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Two vessels separately contain two ideal gases A and B at the same temperature. The pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is :

1. 3/4
2. 1/2
3. 2/3
4. 2

Correct answer: 3/4

Solution

Using the ideal gas equation, PV = nRT, we know that density (ρ) is given by ρ = PM/RT. Since temperature and R are constant, ρ ∝ PM. Given that the pressure of A is twice that of B (P_A = 2P_B) and the density of A is 1.5 times that of B (ρ_A = 1.5ρ_B), we can write 1.5ρ_B = 2P_B * M_A / RT. Simplifying, M_A / M_B = 3/4.

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