A chemical reaction such as the acid-metal reaction of Eq (10.21) need not take place in an electrochemical cell such as the one shown in Fig. 10.5. Much more common is the row 3 case in Fig. 10.4 in which a single electrolyte and the reactive metal M are present. This situation is equivalent to short circuiting the electrochemical cell, which requires that the Nernst potentials of both half-cells be equal:
When this equality prevails, the ion concentrations become adjusted to accommodate this equilibrium requirement. The Nernst potentials for the two half-cell reactions are:
In general, neither of the ion concentrations are at the standard-state value of 1 M, nor need the hydrogen pressure be 1 atm. Combining the preceding equations and solving for the combination of concentrations that constitutes the law of mass action4 yields:
where K is the equilibrium constant of Eq (10.21). Equation (10.31) is the aqueous analog of the equilibrium equations discussed in Chap. 10 (e.g., Eq (10.41) for the slag-melt example). Using the physical symbols for the numerical constant 0.059 in Eq (10.31) permits the equilibrium constant to be expressed in a more familiar form:
K = 10-°(mz+ )/2.3rt = expf zFs°(Mz+ ) J = ex/-M» 1 RT J \ RT
The last form of K in this equation is equivalent to that employed for nonaqueous chemical equilibria, with replacement of AG" in the latter by A^".
The standard electrode potentials in Table 10.1 can be combined to yield equilibrium constants for a wide variety of aqueous ionic reactions, including those that involve solids and gases. For the general case in which the half-cells are denoted by A and B, neither of which is a
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