Question

Two solutions containing $0.75g$ of urea (mol. wt. 60) and $1.5g$ of compound $A$ in $100g$ water, freeze at the same temperature. The molecular weight of $A$ is:

• A. 60
• B. 30
• C. 120
• D. 240

Answer 1

Answer: (C)

Calculate $\Delta T_f$ for both the solutions (containing urea and $A$ ) separately divide the two equations to get the molecular mass of $A$.
Given mass of urea $=0.75g$, mass of $=1.5g$,
mass of water $=100g$, mol. $wt$, of urea $=60.$
$\Delta T_f$ for urea
$=\frac{1000\times K_f\times \text{ mass of urea }}{\text{ mass of water }\times \text{ molecular mass of urea }}$
$=\frac{1000\times K_f\times 0.75}{60\times 100}...(i)$
$\Delta T_f$ for ' $A$ '
$=\frac{1000\times K_f\times \text{ mass of }A}{\text{ mass of water }\times \text{ molecular mass of }A}$
$=\frac{1000\times K_f\times 1.5}{100\times \text{ molecular mass of }A}...(ii)$
Dividing Eq. (i) by (ii), we get
$\frac{1000\times K_f\times 0.75\times 100\times \text{ molar mass of }A}{1000\times K_f\times 1.5\times 60\times 100}$
$=\frac{0.75\times \text{ molecular mass of }A}{1.5\times 60}$
Molecular mass of $A=120$