Simultaneous Equilibria

Learning Goals
You will learn how to obtain the equilibrium constant for two reactions occurring at the same time.

Synopsis
Often we have a solution of one salt of a particular cation and we wish to convert it to anther salt. The reason for wanting to do this may be that the second salt has a preferred solubility in water. During the conversion of one salt, A_aB_b, to the other salt, A_aC_c we would have two simultaneous equilibria occurring, such as

A_aB_b aA⁺ + bB^- with Ksp1 and

aA⁺ + cC^- A_aC_c with K = 1/Ksp2.

From Section 16.2 we remember that the equilibrium constant for the sum of two reactions is the product of the individual reactions. So the equilibrium constant for the sum of these two reactions would be

Knet = Ksp1 x K = Ksp1/Ksp2.

If we then wanted to see if we could convert AgCl to AgBr, we could calculate the equilibrium constant for the reaction AgCl(s) + Br^-(aq) --> AgBr(s) + Cl^-(aq)

using the two reactions

Ag₊(aq) + Br_- AgBr(s) and the reverse of the reaction

Ag₊(aq) + Cl_-(aq) AgCl(s) (remember that the equilibrium constant for the reverse of a reaction is the inverse of the original equilibrium constant).

Review Questions

If you add sufficient I- ions to a solution of AuBr, can you convert AuBr to AuI?
Why might you wish to convert AuBr to AuI?