Question

The depression in freezing point of $0.01M$ aqueous solution of urea, sodium chloride and sodium sulphate are in the ratio:

• A. $1:1:1$
• B. $1:2:3$
• C. $1:2:4$
• D. $2:2:3$

Answer 1

The correct option is B $1:2:3$

Freezing point depression of a solution is given by,
$△T_f=i\times K_f\times m$
where,
$i$ is van't Hoff factor
$△T_f$ is the depression in freezing point.
$K_f$ is molal depression constant.
m is molality of the solution.
Since all the solutions are of $0.01M$, the depression in freezing point depends on the van't Hoff factor.

Number of ions formed,
For urea, $i=1\because \text{it is a non-electrolyte}$
$NaCl,i=2$
$N{a}_{2}S{O}_4,i=3$

Number of ions formed,
$Urea:NaCl:N{a}_{2}S{O}_4$

$0.01mol:(0.01\times 2mol):(0.01\times 3mol$)

$\Rightarrow 1:2:3$

Thus, $\Delta T_f$ is also in the same ratio.