Question

Solubility product of $AgCl$ is $2.8×10^{−10}$ at $25^{∘}C.$ Calculate solubility of the salt in $0.1MAgN{O}_3$ solution

• A. $2.8×10^{−9}$ mol / liter
• B. $2.8×10^{−10}$mol / liter
• C. $3.2×10^{−9}$ mol / liter
• D. $3.2×10^{−12}$ mol /liter

Answer 1

Answer: (A)

In $0.1MAgN{O}_3$
$AgN{O}_3⇌A{g}^{+}+N{O}_3^{−}$
$AgCl⇌A{g}^{+}+C{l}^{−}$
$K_{sp}=\left[A{g}^{+}\right]\left[C{l}^{−}\right]$
Now $\left[A{g}^{+}\right]$ can be taken as $\left[AgN{O}_3\right]$ while $[C{l}^{−}]$ is the solubility of $AgCl$
$∴Cl=\frac{K_{sp}}{\left[A{g}^{+}\right]}=\frac{2.8×10^{−10}}{0.1}$
$∴$ Solubility of $AgCl=2.8×10^{−9}$ mol liter.