Question

The freezing point depression constant for water is $-1.86C$. If $5.00$ g of ${Na}_2{SO}_4$ is dissolved in $45.0$ g $H_{2}O$. The freezing point is changed by $-3.82C$.

Calculate the van't Hoff factor?

• A. $2.63$
• B. $0.311$
• C. $0.38$
• D. $3.8$

Answer 1

The correct option is A $2.63$

Depression in freezing point= $\Delta T_f=i{K}_{f}m$

Given values, $\Delta T_f=-{3.82}^{o}C$

$K_f=-{1.86}^{o}C$

$=?$

Molality= $\frac{5}{142}\times \frac{1000}{45}=0.7824m$

$\Delta T_f=i{K}_{f}m$

$\Rightarrow i=\frac{\Delta T_f}{K_{f}m}=\frac{-3.82}{-1.86\times 0.7824}$

$\Rightarrow i=\frac{3.82}{1.455}=2.62$