`N_(2)O_(4)` is 10% dissociated at a total pressure `P_(1) ` and 20% dissociated at a total pressure `P_(2) .Then ratio 'P_(1)/P_(2)` is

Options

A. `1/2`
B. `2/1`
C. `1/4`
D. `4/1`

Answer

D

Explanation

`N_(2)O_(4) hArr 2 NO_(2)` ltbegt If `alpha` is the degree of dissciation and P is the total pressure , then
` K_(p) = (4alpha^2)/(1-alpha^(2))P `
When `alpha = 0*10`,
` K_(p) = (4(0*10)^(2))/(1-(0*10^(2)))xx P_(1) = (0*04)/(0*99) P_(1) cong 0*04 P_(1) `
When` alpha =0*20`
` K_(p) = (4(0*20)^(2))/(1-(0.2)^(2))xx P_(2) = (0*16)/(0*96) P^(2) cong 0*16 P_(2)`
Thus , ` 0*04 P_(1) = 0*16 P_(2) or (P_(1))/(P_(2)) = (0*16)/(0*04) =4/1` .