Chapter 18, Problem 83E

Consider a concentration cell that has both electrodes made of some metal M. Solution A in one compartment of the cell contains 1.0 M M²⁺. Solution B in the other cell compartment has a volume of 1.00 L. At the beginning of the experiment 0.0100 mole of M(NO₃)₂ and 0.0100 mole of Na₂SO₄ are dissolved in solution B (ignore volume changes), where the reaction

${\text{M}}^{\text{2+}}(aq)+{\text{ SO}}_{\text{4}}{}^{2-}\left(aq\right) \rightleftharpoons {\text{MSO}}_{\text{4}}\left(s\right)$

occurs. For this reaction equilibrium is rapidly established, whereupon the cell potential is found to be 0.44 V at 25°C. Assume that the process

${\text{M}}^{2+}+2{\text{e}}^{-}\to \text{ M}$

has a standard reduction potential of −0.31 V and that no other redox process occurs in the cell. Calculate the value of K_sp for MSO₄(s) at 25°C.