Question

$1kg$ of $0.75$ molal aqueous solution of sucrose can be cooled up to $-4^{\circ }C$ before freezing. The amount of ice (in g) that will be separated out is (Nearest integer)
$[$ Given : $K_f\left(H_{2}O\right)=1.86Kkgmo{l}^{-1}]$

Answer 1

Answer: 518

Let mass of water initially present $=xgm$
$\Rightarrow$ Mass of sucrose $=(1000-x)gm$
$\Rightarrow$ moles of sucrose $=\left(\frac{1000-x}{342}\right)$
$\Rightarrow 0.75=\frac{\left(\frac{1000-x}{342}\right)}{\left(\frac{x}{1000}\right)}$
$\Rightarrow \frac{x}{1000}=\frac{1000-x}{342\times 0.75}$
$\Rightarrow 256.5x=10^6-1000x$
$\Rightarrow x=795.86gm$
$\Rightarrow$ moles of sucrose $=0.5969$
New mass of $H_{2}O=akg$
$\Rightarrow 4=\frac{0.5969}{a}\times 1.86$
$\Rightarrow a=0.2775kg$
$\Rightarrow$ ice separated $=(795.86-277.5)$
$=518.3gm$