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:

1198

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,

\(\pi V = nRT\)

\(⇒ \frac{600}{760} × \frac{500}{1000} = \frac{20}{m} ×0.0821 × 288\)

\(⇒ m = \frac{20  × 0.0821 × 288 × 760 × 1000}{600 × 500}\)

\(⇒ m = \frac{3594.0096}{3}\)

\(∴ m = 1198.0032 ≈ 1198\)