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 Ksp for each of the slightly soluble solids indicated: (a) AgBr: $\left[\mathrm{Ag}^{+}\right]=5.7 \times 10^{-7} M,\left[\mathrm{Br}^{-}\right]=5.7 \times 10^{-7} \mathrm{M}$ (b) $\mathrm{CaCO}_{3} :\left[\mathrm{Ca}^{2+}\right]=5.3 \times 10^{-3} M,\left[\mathrm{CO}_{3}^{2-}\right]=9.0 \times 10^{-7} M$ (c) $\mathrm{PbF}_{2} :\left[\mathrm{Pb}^{2+}\right]=2.1 \times 10^{-3} M,\left[\mathrm{F}^{-}\right]=4.2 \times 10^{-3} M$ (d) $\mathrm{Ag}_{2} \mathrm{CrO}_{4} :\left[\mathrm{Ag}^{+}\right]=5.3 \times 10^{-5} M, 3.2 \times 10^{-3} M$ (e) $\operatorname{In} \mathrm{F}_{3} :\left[\operatorname{In}^{3+}\right]=2.3 \times 10^{-3} M,\left[\mathrm{F}^{-}\right]=7.0 \times 10^{-3} \mathrm{M}$

The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate Ksp for each of the slightly soluble solids indicated:
(a) AgBr: $\left[\mathrm{Ag}^{+}\right]=5.7 \times 10^{-7} M,\left[\mathrm{Br}^{-}\right]=5.7 \times 10^{-7} \mathrm{M}$
(b) $\mathrm{CaCO}_{3} :\left[\mathrm{Ca}^{2+}\right]=5.3 \times 10^{-3} M,\left[\mathrm{CO}_{3}^{2-}\right]=9.0 \times 10^{-7} M$
(c) $\mathrm{PbF}_{2} :\left[\mathrm{Pb}^{2+}\right]=2.1 \times 10^{-3} M,\left[\mathrm{F}^{-}\right]=4.2 \times 10^{-3} M$
(d) $\mathrm{Ag}_{2} \mathrm{CrO}_{4} :\left[\mathrm{Ag}^{+}\right]=5.3 \times 10^{-5} M, 3.2 \times 10^{-3} M$
(e) $\operatorname{In} \mathrm{F}_{3} :\left[\operatorname{In}^{3+}\right]=2.3 \times 10^{-3} M,\left[\mathrm{F}^{-}\right]=7.0 \times 10^{-3} \mathrm{M}$

Key Concepts

Solubility Equilibrium

Solubility equilibrium refers to the dynamic state achieved when a slightly soluble solid is in contact with its saturated solution, such that the rate of dissolution equals the rate of precipitation. This equilibrium condition allows the definition of Ksp and is essential for understanding how ion concentrations are maintained in a saturated solution.

Ionic Concentration in Saturated Solutions

In the context of solubility equilibria, the concentration of each ion present in a saturated solution is used in calculating the solubility product. These concentrations, measured at equilibrium, directly reflect the solubility of the compound and are input into the Ksp expression according to their stoichiometric coefficients.

Solubility Product Constant (Ksp)

Ksp is the equilibrium constant for the dissolution of a sparingly soluble ionic compound, which is expressed as the product of the molar concentrations of the dissolved ions, each raised to the power of its coefficient in the balanced dissolution equation. It is a key measure of the compound’s solubility and predicts whether a precipitate will form under given conditions.

Stoichiometry of Dissolution Reactions

The stoichiometry of the dissolution reaction determines how many ions are produced per formula unit of the sparingly soluble salt and dictates the exponents used in the Ksp expression. Correctly accounting for these stoichiometric ratios is crucial for accurately calculating the solubility product and understanding the dissolution process.

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