Question

A sample of N₂ gas is observed to effuse through a pourous barrier in 4.06 minutes. Under the same conditions, the same number of moles of an unknown gas requires 7.22 minutes to effuse through the same barrier.

The molar mass of the unknown gas is ___g/mol.

Answer 1

Rate of effusion is inversely proportional to square root of molar mass

rate = k*sqrt(1/M)

M is molar mass

If we take ratio, above expression becomes

rate(N2)/rate(unknown) = sqrt (M(unknown)/M(N2))

Or,

time(unknown)/time(N2) = sqrt (M(unknown)/M(N2))

we have:

M(N2) = 28.02 g/mol

PUT values:

time(unknown)/time(N2) = sqrt (M(unknown)/M(N2))

7.22/4.06 = sqrt (M(unknown)/28.02)

sqrt (M(unknown)/28.02) = 1.778

(M(unknown)/28.02) = 3.162

M(unknown) = 88.61 g/mol

Answer: 88.6 g/mol