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Q.
After adding non-volatile solute freezing point of water decreases to $-0.186\,{}^\circ\,C$. Calculate $\Delta T_B$ if $K_f\, = \,1.86\, K\, kg\,$ $mol^{-1}$ and $K_b\, = \,0.521\, K \,kg \,mol^{-1}$
According to Raoult's law, when a non-volatile solid is added to the solvent its vapour pressure decreases and now its vapour pressure would become equal to that of solid solvent at lower temperature. Thus, the freezing point of the solvent decreases.
$\Delta T_{f} \propto m$ (m=molality of solution)
$\Delta T_{f} =K_{f} m , 0.186=1.86 \times m $
$\therefore m =0.1$
Now $\Delta T_{b}=K_{b} \times m=0.521 \times 0.1=0.0521$