`2NO_(2)hArr2NO + O_(2), K = 1.6xx10^(-2)` ,
`NO + (1).(2)O_(2)hArrNO_(2), K' =` ?

Options

A. `K' = (1).(K^(2))`
B. `K' = (1)/(K)`
C. `K' = (1)/(sqrt(K))`
D. None of these

Answer

C

Explanation

`2NO_(2)hArr2NO + O_(2)` ….(i)
`K = 1.6xx10^(-12)`
`NO + (1)/(2)O_(2)hArrNO_(2)` ….(ii)
Reaction (ii) is half of reaction (i)
`K = ([NO]^(2)[O_(2)])/([NO_(2)]^(2))` ....(i)
`K' = ([NO_(2)])/([NO][O_(2)]^(1//2))` ....(ii)
On multiplying (i) and (ii)
`KxxK' = ([NO]^(2)[O_(2)])/([NO_(2)]^(2))xx([NO_(2)])/([O_(2)]^(1//2))`
`= ([NO][O_(2)]^(1//2))/([NO_(2)]) = (1)/(K')`
`KxxK' = (1)/(K'), K = (1)/(K'^(2)), K' = (1)/(sqrt(K))`