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The equilibrium constants for the reacti...

The equilibrium constants for the reactions :
`N_2+O_2 hArr 2NO`
`2NO+ O_2 hArr 2NO_2` are `K_1` and `K_2` respectively . What will be the equilibrium constant for the reactions :
(i)`N_2+2O_2 hArr 2NO_2` and (ii)`2NO_2 hArr N_2+ 2O_2`

A

`K_1 = K_2`

B

`K_2 = sqrt(K_1)`

C

`K_1 = 2K_2`

D

`K_(1) =1/(2)K_2`

Text Solution

Verified by Experts

The correct Answer is:
B
`N_2 +O_2 hArr 2NO " "....(i)`
`1/2 N_(2) + 1/2 O_2 hArr NO " "....(ii)`
For equation number (i)
`K_1=([NO]^2)/([N_2][O_2])" "....(iii)`
For equation number (ii)
`K_2=([NO])/([N_2]^(1//2)[O_2]^(1//2))" "....(iv)`
From equation (iii) & (iv) it is clear that
`K_2 =(K_1)^(1//2)=sqrt(K_1), ` Hence, `K_2=sqrt(K_1)`
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