Question

a sample of N2 (g) escapes through a tiny hole in 69.18s. the same amount of an unknown gas escapes in 58.72s under identical conditions. what is the molar mass of the unknown gas?

Answer 1

The rate of effusion of a gas through a tiny hole is inversely proportional to square of its molecular weight.

The rate of effusion of a gas is proportional to $\sqrt{}$1/M where M = molecular weight

For two different gases, r1/r2 = $\sqrt{}$M2/M1

Now , in this case, rate N2/ rate (unknown) = (V/t)N2/ (V/t) unknown gas = $\sqrt{}$M2/MN2 where v is volume and t is time taken for the gas to escape out

But Volume is same for both gases, therefore t unknown gas/ t N2 = $\sqrt{}$M2/28

                                                                      (58.72/69.18) = $\sqrt{}$M2/28

molar mass of the unknown gas = 20.17 grams