Question

3 g of benzoic acid is added to 25 g of benzene. \( \Delta T_f = 2.5\,\text{K} \) and \( K_f \) of benzene is 5. What is the experimental molecular mass of benzoic acid?

Hint:

If calculated molar mass is double the theoretical formula mass, it strongly implies the solute undergoes 100% dimerization in the solvent (van't Hoff factor $i = 0.5$).

Answer 1

Step 1: Use Freezing Point Depression Formula
\[ \Delta T_f = K_f \cdot m \] \[ \Delta T_f = K_f \cdot \frac{W_2 \times 1000}{M \times W_1} \]

Step 2: Substitute Given Values
\[ \Delta T_f = 2.5,\quad K_f = 5,\quad W_2 = 3 \text{ g},\quad W_1 = 25 \text{ g} \]

Step 3: Put Values in Formula
\[ 2.5 = 5 \times \frac{3 \times 1000}{M \times 25} \]

Step 4: Simplify Equation
\[ 2.5 = 5 \times \frac{3000}{25M} \] \[ 2.5 = \frac{600}{M} \]

Step 5: Calculate Molecular Mass
\[ M = \frac{600}{2.5} = 240 \text{ g/mol} \]

Step 6: Final Answer
\[ \boxed{M = 240 \text{ g/mol}} \]