20 g of a substance were dissolved in 500 mL of water and the osmotic pressure of the solution was found to be 600 mm of mercury at 15°C. The molecular weight of a substance is:
Answer & explanation
Correct answer: option 4
The correct answer is option 4. 1198
Given,
Osmotic pressure, \(\pi = \frac{600}{760}\)
Universal gas constant, \(R = 0.0821 \text{L atm mol}^{-1}K^{-1}\)
Temperature, \(T = 273 + 15 = 288 K \)
Volume, \(V= \frac{500}{1000}L\)
Number of moles, \(n = \frac{20}{m}\), where, \(m\) is the molecular weight of the solute.
We know,
\(\pi V = nRT\)
\(⇒ \frac{600}{760} × \frac{500}{1000} = \frac{20}{m} ×0.0821 × 288\)
\(⇒ m = \frac{20 × 0.0821 × 288 × 760 × 1000}{600 × 500}\)
\(⇒ m = \frac{3594.0096}{3}\)
\(∴ m = 1198.0032 ≈ 1198\)