a' moles of `PCl_(5)` are heated in a closed container to equilibrate `PCl_(5) (g) hArr PCl_(3)(g) + Cl_(2) (g) ` at a pressure of p atm . If x moles of `PCl_(5)` dissociate at equilibrium , then

Options

A. `x/a=(K_(p)/p)^(1//2`
B. ` x/a = (K_(p))/(K_(p) +p)`
C. `x/a = (K_(p)/(K_(p) +p))^(1//2)`
D. ` x/a =((K_(p)+ p)/K_(p))^(1//2)`

Answer

C

Explanation

`x/a ` means degree of dissociation , `alpha`
`{:(,PCl_(5)(g),hArr,PCl_(3)(g),+,Cl_(2) (g)),("Intial moles",1,,0,,0),("Moles at eqm.",1-alpha,,alpha,,alpha):}`
Total moles `= 1 - alpha +alpha+ alpha+=1 +alpha `
At eqm : `p_(pCl_(5))= ((1-alpha)/(1+alpha))p,`
` p_(PCl_(3))= ((alpha)/(1+alpha))p, p_(Cl_(2))= ((alpha)/(1+alpha))p`
` :. K_(p) = (p_(PCl_(3)) xx p_(Cl_(2)))/(p_(PCl_(5)))`
` ((alpha/(1+alpha))p*(alpha/(1+alpha))p)/(((1-alpha)/(1+alpha))p )=alpha^(2)/(1-alpha^(2)) p`
or ` (1-alpha^(2))K_(p) = alpha^(2) p `
or ` K_(p) = alpha^(2) (K_(p) +p) or alpha= (K_(p)/(K_(p)+p))^(1//2)`