Question

Calculate the amount of ice that will separate out on cooling a solution containing $50g$ of ethylene glycol in $200g$ water from $0^{\circ }C$ to $-{9.3}^{\circ }C$. ($K_f$ for water = 1.86 K kg $mo{l}^{-1}$).

• A. $77.42g$
• B. $161.29g$
• C. $48.71g$
• D. $38.71g$

Answer 1

The correct option is D $38.71g$

mass of solute, $w=50g$,

$\Delta T_f={9.3}^{0}C$
$K_f$= 1.86 K kg $mo{l}^{-1}$
molar mass of ethylene glycol, $M=62g/mol$
let mass of remaining liquid water is $W$.
Now, $\Delta T_f=\frac{K_f\times w\times 1000}{m\times W}$
$9.3=\frac{1.86\times 50\times \times 1000}{62\times W}$
$W=161.29g$
Hence, amount of ice separated from $200g$ water $=200-161.29=38.71g$.
Hence, (d) is the correct option.