Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

160 EXPERIMENTAL METHODS FOR FAST REACTIONSThe current is proportional to the rate at which X diffuses to the cathode, afunction which can be expressed mathematically for a spherical electrode on whichX converges from all directions. The situation is complicated by two factors. Becausethe mercury drop is steadily expanding, the surface area increases gradually andalso the surface moves relative to the solution against the concentration gradient.The diffusion current at any time t during the life of the drop is given by an equationfirst derived by IlkoviEE4it = 706nD*cxm*t' pAwhere n is the number of electrons involved in the reduction of one molecule of X,D is the diffusion coefficient of X (cd.sec-'), cx is the concentration of X ( dimole.1-')and m the weight of mercury (mg) flowing from thecapilIaryper second.The IlkoviE equation fits the experimental data quite well despite certain assumptionsof rather doubtful validity used in its derivation-e.g., it supposes no stirringand neglects the curvature of the electrode surface. Because the average diffusioncurrent (Le., the difference between the average current at applied potentials considerablyabove and below the half-wave potential, cf. Fig. 19) is usually measuredit is common to see the IlkoviE equation in the formid = 607nD*cxm%fnwhere t,,, is the drop time in seconds. Now if the depolarizer takes part in a chemicalreaction, the IlkoviE equation is not obeyed, but is modifled in a way depending onthe type of reaction. Several such cases have been discussedb3.A system giving a kinetic current is a well-buffered solution of pyruvic acid,CH3 COCOOH. The relevant reactions can be abbreviatedE-Fig. 20. Polarograms of pyruvic acid buffered at different pH.