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Zirconium phosphate $[Zr_3(PO_4)_4]$ dissociates into three zirconium cations of charge $+4$ and four phosphate anions of charge $-3$. If molar solubility of zirconium phosphate is denoted by $S$ and its solubility product by $K_{sp}$ then which of the following relationship between $S$ and $K_{sp}$ is correct?
$S = {\left\{ {{K_{sp}}/144} \right\}^{1/7}}$
$S = \left\{ {{K_{sp}}/{{(6912)}^7}} \right\}$
$S = {({K_{sp}}/6912)^{1/7}}$
$S = {\{ {K_{sp}}/6912\} ^7}$
Solution
$\left(\mathrm{Zr}_{3}\left(\mathrm{PO}_{4}\right)_{4}\right] \rightarrow 3 \mathrm{Zr}^{4+}+4 \mathrm{P} \mathrm{O}_{4}^{3-}$
$3 \mathrm{S} \quad 4 \mathrm{S}$
$\mathrm{K}_{\mathrm{sp}}=(4 \mathrm{S})^{4}(3 \mathrm{S})^{3}$
$\mathrm{S}=\left(\frac{\mathrm{K}_{\mathrm{sp}}}{6912}\right)^{1 / 7}$
