Step 1: Understanding the Concept:
According to Raoult's law for a dilute solution containing a non-volatile solute, the relative lowering of vapour pressure is equal to the mole fraction of the solute. Step 2: Key Formula or Approach:
\[ \text{RLVP} = \frac{P^\circ - P}{P^\circ} = \text{X}_{\text{solute}} \approx \frac{\text{n}_2}{\text{n}_1} \text{ (for dilute solutions)} \]
Where \(n_2 = w_2 / M_2\) and \(n_1 = w_1 / M_1\). Step 3: Detailed Explanation:
Given:
RLVP = \(0.02\)
Mass of solute (\(w_2\)) = \(20\text{ g}\)
Mass of solvent (\(w_1\)) = \(200\text{ g}\)
Molar mass of solvent (water, \(M_1\)) = \(18\text{ g/mol}\)
\[ 0.02 = \frac{20 / M_2}{200 / 18} \]
\[ 0.02 = \frac{20 \times 18}{200 \times M_2} \]
\[ 0.02 = \frac{1.8}{M_2} \]
\[ M_2 = \frac{1.8}{0.02} = 90\text{ g/mol} \]
Step 4: Final Answer:
The molar mass is \(90\text{ g mol}^{-1}\).