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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?

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

$S = {\{K_{sp} / 144\}}^{1 / 7}$

$S = {\{K_{co} / 6912\}}^{1 / 7}$

$S = {\{K_{sp} / 6912\}}^{7}$

answer is C.

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Detailed Solution

$[{Zr}_{3} {({PO}_{4})}_{4}] ⇌ 3 {Zr}^{4 +} + 4 {PO}_{4}^{3 -} K_{sp} = (3 S)^{3} (4 S)^{4} = 27 S^{3} \times 256 S^{4} = 6912 S^{7} ∴ S = {(\frac{K_{sp}}{6912})}^{1 / 7}$

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