Q.Two vessels contain two ideal gases A and B at the same temperature, the pressure of A be 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 weights of A and B is Q.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 weights of A and B is

to solve  this question first let us assume that the no. of moles of B = n and both the gases are occupying equal volumes .  When they occupy equal volumes  according to the given condition the density of gas A should be 1.5 times that of B.
so  density d of gas B = n_b  x M_b /v  ( where M is the molecular weight of B ).
now density of gas  A = 1.5 x d  = 1.5 x n_b x M_b/v ( from the above eqn )
we also know that density of gas  A = n_a x M_a/v.
therefore , n_a x M_a = 1.5 x n_b x M_b
hence, M_a /M_b =  1.5 x n_b/n_a. ----(1)

        P_a = P_b x 2
n_a x R x T / v = n_b x R x T /v  x 2
n_b/n_a = 1/2.---(2)
now putting (2) in (1),
M_a/M_b  = 1.5 x 0.5 = 0.75 .
hence the ratio of molecular weights of A and B is 0.75.

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