Question

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

a. $\mathit{A}\mathit{g}\mathit{C}\mathit{l}\mathbf{}\mathbf{}\mathbf{}{\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}$

b.$\mathit{A}{\mathit{g}}_{\mathbf{2}}\mathit{S}\mathbf{}\mathbf{}{\mathit{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{49}}$

c.$\mathit{C}\mathit{a}{\mathit{F}}_{\mathbf{2}}\mathbf{}\mathbf{}{\mathit{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{11}}$

d.$\mathit{C}\mathit{u}\mathit{S}\mathbf{}\mathbf{}\mathbf{}{\mathit{K}}_{\mathbf{sp}}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{45}}$

Short answer

Answer

The order of solubility from least to most is $\mathit{C}\mathit{u}\mathit{S}\mathbf{<}\mathit{A}{\mathit{g}}_{\mathbf{2}}\mathit{S}\mathbf{<}\mathit{A}\mathit{g}\mathit{C}\mathit{l}\mathbf{<}\mathit{C}\mathit{a}{\mathit{F}}_{\mathbf{2}}$.

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,

$\mathit{A}\mathit{g}\mathit{C}\mathit{l}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}{\mathit{g}}^{\mathbf{+}}\mathbf{}\mathbf{}\mathbf{+}\mathit{C}{\mathit{l}}^{\mathbf{-}}$

$\mathit{A}\mathit{g}\mathit{C}\mathit{l}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{A}{\mathit{g}}^{\mathbf{+}}\mathbf{}\mathbf{}\mathbf{+}\mathit{C}{\mathit{l}}^{\mathbf{-}}$
S	-	-
-	S	S

The solubility expression is

$$\begin{gathered} {\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}\mathit{S}\mathbf{\times }\mathit{S} \\ {\mathit{S}}^{\mathbf{2}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}} \\ \mathit{S}\mathbf{=}\sqrt{\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}} \\ \mathit{S}\mathbf{=}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}} \end{gathered}$$

Subpart (b)

For $\mathit{A}{\mathit{g}}_{\mathbf{2}}\mathit{S}$,

$\mathit{A}{\mathit{g}}_{\mathbf{2}}\mathit{S}\mathbf{}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{2}\mathit{A}{\mathit{g}}^{\mathbf{+}}\mathbf{}\mathbf{}\mathbf{}\mathbf{+}{\mathit{S}}^{\mathbf{2}\mathbf{-}}$

$\mathit{A}{\mathit{g}}_{\mathbf{2}}\mathit{S}\mathbf{}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{2}\mathit{A}{\mathit{g}}^{\mathbf{+}}\mathbf{}\mathbf{}\mathbf{}\mathbf{+}{\mathit{S}}^{\mathbf{2}\mathbf{-}}$
S	-	-
-	2S	S

The solubility expression is

$$\begin{gathered} {\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}{\left(2S\right)}^{\mathbf{2}}\mathbf{\times }\mathit{S} \\ {\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}\mathbf{4}{\mathit{S}}^{\mathbf{3}} \\ \mathbf{4}{\mathit{S}}^{\mathbf{3}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{49}} \\ \mathit{S}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{42}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{17}} \end{gathered}$$

Subpart (c)

For $\mathit{C}\mathit{a}{\mathit{F}}_{\mathbf{2}}$

$\mathit{C}\mathit{a}{\mathit{F}}_{\mathbf{2}}\mathbf{}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathit{C}{\mathit{a}}^{\mathbf{2}\mathbf{+}}\mathbf{}\mathbf{}\mathbf{+}\mathbf{2}{\mathit{F}}^{\mathbf{-}}$

$\mathit{C}\mathit{a}{\mathit{F}}_{\mathbf{2}}\mathbf{}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathit{C}{\mathit{a}}^{\mathbf{2}\mathbf{+}}\mathbf{}\mathbf{}\mathbf{+}\mathbf{2}{\mathit{F}}^{\mathbf{-}}$
S	-	-
-	S	2S

The solubility expression is

$$\begin{gathered} {\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}\mathit{S}\mathbf{\times }{\left(2S\right)}^{\mathbf{2}} \\ {\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}\mathbf{4}{\mathit{S}}^{\mathbf{3}} \\ \mathbf{4}{\mathit{S}}^{\mathbf{3}}\mathbf{=}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{11}} \\ \mathit{S}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{15}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}} \end{gathered}$$

Subpart (d)

For $\mathit{C}\mathit{u}\mathit{S}$

$\mathit{C}\mathit{u}\mathit{S}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathit{C}{\mathit{u}}^{\mathbf{2}\mathbf{+}}\mathbf{}\mathbf{+}{\mathit{S}}^{\mathbf{2}\mathbf{-}}$

$\mathit{C}\mathit{u}\mathit{S}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathit{C}{\mathit{u}}^{\mathbf{2}\mathbf{+}}\mathbf{}\mathbf{+}{\mathit{S}}^{\mathbf{2}\mathbf{-}}$
S	-	-
-	S	S

The solubility expression is

$$\begin{gathered} {\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}{\mathit{S}}^{\mathbf{2}} \\ {\mathit{S}}^{\mathbf{2}}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{45}} \\ \mathit{S}\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{21}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{23}} \end{gathered}$$

The order of solubility.

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

$\mathit{C}\mathit{u}\mathit{S}\mathbf{<}\mathit{A}{\mathit{g}}_{\mathbf{2}}\mathit{S}\mathbf{<}\mathit{A}\mathit{g}\mathit{C}\mathit{l}\mathbf{<}\mathit{C}\mathit{a}{\mathit{F}}_{\mathbf{2}}$.