Question

Find out the amount of water (in g) separated as ice, if a solution containing $62g$ ethylene glycol in $250g$ water is cooled to $-10^{{}^{\circ }}C$ . $K_f$ for water is $1.86Kkgmo{l}^{-1}$ .

• A. $48$
• B. $64$
• C. $16$
• D. $32$

Answer 1

Answer: (B)

Molecular weight of ethylene glycol
$\left(C_2{H}_6{O}_2\right)=62$
Moles of ethylene glycol $=\frac{Wt}{M.Wt}$
$=\frac{62}{62}=1$
$\Delta T_f=i\times k_f\times m$
$\therefore \Delta T_f=0-\left(-10\right)=10$
$i=1$ for ethylene glycol
$\Delta T_f=1\times 86\times \frac{1}{\frac{250}{1000}}$
$\Delta T_f=1.86\times 4=7.44$
As $\Delta T_f=10$ it implies that some amount of water has frozen and this has led to a greater depression of freezing point.
$10=1.86\times \frac{\frac{62}{62}}{\frac{Wtof{H}_{2}O}{1000}}$
$W_{H_{2}O}=186gm$
Hence, the weight of water that has frozen $\text{=}(250-186)gm$ .
$=64gm$ .