Question

1. the value of the solubility product constant, ksp, for silver carbonate is $8.1 \times 10^{-12}$ at $25^\circ$c.

a. write the chemical equation associated with the solubility-product constant of $ag_2co_3$.
b. calculate the value of $ag^+$ in 100 ml of a saturated solution of $ag_2co_3$ at $25^\circ$c.

Explanation:

Step1: Write dissolution equilibrium equation

$\text{Ag}_2\text{CO}_3(s)
ightleftharpoons 2\text{Ag}^+(aq) + \text{CO}_3^{2-}(aq)$

Step2: Define solubility variable

Let $s = [\text{CO}_3^{2-}]$, so $[\text{Ag}^+] = 2s$

Step3: Substitute into Ksp expression

$K_{sp} = [\text{Ag}^+]^2[\text{CO}_3^{2-}] = (2s)^2(s) = 4s^3$

Step4: Solve for s

$4s^3 = 8.1 \times 10^{-12}$
$s^3 = \frac{8.1 \times 10^{-12}}{4} = 2.025 \times 10^{-12}$
$s = \sqrt[3]{2.025 \times 10^{-12}} \approx 1.265 \times 10^{-4}$

Step5: Calculate $[\text{Ag}^+]$

$[\text{Ag}^+] = 2s = 2 \times 1.265 \times 10^{-4}$

Answer:

a. $\text{Ag}_2\text{CO}_3(s)
ightleftharpoons 2\text{Ag}^+(aq) + \text{CO}_3^{2-}(aq)$
b. $2.53 \times 10^{-4}\ \text{mol/L}$