Mass of gas A , W_{A} = 1g

Mass of gas B, W_{B }= 2g

Pressure exerted by the gas A = 2 bar

Total pressure due to both the gases = 3 bar

In this case temperature & volume remain constant

Now if M_{A} & M_{B} are molar masses of the gases A & B respectively,therefore

p_{A} V= W_{A} RT/M_{A} & P_{total} V = (W_{A}/M_{A} + W_{B}/ M_{B}) RT

= 2 X V = 1 X RT/M_{A }& 3 X V = (1/M_{A} + 2/M_{B})RT

From these two equations, we get

3/2 = (1/M_{A} + 2/M_{B}) / (1 /M_{A}) = (M_{B} + 2M_{A}) / M_{B}

This result in 2M_{A}/ M_{B} = (3/2) -1 = ½

OR M_{B} = 4M_{A}

Thus, a relationship between the molecular masses of A and B is given by

4M_{A} = M_{B }