In each of the following, total pressure set - up at equilibrium is assumed to be equal and is P atm with equilibrium constants `K_(p)` given `:`
`I: CaCO_(3)(s)hArr CaO(s)+CO_(2)(g),K_(1)`
`II : NH_(4)HS(s)hArr NH_(3)(g)+H_(2)S(g),K_(2)`
`III : NH_(2)CO_(2)NH_(4)(s)hArr 2NH_(3)(g) +CO_(2)(g),K_(3)`
In the increasing order `:`

Options

A. `K_(1)=K_(2)=K_(3)`
B. `K_(1)ltK_(2)ltK_(3)`
C. `K_(3)ltK_(2)ltK_(1)`
D. None

Answer

C

Explanation

`I: CaCO_(3)(s)hArr CaO(s)+CO_(2)(g),K_(1)`
`K_(1)=p_(CO_(2))=P`
`II: NH_(4)HS(s)hArr NH_(3)(g)+H_(2)S, K_(2)`
`:. p_(NH_(3))=(P)/(2)` and `p_(H_(2))S=(P)/(2)`
`:. K_(2)=p_(NH_(3)).p_(H_(2)S)=(P)/(2)xx(P)/(2)=(p^(2))/(4)`
`III : NH_(2)CONH_(4)(s) hArr 2NH_(3)(g)+CO_(2)(g),K_(3)`
`p_(NH_(3))=(2)/(3)P," "p_(CO_(2))=(1)/(3)P`
`:. K_(3)=(p_(NH_(3)))^(2)(p_(CO_(2)))=((2P)/(3))^(2)((P)/(3))=(4P^(3))/(27)`
Clearly `K_(3) ltK_(2) ltK_(1)`