Question

A hydrocarbon with molecular formula CnH2n+2 diffuses twice far as SO2 at same temperature. Find out the molecular formula of the hydrocarbon?​

Answer 1

According to Graham's law, the rate of diffusion is inversely proportional to the square root of molecular weight. Hence, methane diffuses twice as fast as sulphur dioxide.

Let x be the gas which diffuses twice as quickly as SO2.

$r \: \alpha \: \frac{1}{m}$

Molar mass of SO2 is 64.

$\\ \frac{r \: so2}{r \: x} \: = \frac{m \: x}{m \: so2} \\ \frac{1}{2} = \sqrt{ \frac{mx}{64} } \\ \frac{64}{4} = mx = 16$

∴ x is CH4 as its molar mass is 16.