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Ch.18 - Aqueous Ionic Equilibrium
All textbooksTro 6th EditionCh.18 - Aqueous Ionic EquilibriumProblem 102b
Chapter 18, Problem 102b

Calculate the molar solubility of MX (Ksp = 1.27⨉10-36) in each liquid or solution. b. 0.25 M MCl2

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Step 1: Understand the dissolution process of MX in water. The dissolution of MX can be represented as: \[ \text{MX} \rightleftharpoons \text{M}^{2+} + \text{X}^{-} \]
Step 2: Write the expression for the solubility product constant (Ksp) for MX. The expression is: \[ K_{sp} = [\text{M}^{2+}][\text{X}^{-}] \]
Step 3: Consider the common ion effect due to the presence of 0.25 M MCl2. Since MCl2 dissociates completely, it contributes 0.25 M of \( \text{M}^{2+} \) ions to the solution.
Step 4: Let the molar solubility of MX be \( s \). The concentration of \( \text{M}^{2+} \) ions from MX will be \( s \), but due to the common ion effect, the total concentration of \( \text{M}^{2+} \) ions will be \( 0.25 + s \). The concentration of \( \text{X}^{-} \) ions will be \( s \).
Step 5: Substitute these concentrations into the Ksp expression: \[ K_{sp} = (0.25 + s)(s) \]. Since \( K_{sp} \) is very small, assume \( s \) is much smaller than 0.25, simplifying the expression to \[ K_{sp} \approx 0.25s \]. Solve for \( s \) to find the molar solubility.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Solubility

Molar solubility refers to the maximum amount of a solute that can dissolve in a given volume of solvent at equilibrium, expressed in moles per liter (M). It is a crucial concept in understanding how substances dissolve and is often determined using the solubility product constant (Ksp) for sparingly soluble salts.
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Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that quantifies the solubility of a sparingly soluble ionic compound. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced dissolution equation. A lower Ksp value indicates lower solubility.
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Common Ion Effect

The common ion effect describes the decrease in solubility of a salt when a common ion is added to the solution. In this case, the presence of MCl2 introduces the ion M+, which shifts the equilibrium of the dissolution reaction of MX, reducing its molar solubility due to Le Chatelier's principle.
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