The equilibrium constant `K_(p_(1))` and `K_(p_(2))` for the reactions `XhArr2Y` and `ZhArrP+Q`, respectively are in the ratio of `1:9`. If the degree of dissociation of `X` and `Z` be equal, then the ratio of total pressure at these equilibrium is:

Options

A. `1:1 `
B. `1:3`
C. `1:9 `
D. `1:36`

Answer

D

Explanation

`{:(X, `therefore K_(p_1) = ([Y]^2)/([X]) = (((2alpha)/(1 + alpha) .P_1)^2)/(((1-alpha)/(1 + alpha) . P_1)) = (4 alpha^2)/(1 - alpha^2) . P_1`
`{:(Z, `therefore = ([P][Q])/([Z]) = (((alpha)/(1 + alpha) . P_2)^2)/(((1 - alpha)/(1 + alpha).P_2)) = (alpha^2)/(1 - alpha^2) . P_2`
`therefore (K_(p_1))/(K_(p_2)) = ((4alpha^2)/(1 - alpha^2).P_1)/((alpha^2)/( 1 - alpha^2).P_2) = 1/9 implies (P_1)/(P_2) = 1/36`