Calculate the solubility of LaF₃ in grams per liter in (c) 0.050 M LaCl₃ 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}) for LaF_3: K_{sp} = [La^{3+}][F^{-}]^3.

Recognize that in a 0.050 M LaCl_3 solution, the concentration of La^{3+} ions is already 0.050 M due to the complete dissociation of LaCl_3.

Assume the solubility of LaF_3 is 's' mol/L. The concentration of F^{-} ions will be 3s, and the concentration of La^{3+} ions will be 0.050 + s.

Substitute these concentrations into the K_{sp} expression and solve for 's', considering that 's' is small compared to 0.050 M, so 0.050 + s \(\approx\) 0.050.

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주요 개념

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Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is a numerical value that represents the equilibrium between a solid and its ions in a saturated solution. For a salt like LaF3, Ksp is determined by the concentrations of the ions produced when the salt dissolves. Understanding Ksp is essential for calculating solubility, especially in the presence of common ions, as it helps predict how much of the salt can dissolve in a given solution.

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, the presence of LaCl3 introduces La³⁺ ions, which shifts the dissolution equilibrium of LaF3 to the left, reducing its solubility. This concept is crucial for understanding how the solubility of LaF3 is affected in a solution already containing La³⁺ ions.

Stoichiometry of Dissolution

Stoichiometry of dissolution involves understanding the ratio of ions produced when a compound dissolves. For LaF3, the dissolution can be represented as LaF3(s) ⇌ La³⁺(aq) + 3F⁻(aq). This stoichiometric relationship is important for calculating the concentrations of La³⁺ and F⁻ ions in solution, which are necessary for determining the solubility of LaF3 in the presence of LaCl3.

Calculate the solubility of LaF3 in grams per liter in (c) 0.050 M LaCl3 solution.