Question

Calculate the amount of ice that will separate of cooling a solution containing 50g of ethylene glycol in 200 g water to $-{9.3}^{\circ }C:$

$[K_{f}forwater=1.86Kmo{l}^{-1}kg]$

• A. $19.35g$
• B. $28.45g$
• C. $38.71g$
• D. $56.9g$

Answer 1

The correct option is C $38.71g$

Ethylene glycol has a molar mass of $62$ g/mol.

Let $x$ g of ice separates out.

Mass of water present in the solution $=200-x$ g

Molality of the solution $=m=\frac{50\times 1000}{62\times (200-x)}=\frac{806.5}{200-x}m$

The depression in the freezing point $=\Delta T_f=0-(-9.3)={9.3}^{o}C$

$\Delta T_f=K_{f}m$

$9.3=1.86\times \frac{806.5}{200-x}$

$200-x=161.29$

$x=38.71$ g

Hence, $38.71$ g of ice will separate out.