Chemistry

Chemistry

Problem

Silver chloride dissolves according to AgCl(s)⇌Ag+(aq)+Cl−(aq)ΔG∘=+55.0 kJ mol−1 at 298 K\mathrm{AgCl(s)} \rightleftharpoons \mathrm{Ag^+(aq)} + \mathrm{Cl^-(aq)} \quad \Delta G^\circ = +55.0\,\text{kJ mol}^{-1}\text{ at }298\,\text{K} Consider a solution at 298 K298\,\text{K} that is already 1.00×10−6 M1.00 \times 10^{-6}\,\text{M} in Ag+\mathrm{Ag^+}. The chloride ion concentration can be adjusted as desired. (R=8.314 J mol−1 K−1R = 8.314\,\text{J mol}^{-1}\,\text{K}^{-1}). a. Part 1: For [Cl−]=1.00×10−9 M[\mathrm{Cl^-}] = 1.00 \times 10^{-9}\,\text{M}, calculate ΔG\Delta G for the dissolution process. Report the value in kJ mol−1\text{kJ mol}^{-1} to three significant figures and indicate whether dissolution is spontaneous under these conditions. b. Part 2: Determine the maximum chloride-ion concentration (to two significant figures) that will still permit spontaneous dissolution of AgCl\mathrm{AgCl} at 298 K298\,\text{K}, assuming [Ag+][\mathrm{Ag^+}] remains fixed at 1.00×10−6 M1.00 \times 10^{-6}\,\text{M}.

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