1. Use elevation in boiling point formula

For a dilute solution, $\Delta T_b = K_b m$ where $m$ is the molality.

2. Calculate elevation in boiling point

Given:

• Boiling point of solution $= 373.535\,\text{K}$
• Boiling point of pure water $= 373.15\,\text{K}$

So, $\Delta T_b = 373.535 - 373.15 = 0.385\,\text{K}$

3. Find molality

$m = \frac{\Delta T_b}{K_b} = \frac{0.385}{0.52} = 0.7404\,\text{mol kg}^{-1}$

4. Use definition of molality

$m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}$

Mass of solvent (water): $75 \times 10^{-3}\,\text{kg} = 0.075\,\text{kg}$

Hence moles of solute, $n = m \times 0.075 = 0.7404 \times 0.075 = 0.05553\,\text{mol}$

5. Calculate molar mass of solute

Mass of solute: $2.5 \times 10^{-3}\,\text{kg} = 2.5\,\text{g}$

Molar mass, $M = \frac{\text{mass}}{\text{moles}} = \frac{2.5}{0.05553} = 45.02\,\text{g mol}^{-1}$

Nearest integer: $\boxed{45}$

6. Comparison with stored answer

Stored correct answer = $45$

Our derived answer also equals $45$, so they agree.