Unknown gas diffusion

Question

A sample of an unknown gas takes 434 s to diffuse through a porous

plug at a given temperature. At the same temperature, N₂(g) takes 175 s

to diffuse through the same plug. What is the molar mass of the unknown

gas? Note: Rate = 1 / time

Answer 1

A sample of an unknown gas takes 434 s to diffuse through a porous

plug at a given temperature. At the same temperature, N₂(g) takes 175 s

to diffuse through the same plug. What is the molar mass of the unknown

gas? Note: Rate = 1 / time

GIVEN

Rate of N2= 1/175 s

Rate of unknown gas = 1/434 s

RELATIONSHIPS

rate A / rate B = √Mb/Ma

1/434 / 1/175 = √28/√M

Simplify the left side, then square both sides

Answer 2

Graham's Law of Effusion:

rate gas₁ / rate gas₂ = √MW₂ / √MW₁

rate gas₁ = 1/434 s

rate N₂ = 1/175 s

MW₁ = ?

MW_N2 = 28.02 g/mole

Solve for MW₁

(1/434) / 1/175) = √28.02 / √x

0.1626 = 28.02 / x

x = 172 g/mole

Molar mass of unknown = 172 g / mole