Читать книгу Geochemistry - William M. White - Страница 146

We can calculate E_H values for reactions not listed in Table 3.3 by algebraic combinations of the reactions and potentials that are listed. There is, however, a catch. Let's see how this works.

Calculate the E_H for the reaction:

Answer: This reaction is the algebraic sum of two reactions listed in Table 3.3:

Since the reactions sum, we might assume that we can simply sum the E_H values to obtain the E_H of the net reaction. Doing so, we obtain an E_H of 0.33 V. However, the true E_H of this reaction is −0.037 V. What have we done wrong?

We have neglected to take into consideration the number of electrons exchanged. In the algebraic combination of E_H values, we need to multiply the E_H for each component reaction by the number of electrons exchanged. We then divide the sum of these values by number of electrons exchanged in the net reaction to obtain the E_H of the net reaction, i.e.,

(3.111)

where the sum is over the component reactions i. Looking at eqn. 3.106, we can see why this is the case. By Hess's law, the ΔG of the net reaction must be the simple sum of the component reaction ΔGs, but E_H values are obtained by multiplying ΔG by z. Equation 3.111 is derived by combining eqn. 3.106 and Hess's law. Using eqn. 3.111, we obtain the correct E_H of −0.037 V.