Question

Find the freezing point of a glucose solution whose osmotic pressure at ${25}^{\circ }C$ is found to be $30$ atm. $K_f\left(water\right)=1.86kgmo{l}^{-1}K$.

• A. $T_f=-{2.28}^{\circ }C$
• B. $T_f=+{2.28}^{\circ }C$
• C. $T_f=-{4.56}^{\circ }C$
• D. $T_f=+{4.56}^{\circ }C$

Answer 1

Answer: (A)

$T_f=-{2.28}^{\circ }C$

The osmotic pressure is given by $\Pi =CRT$

$30=C\times 0.08206\times 298$

$C=1.23M$

Assuming the density of the solution to be $1$ g/ml, we can approximate molarity and molality.

$C=1.23m$

The depression in the freezing point $=\Delta T_f=K_{f}m=1.86\times 1.23={2.28}^{o}C$

The freezing point of pure water is $0^{o}C$.

The freezing point of solution $=0-2.28=-{2.28}^{o}C$