If the solubility product of Zr_3(PO_4)_4 is | vedclass

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(A) The dissociation of $Zr_3(PO_4)_4$ is given by: $Zr_3(PO_4)_{4(s)} \rightleftharpoons 3Zr^{4+}{(aq)} + 4PO_4^{3-}{(aq)}$.
Let the molar solubilit

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$S = (K_{SP} / 6912)^{1/7}$

Vedclass · Answer

(A) The dissociation of $Zr_3(PO_4)_4$ is given by: $Zr_3(PO_4)_{4(s)} \rightleftharpoons 3Zr^{4+}{(aq)} + 4PO_4^{3-}{(aq)}$.
Let the molar solubility be $S$. Then the concentrations of the ions are $[Zr^{4+}] = 3S$ and $[PO_4^{3-}] = 4S$.
The solubility product expression is $K_{SP} = [Zr^{4+}]^3 [PO_4^{3-}]^4$.
Substituting the values: $K_{SP} = (3S)^3 \cdot (4S)^4 = (27S^3) \cdot (256S^4) = 6912S^7$.
Solving for $S$: $S^7 = K_{SP} / 6912$,which gives $S = (K_{SP} / 6912)^{1/7}$.

If the solubility product of $Zr_3(PO_4)_4$ is denoted by $K_{SP}$ and its molar solubility is denoted by $S$,then which of the following relations between $S$ and $K_{SP}$ is correct?

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