Chemical and Ionic Equilibrium 2 Question 5
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5. If solubility product of $\mathrm{Zr}{3}\left(\mathrm{PO}{4}\right){4}$ is denoted by $K{\mathrm{sp}}$ and its molar solubility is denoted by $S$, then which of the following relation between $S$ and $K_{\text {sp }}$ is correct? (2019 Main, 8 April I)
======= ####5. If solubility product of $\mathrm{Zr}{3}\left(\mathrm{PO}{4}\right){4}$ is denoted by $K{\mathrm{sp}}$ and its molar solubility is denoted by $S$, then which of the following relation between $S$ and $K_{\text {sp }}$ is correct? (2019 Main, 8 April I)
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed (a) $S=\left(\frac{K_{\mathrm{sp}}}{144}\right)^{1 / 6}$
(b) $S=\left(\frac{K_{\mathrm{sp}}}{6912}\right)^{1 / 7}$
(c) $S=\left(\frac{K_{\mathrm{sp}}}{929}\right)^{1 / 9}$
(d) $S=\left(\frac{K_{\mathrm{sp}}}{216}\right)^{1 / 7}$
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Answer:
Correct Answer: 5. (a)
Solution:
- Key Idea The concentration of a substance in a saturated solution is defined as its solubility $(S)$.
For $A_{x} B_{y} \rightleftharpoons x A^{y+}+y B^{x-} ; K_{s p}=\left[A^{y+}\right]^{x}\left[B^{x-}\right]^{y}$
For, $\mathrm{Zr}{3}\left(\mathrm{PO}{4}\right)_{4}$,
$$ \begin{aligned} & \mathrm{Zr}{3}\left(\mathrm{PO}{4}\right){4}(s) \rightleftharpoons \underset{3 S \mathrm{M}}{3 \mathrm{Zr}^{4+}}(a q)+\underset{4 \mathrm{SM}}{4 \mathrm{PO}{4}^{3-}(a q)} \ & \quad K_{\mathrm{sp}}=\left[\mathrm{Zr}^{4+}\right]^{3}\left[\mathrm{PO}{4}^{3-}\right]^{4} \ & \quad K{\mathrm{sp}}=(3 S)^{3}(4 S)^{4}=6912 S^{7} \text { or } S=\left(\frac{K_{\mathrm{sp}}}{6912}\right)^{\frac{1}{7}} \end{aligned} $$
Thus, the relation between molar solubility $(S)$ and solubility product $\left(K_{\text {sp }}\right)$ will be
$$ S=\left(\frac{K_{\mathrm{sp}}}{6912}\right)^{1 / 7} $$
