Cadmium(11) chloride is added to a solution of potassium...

Cadmium(11) chloride is added to a solution of potassium hydroxide with a pH of 9.62. $\left(K_{\mathrm{sp}} \mathrm{Cd}(\mathrm{OH})_{2}=2.5 \times 10^{-14}\right)$ (a) At what concentration of $\mathrm{Cd}^{2+}$ does a precipitate first start to form? (b) Enough cadmium(II) chloride is added to make $\left[\mathrm{Cd}^{2+}\right]=0.0013 \mathrm{M}$. What is the $\mathrm{pH}$ of the resulting solution? (c) What percentage of the original hydroxide ion is left in solution?

Cadmium(11) chloride is added to a solution of potassium hydroxide with a pH of 9.62. $\left(K_{\mathrm{sp}} \mathrm{Cd}(\mathrm{OH})_{2}=2.5 \times 10^{-14}\right)$
(a) At what concentration of $\mathrm{Cd}^{2+}$ does a precipitate first start to form?
(b) Enough cadmium(II) chloride is added to make $\left[\mathrm{Cd}^{2+}\right]=0.0013 \mathrm{M}$. What is the $\mathrm{pH}$ of the resulting solution?
(c) What percentage of the original hydroxide ion is left in solution?

Key Concepts

Equilibrium Calculations

Equilibrium calculations involve setting up and solving equations based on the equilibrium constant expressions, such as the Ksp expression for solubility equilibria. These calculations often involve logarithmic transformations when dealing with pH and pOH, and are fundamental for predicting how changes in concentrations affect the position of equilibrium in reactions involving precipitation and dissolution.

Reaction Stoichiometry in Precipitation

Reaction stoichiometry in the context of precipitation involves the quantitative relationship between the reactants and the resulting precipitate as governed by the chemical equation. It is important for determining how much of one ion must be present relative to another for a precipitate to start forming, and for calculating the amounts of substances consumed or remaining at equilibrium.

Solubility Product Constant (Ksp)

The solubility product constant is the equilibrium constant that applies to the dissolution of a sparingly soluble ionic compound. It is the product of the molar concentrations of the ions in solution, each raised to the power of its coefficient in the dissociation equation. This concept is crucial for predicting whether a precipitate will form when ions are combined in solution, as precipitation occurs when the ion product exceeds the Ksp.

Precipitation Equilibrium

Precipitation equilibrium refers to the dynamic balance that exists when the rate of formation of a solid precipitate equals the rate of its dissolution. Understanding this equilibrium helps predict at what ion concentrations a solid begins to form, and it plays a key role in manipulating conditions in order to either precipitate or dissolve compounds in solution.

pH and pOH Relationship

The pH and pOH concepts describe the acidity and basicity of a solution, respectively, and are related by the equation pH + pOH = 14 at 25°C. This relationship allows for the conversion between hydrogen ion and hydroxide ion concentrations, which is essential for calculations involving the pH of solutions and understanding the behavior of bases and acids in various chemical reactions.

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