By Wang Joseph
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Additional info for Analytical Electochemistry. Second Edition
The diffuse double layer becomes small). Under these conditions, 1=CH ) 1=CG , 1=C 9 1=CH or C 9 CH . In contrast, for dilute solutions, CG is very small (compared to CH ) and C 9 CG . Figure 1-13 displays the experimental dependence of the double-layer capacitance upon the applied potential and electrolyte concentration. As expected for the parallel-plate model, the capacitance is nearly independent of the potential or concentration over several hundreds of millivolts. , the Epzc ) with dilute solutions, re¯ecting the contribution of the diffuse layer.
24 FUNDAMENTAL CONCEPTS FIGURE 1-15 Electrocapillary curves for different electrolytes showing the relative strength of speci®c adsorption. ) potential passes through the Epzc . Experimental electrocapillary curves have a nearly parabolic shape around Epzc . Such a parabolic shape corresponds to a linear change of the charge with the potential. The deviation from a parabolic shape depends on the solution composition, particularly on the nature of the anions present in the electrolyte. , halides) with the FIGURE 1-16 Electrocapillary curves of background (j), ethynylestradiol (), b-estradiol (m) and morgestrel (r).
The term a is thus a measure of the symmetry of the activation energy barrier. , FIGURE 1-10 Effect of a change in the applied potential on the free energies of activation for reduction and oxidation. 18 FUNDAMENTAL CONCEPTS an idealized curve). 5 are common for metallic electrodes with a simple electron transfer process. The barrier for reduction at E is thus given by z anFE DGcz DGc;0 1-36 Similarly, examination of the ®gure reveals also that the new barrier for oxidation, z DGaz is lower than DGa;0 : z À 1 À anFE DGaz DGa;0 1-37 By substituting the expressions for DGz (equations 1-36 and 1-37) in equation (1-34), we obtain for reduction z =RT expÀanFE=RT kf A expÀDGc;0 1-38 z =RT exp 1 À anFE=RT kb A expÀDGa;0 1-39 and for oxidation The ®rst two factors in equations (1-38) and (1-39) are independent of the potential, and thus these equations can be rewritten as kf kf expÀanFE=RT 1-40 kb kb exp 1 À anFE=RT 1-41 When the electrode is at equilibrium with the solution, and when the surface concentrations of O and R are the same, E E , and kf and kb are equal: kf expÀanFE=RT kb exp 1 À anFE=RT k 1-42 and correspond to the standard rate constant k .
Analytical Electochemistry. Second Edition by Wang Joseph