At same temperature and pressure, the rate of diffusion of gas ' X ' is 3 3 times that of a gaseous hydrocarbon of molar mass 54 ~g ~mol ⁻¹ . The molar mass of X in g mol ⁻¹ is

Step-by-step solution

According to Graham's law of diffusion rate of diffusion of a gas is inversely proportional to square root of its density. Rate 1 Density But, density of the gas is proportional to its molar mass, thus Rate of diffusion 1 M_m For two gases we have aligned Rate ₁ Rate ₂ & = M_ m₂ M_ m₁ ( Rate ₁ Rate ₂ )^2 & = M_ m₂ M_ m₁ M_ m₂ & = ( Rate ₁ Rate ₂ )^2 M_ m₁ & = ( 1 3 3 )^2 54 & = 1 9 3 54 & = 54 27 =2 ~g ~mol ⁻¹ aligned