GENERAL CHEMISTRY I

Question

An unknown homonuclear diatomic gas effuses 2.34 times faster than smellium gas (molar mass = 175 g/mol). What is the molar mass of the unknown gas? Identify the unknown gas.

Answer 1

Graham's Law of Effusion

The rate of effusion is inversely related to the square root of the molar mass, or in this case...

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

let gas 1 be smellium, rate = 1, MW = 175

let gas 2 be unknown x, rate = 2.34, MW = x

1 / 2.34 = √x / √175

0.427 = √x / 13.2

√x = 5.649

x = 31.9

Unknown (homonuclear diatomic) gas would most likely be oxygen (O₂)