Calculate the solubility of LaF₃ in grams per liter in (b) 0.010 M KF solution.

검증된 단계별 안내

Identify the dissolution reaction of LaF_3: LaF_3(s) \(\rightleftharpoons\) La^{3+}(aq) + 3F^{-}(aq).

Write the expression for the solubility product constant (K_{sp}) of LaF_3: K_{sp} = [La^{3+}][F^{-}]^3.

Recognize that the presence of KF provides a common ion (F^-), which affects the solubility of LaF_3. The concentration of F^- from KF is 0.010 M.

Assume the solubility of LaF_3 is 's' mol/L. Then, [La^{3+}] = s and [F^-] = 0.010 + 3s.

Substitute these concentrations into the K_{sp} expression and solve for 's', considering that 3s is negligible compared to 0.010 M.

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주요 개념

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Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For LaF3, Ksp can be used to determine how much of the compound can dissolve in a given solution, which is essential for calculating its solubility in the presence of other ions.

Common Ion Effect

The common ion effect refers to the decrease in solubility of a salt when a common ion is added to the solution. In this case, adding KF introduces F- ions, which shifts the equilibrium of LaF3 dissolution to the left, reducing its solubility. Understanding this effect is crucial for calculating the solubility of LaF3 in a KF solution, as it directly influences the concentration of La3+ and F- ions in equilibrium.

Stoichiometry of Dissolution

Stoichiometry of dissolution involves understanding the molar ratios of the ions produced when a salt dissolves in water. For LaF3, the dissolution can be represented as LaF3(s) ⇌ La3+(aq) + 3F-(aq). This stoichiometric relationship is vital for calculating the concentrations of La3+ and F- ions in solution, which are necessary for applying Ksp and determining the solubility in the presence of a common ion.

Calculate the solubility of LaF3 in grams per liter in (b) 0.010 M KF solution.