Question

Calculate the molar mass of nonvolatile solute when 4 g of it is dissolved in 100 g solvent that boils at 319.4 K [\(K_b\) = 2.4 K kg \(\text{mol}^{-1}\); B.P of pure solvent = 319 K]

• A. \(220 \text{gmol}^{-1}\)
• B. \(230 \text{gmol}^{-1}\)
• C. \(240 \text{gmol}^{-1}\)
• D. \(250 \text{gmol}^{-1}\)

Hint:

Use \(\Delta T_b = K_b \times \dfrac{w_2\times1000}{M_2\times w_1}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Dissolving a nonvolatile solute raises the boiling point. The rise depends on the molality of the solution.

Step 2: Key Formula or Approach
\[ \Delta T_b = K_b\,m = K_b\,\frac{w_2\times1000}{M_2\,w_1} \]

Step 3: Detailed Explanation
\(\Delta T_b = 319.4 - 319 = 0.4\) K, \(w_2 = 4\) g, \(w_1 = 100\) g.
\[ M_2 = \frac{K_b\,w_2\times1000}{\Delta T_b\,w_1} = \frac{2.4\times4\times1000}{0.4\times100} = \frac{9600}{40} = 240\ \text{g mol}^{-1} \]

Final Answer:
The molar mass of the solute is 240 g/mol, option (C). \[ \boxed{240\ \text{g mol}^{-1}\ \text{(C)}} \]