A solution containing compound ‘X’ in water and a solution containing glucose in water were put in a — Solutions and Colligative Properties Chemistry Question
Question
A solution containing compound ‘X’ in water and a solution containing glucose in water were put in a closed system. By doing this, some water vapour was removed from one solution and got condensed in the other. It is found that when both the solutions were at equilibrium vapour pressure, one solution contains 10% (w/w) of ‘X’ and the other 5% (w/w) glucose. The molar mass (in g/mol) of ‘X’ is
💡 Solution & Explanation
At equilibrium in a closed system (isopiestic), both solutions must have the same vapour pressure, meaning they have the same mole fraction of solute. Solution 1: 10 g X, 90 g water. $X_{\text{solute1}} \approx n / N = (10/M) / (90/18) = (10/M) / 5 = 2/M$. Solution 2: 5 g glucose, 95 g water. $X_{\text{solute2}} \approx n / N = (5/180) / (95/18) = (1/36) / (95/18) = 1/190$. Equating them: $2/M = 1/190 \implies M = 2 \times 190 = 380 \text{ g/mol}$. Therefore, correct answer is 0380.