Question

When $0.2$ mole of urea is dissolved in $100g$ of a solvent, the depression of freezing point is $0.50^{\circ }C$. When $0.3$ mole of non-volatile solute is dissolved in $100g$ of the same solvent, the depression of freezing point will be_____ ${}^{\circ }C$

Answer 1

Answer: 0.75

For the same solvent, the value of $K_f$ remains the same.
${\left(\Delta T_f\right)}_1=K_f{m}_1$
${\left(\Delta T_f\right)}_2=K_f{m}_2$
$K_f=\frac{{\left(\Delta T_f\right)}_1}{m_1}$
and $K_f=\frac{{\left(\Delta T_f\right)}_2}{m_2}$
$\therefore \frac{{\left(\Delta T_f\right)}_2}{m_2}=\frac{{\left(\Delta T_f\right)}_1}{m_1}$
$\therefore {\left(\Delta T_f\right)}_2=\frac{{\left(\Delta T_f\right)}_1}{m_1}\times m_2$
$\therefore {\left(\Delta T_f\right)}_2=\frac{0.50}{\left(\frac{0.2}{0.100}\right)}\times \left(\frac{0.3}{0.100}\right)=\frac{0.50\times 3}{2}$
$=0.75^{\circ }C$