For the reaction
`2HI(g)hArrH_(2)(g)+I_(2)(g)+I_(2)(g)`
The degree of dissociation `(alpha)` of `HI(g)` is related to equilibrium constant `K_(p)` by the expression
a. `(1+2sqrt(K_(p)))/2`, b. `sqrt((1+2K_(p))/2)`
c. `sqrt((2K_(p))/(1+2K_(p)))`, d. `(2sqrt(K_(p)))/(1+2sqrt(K_(p)))`

Options

A. `(1+2sqrt(K_(p))/(2sqrt(K_(p)))`
B. `sqrt((1+2K_(0)/(2))`
C. `sqrt((2K_(p))/(1+2K_(p))`
D. `(2sqrt(K_(p)))/(1+2sqrt(K_(p))`

Answer

D

Explanation

`HI(g) Leftrightarrow (1)/(2)H_(2) (g)+1/2 I_(2) (g)`
`1-alpha " "alpha/2" "alpha/2`
`K_(p)=([(alpha/2)P_(T)])^(2)/((1-alpha)^(2) P_(T)^(2))`
`(alpha)/(1-alpha)=2sqrt(K_(p)) therefore =(2sqrt(K_(P)))/(1+2 sqrt(K_(p))`