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))`
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_(2)O(g),hArr,H_(2)(g),+,1/2O_(2)(g)),("Intial",1 "mole",,0,,0),(" After disco",1-alpha,,alpha,,1/2alpha):}`
Total `=1+ alpha/2`
At eqm : `p_(H_(2)O)= (1-alpha)/(1+alpha/2)xxp = (2(1-alpha)p)/(2+alpha)`
` p_(H_(2))= alpha/(1 +alpha/2)xxp=(alpha p)/(1+ alpha//2)=(2 alpha p)/(2+alpha)`
`p_(O_2) = (alpha/2)/(1+alpha/2) xx p = (alpha p )/(2+alpha)`
` K_(p) = (p_(H_(2))xxp_(O_(2))^(1//2))/(p_(H_(2)O))=(((2alpha p)/(2+alpha))((alpha p)/(2+alpha))^(1//2))/((2(1-alpha)p)/(2+alpha))`
`alpha /(1-alpha) xx ((alpha p)/(2+ alpha))^(1//2) = (alpha^(3//2) p^(1//2))/((1-alpha)(2+alpha)^(1//2))`