Question

Calculate the solubility of each of the followingcompounds in moles per liter. Ignore any acid-baseproperties.
a. Pbl₂, K_sp= 1.4 x 10^-8
b. CdCO₃, K_sp = 5.2 x 10^-12
c. Sr₃(PO₄)₂, Ks = 1 x 10^-31

Short answer

The solubility of each compound in moles per liter can be found

Step-by-step solution

Calculating the solubility of Pbl2

The dissolution equilibrium can be denoted as:

$$\begin{gathered} Pb{I}_2\left(s\right)\iff P{b}^{2+}\left(aq\right)+2I^{-}\left(aq\right) \\ {K}_{sp}=\left[P{b}^{+2}\right]{\left[I^{-}\right]}^2 \\ \left[P{b}^{+2}\right]=smol/L \\ \left[I^{-}\right]=2smol/L \\ {K}_{sp}=\left[s\right]{\left[2s\right]}^2=4s^3 \\ s=\sqrt[3]{\frac{1.4\times {10}^{-8}}{4}} \\ s=1.53\times {10}^{-3}mol/L \end{gathered}$$

Calculating the solubility of CdCO3

The dissolution equilibrium can be denoted as:

$$\begin{gathered} CdC{O}_3\left(s\right)\iff C{d}^{2+}\left(aq\right)+C{O}_3^{2-}\left(aq\right) \\ {K}_{sp}=\left[C{d}^{2+}\right]\left[C{O}_3^{2-}\right] \\ \left[C{d}^{2+}\right]=smol/L \\ \left[C{O}_3^{2-}\right]=2smol/L \\ {K}_{sp}=\left[s\right]\left[s\right]=\left[s^2\right] \\ s=\sqrt[2]{5.2\times {10}^{-12}} \\ s=2.28\times {10}^{-8}mol/L \end{gathered}$$

Calculating the solubility of Sr3(PO4)2

The dissolution equilibrium can be denoted as

$$\begin{gathered} Sr{\left(P{O}_4\right)}_2\left(s\right)\iff 3S{r}^{2+}\left(aq\right)+2P{O}_4^{3-}\left(aq\right) \\ {K}_{sp}={\left[S{r}^{2+}\right]}^3\left[P{O}_4^{3-}\right] \\ \left[S{r}^{+2}\right]=3smol/L \\ \left[P{O}_4^{3-}\right]=2smol/L \\ {K}_{sp}=\left[3s\right]{\left[2s\right]}^2=108s^5 \\ s=\sqrt[5]{K_{sp/108}} \\ s=\sqrt[5]{1\times {10}^{-31}}/108 \\ s=2.47\times {10}^{-7}mol/L \end{gathered}$$