Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

6 ELECTROCHEMICAL METHODS 161The undissociated acid HA is reduced at a more positive potential than (i.e.,“before”) A-. At low pH only one wave, with E+ appropriate to the reduction ofHA, is observed while at high pH again one wave is found, but at the half-wavepotential associated with A-. At intermediate pH both waves are observed (Fig. 20).How does this double wave arise, and how can it be used to measure the rate coefficientsk,, kb?tThe disadvantage of the rigorous approach85 to this type of problem is that themathematics are very difficult for any case except the most simple (e.g., this firstorder reaction). Instead, it is common to consider the somewhat vague conceptof the “reaction layer”. This is an approach which gives a physical idea of the processesinvolved as well as allowing rate coefficients to be derived for more complicatedkinetic mechanisms. The reaction layer is a hypothetical layer surroundingthe electrode within which all the HA molecules produced by reaction (9) reachthe electrode and are reduced. Its thickness p depends on the reverse rate coefficient,k, (p = D*k;*). Suppose the applied potential is only sufficient to dischargeHA. Even when the concentration of HA near the electrode is very small, it will bedischarged and the equilibrium (9) will be disturbed. In this situation, the concentrationof A- near the electrode will decrease and a contribution to the current dueto the diffusion of A- and subsequent production of HA will be added to the(small) contribution due to the diffusion of HA. As the voltage is increased, thecurrent will increase to an (average) maximum value, ik, which is less than id anddepends on the pH and the relative values of k, and k,. On further increasing thevoltage, A- will be discharged and the remainder of the current-voltage curve willbe like that found at high pH. The IlkoviE equation has been modified for thissituationik-=id0.886[(kf K)t,]*cH+1 +0.886[(kfK)f,]*C~+where K = k,/k,. This expression can be modified slightly to take account of sphericaldiffusion and the different diffusion coefficients of A- and HA. The forwardrate coefficient for pyruvate plus a protons6 is 1.3 x 10’O mole.1.-’sec-’.The electrolytic reduction of hydrogen peroxide involves a very large overvoltage,yet H2 0, is a relatively good oxidizing agent. This is why it is possible to find manysystems involving H202 which give a catalytic current. In reaction (8), hydrogenperoxide would be substance E. Ferric ion (X) can be reduced polarographidy toIt was originally thought that each step might arise from the simple discharge of the equilibriumconcentrations of the two species. This was disproved by showing that the pH at whichthe double steps occurred were considerably different from the pKa of the acid (around whichpH the concentrations of A- and HA are similar).References pp. 176-179