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What is the solubility of ${(A^{x +})}_{y} {(B^{y -})}_{x}$ in water at 298 K?

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${(\frac{x^{x} . y^{y}}{K_{sp}})}^{\frac{1}{x + y}}$

${(\frac{K_{sp}}{x^{x} + y^{y}})}^{\frac{1}{xy}}$

${(\frac{K_{sp}}{x^{x} . y^{y}})}^{x + y}$

${(\frac{K_{sp}}{x^{x} . y^{y}})}^{\frac{1}{x + y}}$

answer is B.

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Detailed Solution

If S is solubility,

$K_{sp} = x^{x} . y^{y} . S^{x + y}$

$S^{x + y} = \frac{K_{sp}}{x^{x} . y^{y}}$

$S = {(\frac{K_{sp}}{x^{x} . y^{y}})}^{\frac{1}{x + y}}$

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