Under identical conditions, separate samples of O2 and an unknown gas were allowed to effuse through identical membranes simultaneously.

Question

After a certain amount of time, it was found that 7.75 mL of O₂ had passed through the membrane, but only 3.63 mL of of the unknown gas had passed through.

What is the molar mass of the unknown gas?

Answer 1

See Graham's Law of Effusion

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

Let gas 1 be O₂. Molar mass = 32 g / mol

Let x be gas 2. Molar mass = unknown

rate gas 1 = 7.75 ml/unit time

rate gas 2 = 3.63 ml / unit time

7.75 / 3.63 = sqrt x / sqrt 36

2.135 = sqrt x / 6

sqrt x = 12.81

x = 164 = molar mass of unknown gas