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Problem 17.85

Use thermodynamic data from Appendix C to obtain a value of K_{sp} for Ag_{2}SO_{4}, and compare your result with the one found in the table of solubility product constants in Appendix C.

The reaction is:

Ag_{2}SO_{4}(*s*)2 Ag^{+}(*aq*) + SO_{4}^{2–}(*aq*)

G^{o}_{f}(SO_{4}^{2–})
= –744.5 kJ/mol

G^{o}_{f}(Ag^{+})
= 77.11 kJ/mol

G^{o}_{f}(Ag_{2}SO_{4})
= –618.5 kJ/mol

G^{o} = [2(77.11) + –744.5] – [–618.5]
= 28.2 kJ

G^{o} = –RTln K_{eq} = –RTlnK_{sp}

28200 = –(8.314)(298)ln K_{sp}

ln K_{sp} = –11.4

K_{sp} = e^{–11.4} = __1__×10^{–5}

From the Table, K_{sp} = 1.4×10^{–5}; the two values are the same, within error.