How to calculate the absolute rate of diffusion for 2 gases under the same conditions

Question

The absolute rate of diffusion of hydrochloric gas is found to be 1.40 × 10^-4 m/s. What is the absolute rate of diffusion of ammonia gas (in m/s) under the same conditions?

Answer 1

Grahams Law of Effusion:

rate gas 1 / rate gas 2 = sqrt MW gas 2 / sqrt MW gas 1

Hydrochloric acid (HCl) MW = 36.5 g / mol

Ammonia (NH₃) MW = 17 g / mol

Without doing any calculations, we can see that molar mass of HCl is just a little more than twice that of the molar mass of NH₃ (36.5 vs 17). So we know that the rate of NH3 diffusion/effusion will be greater than that for HCl

rate HCl = 1.40x10^-4 m/s

rate NH₃ = x

1.40x10^-4 / x = √17 / √36.5

1.40x10^-4 / x = 0.682

x = 2.05x10^-4 m/s = rate of diffusion/effusion of NH₃