Question # If the densities of methane and oxygen are in the ratio 1: 2 , the ratio of rate of diffusion of ( O_{2} ) and ( C H_{4} ) is respectively

# If the densities of methane and oxygen are in the ratio 1: 2 , the ratio of rate of diffusion of ( O_{2} ) and ( C H_{4} ) is respectively

(a) 1: 2

(b) ( 1: 1 cdot 414 )

(c) 2: 1

(d) ( 1 cdot 414: 1 )

Solution

Molar mass ( =2 times ) Vapor density

Vapor density of methane = v

Vapor density of oxygen ( =mathrm{v}^{prime} )

( frac{m}{m^{prime}}=frac{2 times v}{2 times v^{prime}}=frac{1}{2} )

Molar mass of methane = m

Molar mass of oxygen ( =mathrm{m}^{prime} )

According Graham Duh-em law of diffusion:

rate of diffusion of the gas ( propto sqrt{frac{1}{text { Molar mass of the gas }}} )

Rate of diffusion of methane = r

Rate of diffusion of oxygen ( =r^{prime} )

( frac{r}{r^{prime}}=sqrt{frac{m^{prime}}{m}}=sqrt{frac{2 m}{m}}=frac{sqrt{2}}{1} )

Ratio of rate of diffusion oxygen and methane will be ( sqrt{2}: 1 . ). .