Question

Order the following solids (a-d) from least soluble to most soluble. Ignore any potential reactions of the ions with water.

1. $\mathbf{AgCl}{\mathbf{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}$
2. ${\mathbf{Ag}}_{\mathbf{2}}\mathbf{S}{\mathbf{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{49}}$
3. ${\mathbf{CaF}}_{\mathbf{2}}{\mathbf{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{11}}$
   
4. $\mathbf{CuS}{\mathbf{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{45}}$

Short answer

The order of solubility from least to most is $\mathrm{CuS}<{\mathrm{Ag}}_2\mathrm{S}<\mathrm{AgCl}<{\mathrm{CaF}}_2$.

Step-by-step solution

Definition of solubility

The maximum amount of a substance that will dissolve in a given amount of solvent at a specified temperature is defined as solubility

Subpart (a)

The solubility values for the given sparingly salts are calculated as

For AgCl,

$\mathrm{AgCl}\rightleftharpoons {\mathrm{Ag}}^{+}+{\mathrm{Cl}}^{-}$

S	-	-
-	S	S

The solubility expression is

$\begin{array}{l}{\mathrm{K}}_{\mathrm{sp}}=\mathrm{S}\times \mathrm{S}\\ {\mathrm{S}}^2=1.6\times {10}^{-10}\\ \mathrm{S}=\sqrt{1.6\times {10}^{-10}}\\ \mathrm{S}=8\times {10}^{-6}\end{array}$

Subpart (b)

For ${\mathrm{Ag}}_2\mathrm{S}$,

${\mathrm{Ag}}_2\mathrm{S}\rightleftharpoons 2{\mathrm{Ag}}^{+}+{\mathrm{S}}^{2-}$

S	-	-
-	2S	S

The solubility expression is

$\begin{array}{l}{\mathrm{K}}_{\mathrm{sp}}={\left(2\mathrm{S}\right)}^2\times \mathrm{S}\\ {\mathrm{K}}_{\mathrm{sp}}=4{\mathrm{S}}^3\\ 4{\mathrm{S}}^3=1.6\times {10}^{-49}\\ \mathrm{S}=3.42\times {10}^{-17}\end{array}$

Subpart (c)

For ${\mathrm{CaF}}_2$

${\mathrm{CaF}}_2\rightleftharpoons {\mathrm{Ca}}^{2+}+2{\mathrm{F}}^{-}$

${\mathrm{CaF}}_2\rightleftharpoons {\mathrm{Ca}}^{2+}+2{\mathrm{F}}^{-}$
S	-	-
-	S	2S

The solubility expression is

$\begin{array}{l}{\mathrm{K}}_{\mathrm{sp}}=\mathrm{S}\times {\left(2\mathrm{S}\right)}^2\\ {\mathrm{K}}_{\mathrm{sp}}=4{\mathrm{S}}^3\\ 4{\mathrm{S}}^3=4\times {10}^{-11}\\ \mathrm{S}=2.15\times {10}^{-4}\end{array}$

Subpart (d)

For $CuS$

$\mathrm{CuS}\rightleftharpoons {\mathrm{Cu}}^{2+}+{\mathrm{S}}^{2-}$

$\mathrm{CuS}\rightleftharpoons {\mathrm{Cu}}^{2+}+{\mathrm{S}}^{2-}$
S	-	-
-	S	S

The solubility expression is

$\begin{array}{l}{\mathrm{K}}_{\mathrm{sp}}={\mathrm{S}}^2\\ {\mathrm{S}}^2=8.5\times {10}^{-45}\\ \mathrm{S}=9.21\times {10}^{-23}\end{array}$

The order of solubility.

By the above calculations, the order of solubility from least to most is

$\mathbf{CuS}\mathbf{<}{\mathbf{Ag}}_{\mathbf{2}}\mathbf{S}\mathbf{<}\mathbf{AgCl}\mathbf{<}{\mathbf{CaF}}_{\mathbf{2}}$.