Question

When the same amount of the solute \(P\) and \(Q\) are separately dissolved in 500 g water, the \(\Delta T_f\) values are 0.15 K and 0.30 K respectively. If the molecular weight of \(P\) is 80 g mol\(^{-1}\), then the molecular weight of \(Q\) is

• A. 30 g mol\(^{-1}\)
• B. 60 g mol\(^{-1}\)
• C. 40 g mol\(^{-1}\)
• D. 45 g mol\(^{-1}\)
• E. 160 g mol\(^{-1}\)

Hint:

For same mass of solute in same solvent, higher depression in freezing point means lower molecular mass.

Answer 1

The Correct Option is C

Concept: For the same solvent and same mass of solute: \[ \Delta T_f \propto \frac{1}{M} \] where \(M\) is molecular mass.

Step 1: Use inverse relation.
\[ \frac{\Delta T_P}{\Delta T_Q}=\frac{M_Q}{M_P} \]

Step 2: Substitute values.
\[ \frac{0.15}{0.30}=\frac{M_Q}{80} \]

Step 3: Calculate \(M_Q\).
\[ M_Q=80\times\frac{0.15}{0.30}=40\ \text{g mol}^{-1} \]