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NCERT Class XI Chemistry Equilibrium Solutions

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Question : 72 of 73
Marks: +1, -0
What is the minimum volume of water required to dissolve 1 g of calcium sulphate at 298 K? (For calcium sulphate, KspK_{sp} is 9.1 × 10−610^{-6})
Solution:  
CaSO4(s)\mathrm{CaSO}_{4(s)} ⇌ Ca(aq)2++SO4(aq)2−\mathrm{Ca}^{2+}_{(aq)} + \mathrm{SO}^{2-}_{4(aq)}
If S is the solubility of CaSO4\mathrm{CaSO}_4 in mol L−1\mathrm{mol\,L^{-1}}, then
KspK_{sp} = [Ca2+]×[SO42−][\mathrm{Ca}^{2+}] \times [\mathrm{SO}^{2-}_4] = S2S^2
or , S = Ksp\sqrt{K_{sp}} = 0.1×10−6\sqrt{0.1 \times 10^{-6}} = 3.02 × 10−3 mol L−110^{-3}\,\mathrm{mol\,L^{-1}}
= 3.02 × 10−310^{-3} × 136 g L−1\mathrm{g\,L^{-1}} = 0.411 g L−1\mathrm{g\,L^{-1}}
(Molar mass of CaSO4\mathrm{CaSO}_4 = 136 g mol−1\mathrm{g\,mol^{-1}})
Thus, for dissolving 0.411 g, water required = 1 L
∴ For dissolving 1 g, water required = 10.411\frac{1}{0.411} L = 2.43 L
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