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Question
A sparingly soluble salt having general formula \[\ce{A^{p+}_x B^{q-}_y}\] and molar solubility S is in equilibrium with its saturated solution. Derive a relationship between the solubility and solubility product for such salt.
Solution
The equation can be written as-
\[\ce{A^{p+}_x B^{q-}_y ⇌ xA^{p+} (aq) + yB^{q-} (aq)}\]
S moles of A and B dissolves to give x S moles of Ap+ and y Bq-.
\[\ce{K_{sp} = [A^{p+}] [Bq^{-}]^y}\]
= `[x^5]^x [y^5]^y`
= `x^{x}y^{y} 5^{x + y}`
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