Question

The freezing point of water is depressed by ${0.37}^{\circ }C$ in a 0.01 molal $NaCl$ solution. The freezing point of 0.02 molal solution of the urea is depressed by:

• A. ${0.37}^{\circ }C$
• B. ${0.74}^{\circ }C$
• C. ${0.185}^{\circ }C$
• D. $0^{\circ }C$

Answer 1

The correct option is A ${0.37}^{\circ }C$

As we know that,

$\Delta t_f=i{k}_{f}m$

where, $\Delta t_f$ = depression in freezing point

$i$=van't - Hoff factor

$m$=molarity

and $k_f$=freezing point depression constant.

For 0.01 molal $NaCl$ solution

$0.37=2{\times k}_f\times 0.01$

$\therefore k_f=\frac{0.37}{2\times 0.01}$....(i)

For 0.02 molal urea solution

$\Delta t_f=1\times k_f\times 0.02$

$\therefore k_f=\frac{\Delta t_f}{0.02}...\left(ii\right)$

From Eqs (i) and (ii)

$\frac{0.37}{2\times 0.01}=\frac{\Delta t_f}{0.02}$

$\Delta t_f=\frac{0.37\times 0.02}{2\times 0.01}$

$\therefore t_f={0.37}^{\circ }C$

Hence, the correct option is $\text{A}$