Question

Consider a sparingly soluble salt, zirconium phosphate $\left[Z{r}_3\right(P{O}_4{)}_4]$. If molar solubility of zirconium phosphate is denoted by $s$ and its solubility product by $K_{sp}$ , then which of the following relationship holds true?

• A. $s={\left(\frac{K_{sp}}{144}\right)}^{\frac{1}{7}}$
• B. $s={\left(\frac{K_{sp}}{144}\right)}^7$
• C. $s={\left(\frac{K_{sp}}{6912}\right)}^{\frac{1}{7}}$
• D. $s={\left(\frac{K_{sp}}{6912}\right)}^7$

Answer 1

The correct option is C $s={\left(\frac{K_{sp}}{6912}\right)}^{\frac{1}{7}}$

The dissociation equation at equilibrium is :

$\left[\right(Zr{)}_3\left(P{O}_4{)}_4\right]\left(s\right)\rightleftharpoons 3Z{r}^{4+}\left(aq\right)+4P{O}_4^{3-}\left(aq\right)Equilibrium:C-s3s4s$

Solubility of Zirconium Phosphate = s
$\left[Z{r}^{4+}\right]=3s$
$\left[P{O}_4^{3-}\right]=4s$
$\therefore K_{sp}=\left[Z{r}^{4+}{]}^3\right[P{O}_4^{-3}{]}^4$

$K_{sp}=(3s{)}^3\times (4s{)}^4$

$K_{sp}=6912\times s^7$

$s={\left(\frac{K_{sp}}{6912}\right)}^{\frac{1}{7}}$