a This point force-fit to theory in process of calculating the “apparent electrode area” [see Reference (2) for details].
(
(
)
)
RESULTS AND DISCUSSION
cm sec-1 and a = The rate parameters k, = 4.0 X 0.30 were determined t o give the best fit between theory and experiment. Table I provides a quantitative comparison between experimental values of certain significant features of the second harmonic response and the corresponding theoretical cm sec-l and a! = 0.3. The experivalues for k, = 4 X mental and theoretical quantities refer to observations made at the end of natural drop life. As shown in Table I, the best fit of theory and experiment in the present case is less satisfactory than in previous reports (I, 2). Nevertheless, the theory-experiment match must be considered reasonable, as the magnitudes of the disparities are well within the realm where they can be rationalized in terms of errors in theoretically estimating spherical diffusion effects. Other factors such as potential-dependent a values (IO,13-15) also might be contributing. (13) R. A. Marcus, J. Chem. Phys., 43,679(1965).
The feature which is by far the most important and which served as the stimulus for submitting these results is the fact that the set of apparent charge transfer rate parameters indicated for the zinc system by second harmonic data ( k , = 4 X cm sec-’, a! = 0.30) is perfectly consistent with the fundamental harmonic investigations of Timmer et al. (9). One is led t o the plausible conclusion that, without exact correction for spherical effects associated with relatively slow charge transfer steps, the charge transfer rate parameters yielding the best fit of second harmonic theory and experimental data are apparently as reliable as those obtained for faster charge transfer processes (2).
RECEIVED for review August 18, 1969. Accepted October 27, 1969. Work supported by National Science Foundation Grant GP7985. T.G.M. was a n NIH Graduate Fellow. (14) R. Parsons and E. Passeron, J. Electroanal. Chem., 12, 524 (1966). (15) M. Sluyters-Rehbach, B. Timmer, and J. H. Sluyters, 2. Physik. Chem. N.F., 52, 89 (1967).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 1, JANUARY 1970
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