A metal M from sparingly metal sulphate. The logarithm of concentration of dissolved metal ion in a solution saturated in the metal sulphate is plotted below as a function of logarithm of concentration of sulphate ion in solution. The molecular formula of metal sulphate is $M_{x} {({SO}_{4})}_{y}$ . Then find value of z in $z \times 10^{+ 6}$ , $z = \frac{x + y}{K_{s p} o f M_{x} {(S O_{4})}_{y}}$ , x and y are minimum integer co-efficient.

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answer is 300.

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Detailed Solution

$K_{S P} = [M^{y +}] {[S O_{4}^{2 -}]}^{y} \log K_{S P} = x \log [M^{y +}] + y \log [S O_{4}^{2 -}] F r o m p l o t \log [M^{y +}] = \frac{\log K_{S P}}{x} + \frac{y}{x} \log [S O_{4}^{2 -}] \frac{y}{x} = \frac{2}{4} = \frac{1}{2} x = 2 a n d y = 1 K_{S P} = {[10^{- 2}]}^{2} \times 10^{- 8} M^{3} z = \frac{x + y}{K_{S P} o f M_{x} {(S O_{4})}_{y}} = \frac{2 + 1}{10^{- 8}} = 300 \times 10^{6}$

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