Question

The concentration of Ag⁺ in a solution saturated withAg₂C₂O₄(s) is 2.2 x 10^-4 M. Calculate K_sp for Ag₂C₂O₄.

Short answer

Thevalue of K_sp can be found as$5.32\times {10}^{-12}$

Step-by-step solution

Solubility

The solubility can be represented with mol./L. The given silver salt’s solubility is$2.2\times {10}^{-4}mol/L$

Calculating the value of Ksp

The dissolution equilibrium can be denoted as

$$\begin{gathered} A{g}_2{C}_2{O}_4\left(s\right)\iff 2A{g}^{+}\left(aq\right)+C_2{O_4}^{2-}\left(aq\right) \\ {K}_{sp}={\left[A{g}^{+}\right]}^2\left[C_2{O_4}^{-}\right] \\ \left[A{g}^{+}\right]=smol/L \\ \left[C_2{O_4}^{-}\right]=s/2mol/L \\ {K}_{sp}={\left[s\right]}^2\left[s/2\right]=s^3/2 \\ {K}_{sp}=\frac{{\left[2.2\times {10}^{-4}\right]}^3}{2} \\ {K}_{sp}=5.32\times {10}^{-12} \end{gathered}$$