Question

How much ice will separate if a solution containing 25 g of ethylene glycol $\left[C_2{H}_4{\left(OH\right)}_2\right]$ in 100g of water is cooled to ${10}^{o}C$?

$K_f\left(H_{2}O\right)$ = $1.86$ (25.05 g)

Answer 1

Depression in freezing point

$\Delta T_f={10}^{o}C$

Mass of glycol= $25g$, Mass of $H_{2}O=100g$

$\Delta T_f=K_f\times m$ ; $m=$ molality

$\Rightarrow 10=1.86\times m$

$\Rightarrow m=\frac{10}{1.86}=5.37$

$\Rightarrow m=\frac{25/62}{W_{H_{2}O}\times 1000}$ (Molar mass of ethylene glycol=$62$)

$\Rightarrow 5.37=\frac{403.22}{W_{H_{2}O}}$

$\therefore W_{H_{2}O}=75.08g$

Hence the mass of ice separated from $H_{2}O$

$=100-75.08$

$=24.92g$ .