Question

A mass of 0.017 g of silver dichromate (${\mathbf{Ag}}_2{\mathbf{Cr}}_2{\mathbf{O}}_7$) will dissolve in 300 mL of water at 25°C. Calculate the solubility product constant Ksp of silver dichromate.

Short answer

The value of ${\mathrm{K}}_{\mathrm{sp}}=6.57\times {10}^{-15}$.

Step-by-step solution

Solubility

The solubility of a solution can be defined as the maximum amount of solute that can be dissolved in 100g of solvent.

For some solids, the solubility increases with the increase in temperature, and for some solids, the solubility decreases with the increase in temperature.

For some solids, the solubility is not effected by the temperature.

The solubility is measured in $\mathbf{mol}/\mathbf{L}$.

Solubility of Ag2Cr2O7

Given 0.017 g of silver dichromate dissolves in 300 mL of water.

The molar mass of ${\mathrm{Ag}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$is 431.72 g/mol.

$\begin{array}{c}\mathrm{Solubility}\left(\mathrm{s}\right)=\frac{0.017\mathrm{g}}{431.72\mathrm{g}/\mathrm{mol}}\times \frac{1}{0.300\mathrm{L}}\\ =1.18\times {10}^{-5}\mathrm{mol}/\mathrm{L}\end{array}$

 Step 3: Calculation of solubility product

The solubility of silver dichromate is as shown below:

$\begin{array}{l}{\mathrm{Ag}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7\left(\mathrm{s}\right)\rightleftharpoons 2{\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)+{\mathrm{Cr}}_2{{\mathrm{O}}_7}^{2-}\left(\mathrm{aq}\right)\\ 2\mathrm{s}\mathrm{s}\\ {\mathrm{K}}_{\mathrm{sp}}={\left(2\mathrm{s}\right)}^2\times \mathrm{s}\\ =4{\mathrm{s}}^3\\ =4{(1.18\times {10}^{-5})}^3\\ =6.57\times {10}^{-15}\end{array}$