Question

A sample of gas is observed to effuse through a pourous barrier in 4.98 minutes. Under the same conditions, the same number of moles of an unknown gas requires 6.34 minutes to effuse through the same barrier. The molar mass of the unknown gas is ______g/mol.

Answer 1

To solve this numerical which gas is used as sample need to be known because in equation molecular mass of sample gas is included.

Let molecular mass of sample gas = X g/ mol = M1

Molecular mass of unknown gas = Y g/mol = M2

Rate of effusion of sample gas = 4.98 min = r1

Rate of effusion of unknown gas = 6.34 min = r2

By Graham's law

r1/ r2 = √ ( M2/ M1)

4.98 / 6.34 = √( Y/ X )

0.7855 = √ Y/ X

Y/ X = 0.7855² = 0.6170

Y = 0.6170 x X

Just by multiplying molecular mass of sample gas with 0.6170 we will get molecular mass of unknown gas.