20% of Acetic acid is dissociated when its 5 g is added to 500 ml of water. The depression in the freezing point of such water is_______ x 10^-3°C. Atomic mass of C, H and O are 12,1 and 16 a.m.u. respectively.
[Given : Molal depression constant and density of water are 1.86 K kg mol^-1 and 1 g cm^-3 respectively]

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Detailed Solution

Molality of given acetic acid solution is
$\begin{array}{l} = \frac{5 g}{60 g \cdot {mol}^{- 1}} \times \frac{1}{0.5 kg} \\ = \frac{1}{6} mol {kg}^{- 1} \end{array}$
Degree of dissociation = 0.2
Van’t Hoff factor $(i) = 1.2$
Depression in freezing point $({ΔT}_{f})$
$\begin{array}{l} = K_{f} . i . m \\ = (1.86) (1.2) (\frac{1}{6}) \\ = 0.372 K or 0 . 372^{\circ} C \\ = 372 \times {10^{- 3}}^{\circ} C \end{array}$

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