Question

Calculate the molar mass of a nonvolatile solute if 6.4 g of it dissolved in 100 g water produces a relative lowering in vapour pressure of \(0\cdot 016\) at 300 K.

• A. \(60\text{ gmol}^{-1}\)
• B. \(66\text{ gmol}^{-1}\)
• C. \(72\text{ gmol}^{-1}\)
• D. \(84\text{ gmol}^{-1}\)

Hint:

Relative lowering equals the mole fraction of solute, which is about n2/n1 for a dilute solution.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Raoult's law for a non-volatile solute: the relative lowering of vapour pressure equals the mole fraction of the solute, \(\frac{p^0 - p}{p^0} = x_2 \approx \frac{n_2}{n_1}\) for a dilute solution.

Step 2: Moles of solvent:
\(n_1 = \frac{100}{18} = 5.556\) mol of water.

Step 3: Solve for the molar mass:
\[ 0.016 = \frac{w_2/M_2}{n_1} = \frac{6.4}{M_2\times 5.556} \]
\[ M_2 = \frac{6.4}{0.016\times 5.556} = \frac{6.4}{0.0889} = 72\text{ g mol}^{-1} \]
This is option (C). The temperature of 300 K is not needed for this calculation.

Final Answer:
The molar mass of the solute is about 72 g/mol, option (C). \[ \boxed{72\text{ g mol}^{-1}} \]