Silver chromate is sparingly soluble in aqueous solutions. The Ksp of Ag2CrO4 is 1.12×10-12. What is the solubility (in mol/L) of silver chromate in 1.10M potassium chromate aqueous solution? What is the solubility (in mol/L) of silver chromate in 1.10M silver nitrate aqueous solution? What is the solubility (in mol/L) of silver chromate in pure water?
The Correct Answer and Explanation is:
To find the solubility of silver chromate (Ag₂CrO₄) under various conditions, we use its solubility product constant (Ksp):
$$
K_{sp} = [Ag^+]^2[CrO_4^{2-}] = 1.12 \times 10^{-12}
$$
1. Solubility in pure water:
Let solubility = s mol/L
Then:
- $[Ag^+] = 2s$
- $[CrO_4^{2-}] = s$
Substitute into the Ksp expression:
$$
K_{sp} = (2s)^2(s) = 4s^3
$$
$$
1.12 \times 10^{-12} = 4s^3
\Rightarrow s^3 = \frac{1.12 \times 10^{-12}}{4} = 2.8 \times 10^{-13}
\Rightarrow s = \sqrt[3]{2.8 \times 10^{-13}} \approx 6.54 \times 10^{-5} \text{ mol/L}
$$
✅ Solubility in pure water = 6.54 × 10⁻⁵ mol/L
2. Solubility in 1.10 M K₂CrO₄:
K₂CrO₄ fully dissociates, providing $[CrO_4^{2-}] = 1.10$ M. Let the solubility of Ag₂CrO₄ be s mol/L:
- $[Ag^+] = 2s$
- $[CrO_4^{2-}] \approx 1.10$ M (common ion)
Substitute into Ksp:
$$
K_{sp} = (2s)^2(1.10) = 4s^2(1.10)
\Rightarrow 1.12 \times 10^{-12} = 4.4s^2
\Rightarrow s^2 = \frac{1.12 \times 10^{-12}}{4.4} = 2.545 \times 10^{-13}
\Rightarrow s = \sqrt{2.545 \times 10^{-13}} \approx 1.59 \times 10^{-7} \text{ mol/L}
$$
✅ Solubility in 1.10 M K₂CrO₄ = 1.59 × 10⁻⁷ mol/L
3. Solubility in 1.10 M AgNO₃:
AgNO₃ fully dissociates, providing $[Ag^+] = 1.10$ M. Let the solubility of Ag₂CrO₄ be s mol/L:
- $[CrO_4^{2-}] = s$
- $[Ag^+] = 1.10 + 2s \approx 1.10$ (since s is small)
Substitute into Ksp:
$$
K_{sp} = (1.10)^2(s) = 1.21s
\Rightarrow s = \frac{1.12 \times 10^{-12}}{1.21} \approx 9.26 \times 10^{-13} \text{ mol/L}
$$
✅ Solubility in 1.10 M AgNO₃ = 9.26 × 10⁻¹³ mol/L
Explanation (Summary)
Silver chromate (Ag₂CrO₄) is a sparingly soluble salt. Its solubility is governed by its Ksp, which is an equilibrium constant describing the extent to which it dissolves into its ions. When no additional ions are present, we use the stoichiometry of dissociation to calculate solubility directly, finding it to be 6.54 × 10⁻⁵ mol/L in pure water.
However, the solubility significantly decreases in solutions containing common ions due to the common ion effect. In 1.10 M K₂CrO₄, the high concentration of chromate ions suppresses dissolution of Ag₂CrO₄, reducing its solubility to 1.59 × 10⁻⁷ mol/L. In 1.10 M AgNO₃, the abundant silver ions create an even stronger suppression, dropping solubility further to 9.26 × 10⁻¹³ mol/L. This illustrates how ionic equilibria shift in response to the surrounding environment—a fundamental principle in solution chemistry.