Question

P and Q combine to form two compounds \( PQ_2 \) and \( PQ_3 \). If 1 g \( PQ_2 \) in 51 g benzene gives depression of freezing point \(0.8^\circ C\) and 1 g \( PQ_3 \) gives \(0.625^\circ C\). ( \(K_f = 5.1\) ). Find atomic masses of P and Q.

• A. 35, 55
• B. 45, 45
• C. 55, 45
• D. 55, 35

Hint:

Colligative trick: \begin{itemize} \item Same solvent mass ⇒ depression ∝ \(1/M\). \end{itemize}

Answer 1

The Correct Option is D

Concept: Freezing point depression: \[ \Delta T_f = K_f \frac{w}{M} \frac{1000}{W} \] Here solvent mass same ⇒ \[ \Delta T_f \propto \frac{1}{M} \] Step 1: {\color{red}Molar mass ratio.} \[ \frac{\Delta T_1}{\Delta T_2} = \frac{M_2}{M_1} \] \[ \frac{0.8}{0.625} = \frac{M(PQ_3)}{M(PQ_2)} \] \[ \frac{8}{6.25} = 1.28 = \frac{M_3}{M_2} \] Step 2: {\color{red}Let atomic masses.} Let P = \( x \), Q = \( y \). \[ M(PQ_2) = x + 2y \] \[ M(PQ_3) = x + 3y \] Step 3: {\color{red}Use ratio.} \[ \frac{x+3y}{x+2y} = 1.28 \] \[ x+3y = 1.28x + 2.56y \] \[ 0.28x = 0.44y \Rightarrow \frac{x}{y} = \frac{44}{28} \approx \frac{11}{7} \] Step 4: {\color{red}Match options.} Closest integer ratio: \[ P=55,\quad Q=35 \]