## Equilibrium constants of aqueous ionic reactions

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

## Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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