The following concentrations are found in mixtures of ions...

The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate $K_{\mathrm{sp}}$ for each of the slightly soluble solids indicated: (a) TICl: $[\mathrm{T}]^{+} ]=1.21 \times 10^{-2} \mathrm{M},\left[\mathrm{Cl}^{-}\right]=1.2 \times 10^{-2} \mathrm{M}$ (b) $\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{4} :\left[\mathrm{Ce}^{4+}\right]=1.8 \times 10^{-4} M,\left[\mathrm{IO}_{3}^{-}\right]=2.6 \times 10^{-13} \mathrm{M}$ (c) $\mathrm{Gd}_{2}\left(\mathrm{SO}_{4}\right)_{3} :\left[\mathrm{Gd}^{3+}\right]=0.132 \mathrm{M},\left[\mathrm{SO}_{4}^{2-}\right]=0.198 \mathrm{M}$ (d) $\mathrm{Ag}_{2} \mathrm{SO}_{4} :\left[\mathrm{Ag}^{+}\right]=2.40 \times 10^{-2} M,\left[\mathrm{SO}_{4}^{2-}\right]=2.05 \times 10^{-2} \mathrm{M}$ (e) $\mathrm{BaSO}_{4} :\left[\mathrm{Ba}^{2+}\right]=0.500 \mathrm{M},\left[\mathrm{SO}_{4}^{2-}\right]=2.16 \times 10^{-10} \mathrm{M}$

The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate $K_{\mathrm{sp}}$ for each of the slightly soluble solids indicated:
(a) TICl: $[\mathrm{T}]^{+} ]=1.21 \times 10^{-2} \mathrm{M},\left[\mathrm{Cl}^{-}\right]=1.2 \times 10^{-2} \mathrm{M}$
(b) $\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{4} :\left[\mathrm{Ce}^{4+}\right]=1.8 \times 10^{-4} M,\left[\mathrm{IO}_{3}^{-}\right]=2.6 \times 10^{-13} \mathrm{M}$
(c) $\mathrm{Gd}_{2}\left(\mathrm{SO}_{4}\right)_{3} :\left[\mathrm{Gd}^{3+}\right]=0.132 \mathrm{M},\left[\mathrm{SO}_{4}^{2-}\right]=0.198 \mathrm{M}$
(d) $\mathrm{Ag}_{2} \mathrm{SO}_{4} :\left[\mathrm{Ag}^{+}\right]=2.40 \times 10^{-2} M,\left[\mathrm{SO}_{4}^{2-}\right]=2.05 \times 10^{-2} \mathrm{M}$
(e) $\mathrm{BaSO}_{4} :\left[\mathrm{Ba}^{2+}\right]=0.500 \mathrm{M},\left[\mathrm{SO}_{4}^{2-}\right]=2.16 \times 10^{-10} \mathrm{M}$

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the dissolution of a sparingly soluble ionic compound. It quantifies the product of the molar concentrations of the ions at equilibrium, each raised to the power of its coefficient in the balanced dissolution reaction. Ksp provides insight into the degree of solubility; a small Ksp value indicates that the salt is only slightly soluble in water.

Dissolution Equilibrium

Dissolution equilibrium refers to the dynamic equilibrium established when a sparingly soluble solid dissolves in a solvent to form its constituent ions, and these ions in solution can recombine to form the original solid. In this state, the rate of the dissolution process equals the rate of the precipitation process, and the ion concentrations remain constant, making it possible to define an equilibrium constant (Ksp) for the process.

Stoichiometry in Equilibrium Expressions

The stoichiometry of a dissolution reaction is crucial in writing the correct expression for the solubility product constant. Each ion's concentration in the Ksp expression is raised to the power of its coefficient from the balanced chemical equation. This ensures that the contributions of each ion, based on how many are produced per formula unit of the solute, are accurately reflected in the equilibrium calculation.

Ionic Concentrations

Ionic concentrations refer to the molar amounts of ions present in solution at equilibrium. These concentrations are used directly in the equilibrium expression to calculate the Ksp of a sparingly soluble salt. Accurate measurement or estimation of these ion concentrations is necessary for determining how much of the solid has dissolved and, consequently, for computing the solubility product.

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