Define 'Cryoscopic constant'. Derive the relation between elevati… - Vidyadip

Question

Define 'Cryoscopic constant'. Derive the relation between elevation of boiling point and molar mass of solute.

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Answer

Cryoscopic constant or the Molal depression constant is defined as the depression in freezing point when one mole of non-volaitile solute is dissolved in one kilogram of solvent. Its unit is K.Kg.mol-1
The elevation in the boiling point is given by the expression $\Delta T_b=K_b \cdot m$ .....(1)
The molality is given by the expression $m=\frac{W_2}{M_2 \cdot W_1} \ldots$ (2)
Substitute equation (2) in equation (1)
$\Delta T_b=K_b \cdot \frac{W_2}{M_2 \cdot W_1}$
Hence, the expression for the molar mass of the solute is
$M_2=\frac{K_b \cdot W_2}{\Delta T_b \cdot W_1}$

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