Silver chloride, \(\mathrm{AgCl}(\mathrm{s})\), is an "insoluble" strong
electrolyte. (a) Write the equation for the dissolution of \(\mathrm{AgCl}(s)\)
in \(\mathrm{H}_{2} \mathrm{O}(l)\). (b) Write the expression for \(K_{c}\) for
the reaction in part (a). (c) Based on the thermochemical data in Appendix \(C\)
and Le Châtelier's principle, predict whether the solubility of
\(\mathrm{AgCl}\) in \(\mathrm{H}_{2} \mathrm{O}\) increases or decreases with
increasing temperature. (d) The equilibrium constant for the dissolution of
\(\mathrm{AgCl}\) in water is \(1.6 \times 10^{-10}\) at \(25^{\circ} \mathrm{C}\).
In addition, \(\mathrm{Ag}^{+}(a q)\) can react with \(\mathrm{Cl}^{-}(a q)\)
according to the reaction
$$
\mathrm{Ag}^{+}(a q)+2 \mathrm{Cl}^{-}(a q) \rightleftharpoons
\mathrm{AgCl}_{2}^{-}(a q)
$$
where \(K_{c}=1.8 \times 10^{5}\) at \(25^{\circ} \mathrm{C}\). Although
\(\mathrm{AgCl}\) is "not soluble" in water, the complex \(\mathrm{AgCl}_{2}{
}^{\prime}\) is soluble. At \(25^{\circ} \mathrm{C}\), is the solubility of
\(\mathrm{AgCl}\) in a \(0.100 \mathrm{M} \mathrm{NaCl}\) solution greater than
the solubility of \(\mathrm{AgCl}\) in pure water, due to the formation of
soluble \(\mathrm{AgCl}_{2}^{-}\)ions? Or is the \(\mathrm{AgCl}\) solubility in
\(0.100 \mathrm{M} \mathrm{NaCl}\) less than in pure water because of a Le
Châtelier-type argument? Justify your answer with calculations. (Hint: Any
form in which silver is in solution counts as "solubility.")
