The ionization constant of benzoic acid is 6.46 × 10–5 and Ksp for silver benzoate is 2.5 × 10–13. How many times is silver benzoate more soluble in a buffer of pH 3.19 compared to its solubility in pure water?
Solution and Explanation
Since pH = 3.19,
Let the solubility of C6H5COOAg be x mol/L.
Then,
Thus, the solubility of silver benzoate in a pH 3.19 solution is 1.66 × 10-6 mol/L. Now, let the solubility of C6H5COOAg be x' mol/L.
Then [Ag+]=x'M and [CH3COO-]=x'M
\(K_{sp}=[Ag^+][CH3COO^-]\)
\(K_{sp}=(x')^2\)
\(x'=\sqrt{K_{sp}}=\sqrt{2.5\times10^{-13}}=5\times10^{-7}\,mol/L\)
\(\therefore \,\frac{x}{x'}=\frac{1.66\times10^{-6}}{5\times10^{-7}}=3.32\)
Hence, C6H5COOAg is approximately 3.317 times more soluble in a low-pH solution.
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Concepts Used:
Equilibrium Constant
The equilibrium constant may be defined as the ratio between the product of the molar concentrations of the products to that of the product of the molar concentrations of the reactants with each concentration term raised to a power equal to the stoichiometric coefficient in the balanced chemical reaction.
The equilibrium constant at a given temperature is the ratio of the rate constant of forwarding and backward reactions.
Equilibrium Constant Formula:
Kequ = kf/kb = [C]c [D]d/[A]a [B]b = Kc
where Kc, indicates the equilibrium constant measured in moles per litre.
For reactions involving gases: The equilibrium constant formula, in terms of partial pressure will be:
Kequ = kf/kb = [[pC]c [pD]d]/[[pA]a [pB]b] = Kp
Where Kp indicates the equilibrium constant formula in terms of partial pressures.
- Larger Kc/Kp values indicate higher product formation and higher percentage conversion.
- Lower Kc/Kp values indicate lower product formation and lower percentage conversion.
Medium Kc/Kp values indicate optimum product formation.
Units of Equilibrium Constant:
The equilibrium constant is the ratio of the concentrations raised to the stoichiometric coefficients. Therefore, the unit of the equilibrium constant = [Mole L-1]△n.
where, ∆n = sum of stoichiometric coefficients of products – a sum of stoichiometric coefficients of reactants.