Fundamental Studies with the Dropping Mercury Electrode.¹ III. Influence of Capillary Characteristics on the Diffusion Current and Residual Current

Abstract

From theoretical considerations presented originally by Ilkovif, * which have been discussed in detail el~ewhere,'.~ a diffusion controlled limiting current observed with the dropping electrode should obey the equation id = knD1/2Cmz/rt1/s = ICm'/at '/a in which i d is expressed in microamperes, k is a constant whose theoretical value is 605 a t 25') n is the number of electron equivalents per molar unit of the elecirode reaction, D is the diffusion coefficient (cm.z/sec.) of the reducible or oxidizable substance, C is its concentration (millimoles per liter), m is the rate of mercury flow (mg./sec.) from the dropping electrode capillary, and t is the drop time (sec.). The quantity I , which theoretically is equal to knD1/2, and which is experimentally determinable as id/(c?nz'8t1'e), is the "diffusion current constant. ' ' 4Recently it was pointed out4 that the performance of practical polarographic analyses can be simplified and greatly expedited when the I-value of the substance being determined is already known in a particular supporting electrolyte, because it is then only necessary to determine i d in an unknown case, measure the m and t values of the particular dropping electrode that is used, and then apply equation 1 to calculate C. Thus, calibration of each dropping electrode with known concentrations of the substance being determined can be dispensed with. Obviously, this method will be reliable only if id is strictly proportional to C and to mz/3tl/6, that is, if I is independent of these quantities, as predicted .by eq. 1. Results (1) For papers I and 11 of this series see, J. J. Lingane and I. M . (2) D. Ilkovi6, Cd1. Czechoslov. C h o n . Commun.. 6, 498 (1934); (3) I. M. Kolthoff and J . J. Lingane, "Polarography," Inter-(4) J. J. Lingant., I n d . Rnn. Chetn., A n d . E d . , 16, 583 (1943). obtained by numerous investigators demonstrateconclusively that i d is exactly proportional to C in every case in which the limiting current is known to be diffusion controlled, and when proper correction is made for the residual c~r r e n t , '~~ but the reliability of the predicted linear relation between i d and mz/at1/6 has not been demonstrated satisfactorily over a large range of m and t values.The only previous systematic study of the relation between i d and mz/at1/6 was carried out some years ago by M a a~,~ who obtained data for the diffusion current of cadmium ion in 0.1 N potassium chloride with about thirty different dropping electrode capillaries. The corresponding diffusion current constants of cadmium ion computed from Maas' data show no definite trend when plotted against ma/atl/e (compare Fig. l), but the precision of these data is too poor (ca. * 2%), and the range of mz/at'/6 values too limited (from about 0.6 to 1.5 rng.'la set.-'/') to constitute a very rigorous test of eq. 1.These facts prompted us to investigate more carefully the relation between i d and over as large a'range of m and t values as possible. The results obtained demonstrate conclusively that i d is not an exact linea...

Validity of the Ilkovic and other standard direct and alternating current polarographic equations at short drop time

“…Figure l29 also shows the same plot for the cadmium(II) electrode process in 1M HC1 Cd(II) + 2e = Cd(amalgam) (8) using mercury column heights from 30 (t = 4.51, m = 1.64 mg sec-1) to 57.6 cm (t = 2.18 sec, m = 3.49 mg sec-1). The same capillary was used as for the bismuth(III) case but m and t were measured at a different potential, corresponding to the cadmium electrode process's E1/2 value of -0.62 V vs. Ag|AgCl.…”

An Introduction to Polarographic Methods and Their Application to the Analysis of Plant Material

“…Occasionally the advantages lie with the polarographic method, however; for example, Gillam (1945) determined ascorbic acid in fruits and vegetables, by extracting with oxalic and metaphosphoric acids at pH 3-5, and recording the currentvoltage curves for the coloured extract, using a dropping mercury electrode. Ketosteroids (Barnett, Henly & Morris, 1946) and components of the Vitamin B complex (Lingane & Davis, 1941) have been estimated by means of the polarograph. It may be possible to estimate adenine in hydrolysates of nucleic acids (Heath, 1946).…”

“…Thus Lingane (19456) foretold the substance formed when picric acid is reduced. The polarographic curves suggested a reduction reaction involving seventeen electrons per molecule, corresponding to the reduction product di-(4-hydroxy-3, 5-diaminophenyl) hydrazine, A great many organic substances are reducible at the dropping mercury electrode, and give well-defined diffusion currents, but the reactions are rarely reversible, and are usually dependent on the nature of the supporting electrolyte, and frequently on the hydrogen ion concentration (Miiiller, 1939;Pasternak & V. Halben, 1946), However, the polarographic waves may often be used for analytical purposes, providing the test solution is free from other reducible substances which would interfere with the estimation (Lingane & Davis, 1941;Beaver & Kauwitz, 1944).…”

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“…Thus Lingane (19456) foretold the substance formed when picric acid is reduced. The polarographic curves suggested a reduction reaction involving seventeen electrons per molecule, corresponding to the reduction product di-(4-hydroxy-3, 5-diaminophenyl) hydrazine, A great many organic substances are reducible at the dropping mercury electrode, and give well-defined diffusion currents, but the reactions are rarely reversible, and are usually dependent on the nature of the supporting electrolyte, and frequently on the hydrogen ion concentration (Miiiller, 1939;Pasternak & V. Halben, 1946), However, the polarographic waves may often be used for analytical purposes, providing the test solution is free from other reducible substances which would interfere with the estimation (Lingane & Davis, 1941;Beaver & Kauwitz, 1944).…”

“…Occasionally the advantages lie with the polarographic method, however; for example, Gillam (1945) determined ascorbic acid in fruits and vegetables, by extracting with oxalic and metaphosphoric acids at pH 3-5, and recording the currentvoltage curves for the coloured extract, using a dropping mercury electrode. Ketosteroids (Barnett, Henly & Morris, 1946) and components of the Vitamin B complex (Lingane & Davis, 1941) have been estimated by means of the polarograph. It may be possible to estimate adenine in hydrolysates of nucleic acids (Heath, 1946).…”