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For the reaction N(2(g)) +O(2(g)) Leftri...

For the reaction `N_(2(g)) +O_(2(g)) Leftrightarrow 2NO_(g)`, the equilibrium constantis `K_1`. The equilibrium constants is `K_2` for the reaction `2NO_(g)+O_(2(g)) Leftrightarrow 2NO_(2(g))`. What is the K for the reaction `NO_(2(g)) Leftrightarrow 1/2 N_(2(g))+O_(2(g))?`

A

`(1)/(2K_(1)K_(2))`

B

`1/(4K_(1)4K_(2))`

C

`[1/(K_(1)K_(2))]^(1//2)`

D

`1/(K_(1) K_(2))`

Text Solution

Verified by Experts

The correct Answer is:
C

`N_(2)+O_(2) Leftrightarrow 2NO, K_1`
`2NO+O_2 Leftrightarrow 2NO_2, K_2`
`NO_2 Leftrightarrow 1/2 N_2 +O_2 , K`
`K_(1)=([NO]^2)/([N_2] [O_2]) , K_(2)=([NO_2]^2)/([NO]^2 [O_2])`
`K=([N_2]^(1/2) [O_2])/([NO_2])=sqrt(([N_2] [O_2] xx [NO]^2 [O_2])/([NO]^2 xx [NO_2]^2)) rArr sqrt(1/(K_1 K_2))`
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