The equilibrium constants for the following reactions
`N_(2) (g) + 3H_(2)(g) hArr 2NH_(3) (g) N_(2) (g) + O_(2) (g) hArr 2NO(g)`
`" and " H_(2)(g) +1//2 O_(2) (g) hArr H_(2)O (Ig) " are " K_(1) ,K_(2) " and " K_(3)` respectively.
The equilibrium constant (K) for the reaction
`2NH_(3) (g) + 2^(1)//2) O_(2) (g) hArr 2NO(g) +3H_(2) O(I) " is "`

Options

A. `K_(1)K_(2)//K_(3)`
B. `K_(2)K_(3)^(3)//K_(1)`
C. `K_(2)K_(3)^(2)//K_(1)`
D. `K_(2)K_(3)//K_(1)`

Answer

B

Explanation

Desired equilibrium equation is
`2NH_(3)(g)+(5)/(2)O_(2)(g)hArr 2NO(g)+3H_(2)O(l)`
It can be obtained by reversing the first equation, multiplying the third equation by 3, and adding the second equation to them:
`2NH_(3)hArr N_(2)+3H_(2), 1//K_(1)`
`3H_(2)+(3)/(2)O_(2)hArr 3H_(2)O, K_(3)^(3)`
`(N_(2)+O_(2)hArrr 2NO, K_(2))/(2NH_(3)+(5)/(2)O_(2)hArr 2NO+3H_(2)O, K_(eq)=(K_(2)K_(3)^(3))/(K_(1)))`