Q49 / 180 · AIIMS 2011 · Chemistry

$K_{s p}$ of $\mathrm{CaSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$ is $9 \times 10^{-6}$, find the volume for $1 \mathrm{~g}$ of $\mathrm{CaSO}_4$ (M.wt. = 136).

  • Correct answer
    A
    2.45 litre
  • B
    5.1 litre
  • C
    4.52 litre
  • D
    3.2 litre

Solution

$$ \begin{aligned} & \text { } \mathrm{CaSO}_{4(s)} \rightleftharpoons \mathrm{Ca}^{2+}{ }_{(a q)}+\mathrm{SO}_4{ }^{2-}{ }_{(a q)} \\ & S \\ & K_{s p}=S^2=9 \times 10^{-6} \\ & S=3 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \end{aligned} $$ Solubility in $\mathrm{g}$ litre $^{-1}=$ molecular mass $\times S$ $$ =136 \times 3 \times 10^{-3}=408 \times 10^{-3} \mathrm{~g} \mathrm{~L}^{-1} $$ $408 \times 10^{-3} \mathrm{~g}$ of $\mathrm{CaSO}_4$ present in 1 litre $1 \mathrm{~g}$ of $\mathrm{CaSO}_4$ present is $\frac{1}{408 \times 10^{-3}}=2.45$ litre

Hence, the correct answer is option: 'A'.

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