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...
