Chap29 solutions

Physical Chemistry

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29 Dynamics of electron transfer Solutions to exercises Discussion questions E29.1(b) No solution. E29.2(b) The net current density at an electrode is j ; j 0 is the exchange current density; α is the transfer coefficient; f is the ratio F/RT ; and η is the overpotential. (a) j = j 0 f η is the current density in the low overpotential limit. (b) j = j 0 e ( 1 α)f η applies when the overpotential is large and positive. (c) j = − j 0 e αf η applies when the overpotential is large and negative. E29.3(b) In cyclic voltammetry, the current at a working electrode is monitored as the applied potential differ- ence is changed back and forth at a constant rate between pre-set limits (Figs 29.20 and 29.21). As the potential difference approaches E (Ox, Red) for a solution that contains the reduced component (Red), current begins to flow as Red is oxidized. When the potential difference is swept beyond E (Ox, Red), the current passes through a maximum and then falls as all the Red near the electrode is consumed and converted to Ox, the oxidized form. When the direction of the sweep is reversed and the potential difference passes through E (Ox, Red), current flows in the reverse direction. This current is caused by the reduction of the Ox formed near the electrode on the forward sweep. It passes through the maximum as Ox near the electrode is consumed. The forward and reverse current maxima bracket E (Ox, Red), so the species present can be identified. Furthermore, the forward and reverse peak currents are proportional to the concentration of the couple in the solution, and vary with the sweep rate. If the electron transfer at the electrode is rapid, so that the ratio of the concentrations of Ox and Red at the electrode surface have their equilibrium values for the applied potential (that is, their relative concentrations are given by the Nernst equation), the voltammetry is said to be reversible . In this case, the peak separation is independent of the sweep rate and equal to ( 59 mV )/n at room temperature, where n is the number of electrons transferred. If the rate of electron transfer is low, the voltammetry is said to be irreversible . Now, the peak separation is greater than ( 59 mV )/n and increases with increasing sweep rate. If homogeneous chemical reactions accompany the oxidation or reduction of the couple at the electrode, the shape of the voltammogram changes, and the observed changes give valuable information about the kinetics of the reactions as well as the identities of the species present. E29.4(b) Corrosion is an electrochemical process. We will illustrate it with the example of the rusting of iron, but the same principles apply to other corrosive processes. The electrochemical basis of corrosion in the presence of water and oxygen is revealed by comparing the standard potentials of the metal reduction, such as Fe 2 + ( aq ) + 2e Fe ( s ) E = − 0 . 44 V with the values for one of the following half-reactions In acidic solution (a) 2 H + ( aq ) + 2 e H 2 ( g ) E = 0 V (b) 4 H + ( aq ) + O 2 ( g ) + 4 e 2H 2 O ( l ) E
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