Question

What mass of ZnS $\left(k_{sp}=2.5\times {10}^{-22}\right)$will dissolve in 300.0 mL of 0.050M Zn(NO₃)₂? Ignore the basic properties of S^2-.

Short answer

The mass of ZnS that will dissolve in 300.0 mL of0.050M Zn(NO₃)₂ is 1.5 x 10^-19.

Step-by-step solution

Definition of mass

A measure of the amount of matter in an object is defined as mass.

Calculations

The expression for the solubility constant of ZnS is

$K_{sp}=\left[Z{n}^{2+}\right]\left[S^{2-}\right]$

Substituting the values,

$$\begin{gathered} 2.5\times {10}^{-22}=(0.05+x)x \\ x=50\times {10}^{-22}\mathrm{l} \\ x=5.0\times {10}^{-21} \end{gathered}$$

Solubility of ZnS is

$\mathit{S}\mathit{o}\mathit{l}\mathit{u}\mathit{b}\mathit{i}\mathit{l}\mathit{i}\mathit{t}\mathit{y}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{Z}\mathit{n}\mathit{S}\mathbf{=}\frac{\mathbf{m}\mathbf{a}\mathbf{s}\mathbf{s}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{Z}\mathbf{n}\mathbf{S}}{\mathbf{V}\mathbf{o}\mathbf{l}\mathbf{u}\mathbf{m}\mathbf{e}\mathbf{\left(}\mathbf{L}\mathbf{\right)}\mathbf{\times }\mathbf{M}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{ }\mathbf{m}\mathbf{a}\mathbf{s}\mathbf{s}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{Z}\mathbf{n}\mathbf{S}}$

Rearranging the formula to determine the mass of ZnS

$\mathit{m}\mathit{a}\mathit{s}\mathit{s}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{Z}\mathit{n}\mathit{S}\mathbf{=}\mathit{S}\mathit{o}\mathit{l}\mathit{u}\mathit{b}\mathit{i}\mathit{l}\mathit{i}\mathit{t}\mathit{y}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{Z}\mathit{n}\mathit{S}\mathbf{\times }\mathit{V}\mathit{o}\mathit{l}\mathit{u}\mathit{m}\mathit{e}\mathbf{\left(}\mathit{L}\mathbf{\right)}\mathbf{\times }\mathit{M}\mathit{o}\mathit{l}\mathit{a}\mathit{r}\mathbf{ }\mathit{m}\mathit{a}\mathit{s}\mathit{s}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{Z}\mathit{n}\mathit{S}$

Substituting the values,

role="math" localid="1649151932684" $$\begin{gathered} mass of ZnS=5.0\times {10}^{-21}mol/L\times 0.3 L\times 97.474 g/mol \\ mass of ZnS=146.211\times {10}^{-21} \\ \mathit{m}\mathit{a}\mathit{s}\mathit{s}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{Z}\mathit{n}\mathit{S}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{19}}\mathit{g} \end{gathered}$$