# 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

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.

I hope I was able to clear ur doubt ,

If yes then pls click the smiley button :)

**
**