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Question 16.8: Using ΔG°f tables in Appendix 1, calculate the solubility pr...

Using ΔG°_{f} tables in Appendix 1, calculate the solubility product constant, K_{sp}, for PbCl_{2} at 25°C.

ANALYSIS
equation for dissolving PbCl_{2}(PbCl_{2}(s) → Pb^{2+}(aq)  +  2Cl^{-}(aq))
T(25°C)		 Information given:
ΔG°_{f} values (Appendix 1)
R value		 Information implied:
K_{sp} Asked for:

STRATEGY

1. Obtain ΔG°_{f} values from Appendix 1 and substitute into Equation 16.3.

ΔG°_{reaction} = ΣΔG°_{f_{  products}} – ΣΔG°_{f_{  reactants}}                    (16.3)
2. Substitute into Equation 16.5 to find K_{sp}, which is K.

ΔG° = -RT ln K                         (16.5)

ΔG° = -RT ln K_{sp}

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ΔG° = ΔG°_{f}  Pb^{2+}(aq)  +  2ΔG°_{f}  Cl^{-}(aq)  –  ΔG°_{f}  PbCl_{2}(s)

= -24.4 kJ + 2(-131.2 kJ) + 314.1 kJ = +27.3 kJ

ΔG° = -RT ln K_{sp}; 27.3 kJ = -(0.00831 kJ/K)(298 K) ln K_{sp}

ln K_{sp} = -11.0 → K_{sp} = e^{-11.0}  =  1.7  ×  10^{-5}

 ΔG°

 

K_{sp}

END POINT

This is the value listed in Chapter 15 for K_{sp} of PbCl_{2}.

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