Gases are effusing out through a pin hole of a container containing gas mixture of $H_2$, He and $CH_4$. What should be the composition of the gas mixture, so that in the initial form, gas mixture effused out will have equal compositions for all gases?

To achieve equal molar composition in the effused gas, the rate of effusion multiplied by the mole fraction in the container must be identical for all three gases. According to Graham's law, the rate of effusion is inversely proportional to the square root of the molar mass, so the required mole fraction in the container is directly proportional to the square root of the molar mass. Using the molar masses of 2 for hydrogen, 4 for helium, and 16 for methane gives required proportions of 1.414, 2, and 4. Therefore, the necessary composition of the initial gas mixture is 1.414 : 2 : 4.

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