Question

If solubility product of $Z{r}_3(P{O}_4{)}_4$ is denoted by $K_{sp}$ and its molar solubility is denoted by S, then which of the following relation between S and $K_{sp}$ is correct?

• A. $S={\left(\frac{K_{sp}}{144}\right)}^{1/6}$
• B. $S={\left(\frac{K_{sp}}{6912}\right)}^{1/7}$
• C. $S={\left(\frac{K_{sp}}{929}\right)}^{1/9}$
• D. $S={\left(\frac{K_{sp}}{216}\right)}^{1/7}$

Answer 1

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

$Z{r}_3\left(P{O}_4{)}_4\right(s)\rightleftharpoons \underset{3S}{3Z{r}^{4+}(aq.)}+\underset{4S}{4P{O}_4^{3-}}(aq.)$
Solubility product is given by
$K_{sp}=\left[Z{r}^{4+}{]}^3\right[P{O}_4^{3-}{]}^4$
$K_{sp}=\left(3S{)}^3\right(4S{)}^4$
$K_{sp}=6912S^7$
$S={\left(\frac{K_{sp}}{6912}\right)}^{1/7}$