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 the dissociation of X and Z be equal , then the ratio of the total pressure at these equlibria is

Options

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

Answer

D

Explanation

`underset(x - alpha)(X) hArr underset(2alpha)(2Y)` ` underset(1 - alpha)(Z) hArr underset(alpha)(P) + underset(alpha)(Q)`
`K_(P_(1))=((2alpha)/(1+alpha)P_(T_1))^(2)/(((1-alpha)/(1+alpha)P_(T_2))) K_(P_(2))=(((alpha)/(1+alpha)Pr_(2))((alpha)/(1+alpha)Pr_(2)))/(((1-alpha)/(1+alpha)P_(T_(2))))`
`(K_(P_(1)))/(K_(P_2))=((2alpha)/(1+alpha)P_(T_(1)))^(2)/(((1-alpha)/(1+alpha)P_(T_(2))))xx(((1-alpha)/(1+alpha)P_(T_(2))))/(((alpha)/(1+alpha)P_(T_(2)))(\(alpha)/(1+alpha)P_(T_(2))))`
`(1)/(9)=(4P_(T_(1)))/(P_(T_(2))), (P_(T_(1)))/(P_(T_(2)))=(1)/(36)`