Silver oxalate, Ag2C2O4, is slightly soluble in water. In the saturated solution the oxalate ion concentration is 1.1 x 10-4 M. What is the Ksp for Ag2C2O4?
The Correct Answer and Explanation is :
To calculate the solubility product constant (Ksp) for silver oxalate (Ag₂C₂O₄), we need to follow these steps:
Step 1: Write the Dissolution Equation
The dissolution of silver oxalate in water can be represented as follows: Ag2C2O4(s)⇌2Ag+(aq)+C2O42−(aq)\text{Ag}_2\text{C}_2\text{O}_4 (s) \rightleftharpoons 2\text{Ag}^+ (aq) + \text{C}_2\text{O}_4^{2-} (aq)
Step 2: Set Up the Expression for Ksp
The solubility product (Ksp) is the product of the concentrations of the ions produced in the dissolution, each raised to the power of their stoichiometric coefficients. For silver oxalate, the expression for Ksp is: Ksp=[Ag+]2[C2O42−]K_{sp} = [\text{Ag}^+]^2[\text{C}_2\text{O}_4^{2-}]
Step 3: Use the Given Oxalate Ion Concentration
From the problem, the concentration of the oxalate ion [C2O42−][ \text{C}_2\text{O}_4^{2-} ] is given as 1.1×10−4 M1.1 \times 10^{-4} \, \text{M}. Since two moles of silver ions are produced for every mole of oxalate ion in the dissociation of silver oxalate, the concentration of silver ions [Ag+][ \text{Ag}^+ ] will be twice the concentration of oxalate ions: [Ag+]=2×[C2O42−]=2×1.1×10−4 M=2.2×10−4 M[\text{Ag}^+] = 2 \times [\text{C}_2\text{O}_4^{2-}] = 2 \times 1.1 \times 10^{-4} \, \text{M} = 2.2 \times 10^{-4} \, \text{M}
Step 4: Substitute into the Ksp Expression
Now that we have the concentrations of both ions, we can substitute them into the Ksp expression: Ksp=(2.2×10−4)2×(1.1×10−4)K_{sp} = (2.2 \times 10^{-4})^2 \times (1.1 \times 10^{-4})
Step 5: Calculate the Ksp
Ksp=(4.84×10−8)×(1.1×10−4)=5.324×10−12K_{sp} = (4.84 \times 10^{-8}) \times (1.1 \times 10^{-4}) = 5.324 \times 10^{-12}
Final Answer:
The Ksp for Ag₂C₂O₄ is approximately 5.3×10−125.3 \times 10^{-12}.
Explanation:
To summarize, the Ksp of a sparingly soluble compound like silver oxalate reflects the equilibrium concentrations of its ions in solution. The solubility of Ag₂C₂O₄ in water is quite low, with the concentration of both silver and oxalate ions being relatively small. The Ksp value, a product of these concentrations raised to the power of their respective coefficients in the dissolution equation, quantifies the extent to which the compound dissolves in water. The higher the Ksp, the more soluble the compound; conversely, a low Ksp indicates low solubility, which is the case here for silver oxalate.