(a) Write the equilibrium constant expression for the reaction $$ \mathrm{PbI}_{2}(s) \leftrightarrows \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q) $$ (b) How would the equilibrium be affected if \(\mathrm{PbI}_{2}(s)\) were added? (c) How would the equilibrium be affected if \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(s)\) were added? (Hint: Don't forget that \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) is a water-soluble salt.)

To write the equilibrium constant expression for the given reaction, we recall that the equilibrium constant is the product of the molar concentration of the products raised to their stoichiometric coefficients, divided by the product of the molar concentration of the reactants raised to their stoichiometric coefficients. For the given reaction: \[ \mathrm{PbI}_{2}(s) \leftrightarrows \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q) \] The equilibrium constant expression can be written as: \[ K_\mathrm{c}=\frac{[\mathrm{Pb}^{2+}(a q)][\mathrm{I}^{-}(a q)]^2}{[\mathrm{PbI}_{2}(s)]} \] However, since the concentration of a pure solid (\(\mathrm{PbI}_{2}(s)\)) does not influence the equilibrium constant, we can modify the expression as follows: \[ K_\mathrm{c}=[\mathrm{Pb}^{2+}(a q)][\mathrm{I}^{-}(a q)]^2 \]

When more \(\mathrm{PbI}_{2}(s)\) is added to the system, the concentration of the solid does not change, since the amount of solid in the system does not affect the equilibrium constant. Therefore, adding \(\mathrm{PbI}_{2}(s)\) will not have any effect on the position of the equilibrium.

When \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(s)\) is added to the system, it will dissolve in water as it is a water-soluble salt, forming \(\mathrm{Pb}^{2+}(a q)\) and \(2\mathrm{NO}_{3}^{-}(a q)\) ions. The increase in the concentration of \(\mathrm{Pb}^{2+}(a q)\) will shift the equilibrium of the given reaction to the left to minimize the change according to Le Chatelier's principle. This will result in the formation of more \(\mathrm{PbI}_{2}(s)\) and a decrease in the concentration of \(\mathrm{I}^{-}(a q)\).