The equilibrium constant `(K_(p))` for the decomposition of gaseous `H_(2)O`
`H_(2)O(g)hArr H_(2)(g)+(1)/(2)O_(2)(g)`
is related to the degree of dissociation `alpha` at a total pressure P by

Options

A. `K_p=(alpha^3 P^(1//2))/((1+alpha)(2+alpha)^(1//2))`
B. `K_p=(alpha^3 p^(3//2))/((1-alpha)(2+alpha)^(1//2))`
C. `K_p=(alpha^(3//2) P^2)/((1-alpha)(2+alpha)^(1//2))`
D. `K_p=(alpha^(3//2) P^(1//2))/((1-alpha)(2+alpha)^(1//2))`

Answer

D

Explanation

`H_2O(g) hArr H_2(g) + 1/2O_2(g)`
If the degree of dissociation is `alpha`
`{:("Initial conc.",1,0,0),("At equiv", 1-alpha,alpha,alpha//2):}`
Total no. of moles of equilibrium =`1-alpha+alpha+alpha//2`
`=1+alpha//2`
`p(H_2O)=(1-alpha)/(1+alpha//2).P`
`p(H_2)=alpha/(1+alpha//2).P`
`p(O_2)=(alpha//2)/(1+alpha//2).P`
`K_p=((p_(H_2))(p_(O_2))^(1//2))/((p_(H_2O)))=((alpha/(1+alpha//2)P)((alpha//2)/(1+alpha//2)P))/((1-alpha)/(1+alpha//2)P)`
`=(((2alpha)/(2+alpha)P)(alpha/(2+alpha)P)^(1//2))/((2(1-alpha))/(2+alpha)P)=(alpha^(3//2)P^(1//2))/((1-alpha)(2+alpha)^(1//2))`