The equilibrium constant for the given reaction $N_2\left(g\right)+2O_2\left(g\right)\rightleftharpoons 2N{O}_2$(g) is 100. What is the equilibrium constant for the reaction given below:

$N{O}_2\left(g\right)\rightleftharpoons 1/2N_2\left(g\right)+O_2\left(g\right)$.

Given: It is given that for reaction 1st : $N_2\left(g\right)+2O_2\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right);K_c=[NO{]}^2/[N_2\left]\right[O_2{]}^2=100$

We have to find the KC for reaction 2nd : $N{O}_2\left(g\right)\rightleftharpoons 1/2N_2\left(g\right)+O_2\left(g\right)$

Explanation: On reversing reaction 1st we get $K_c’=1/K_c=1/100$ (i.e., reciprocal of $K_c$)

Since reaction 2 = ½ of the reversed reaction 1st,

therefore $K_c’’$ for reaction 2nd is $1/(K_c’{)}_{1/2}$

i.e., $K_c’’=1/(100{)}^{1/2}=1/10=0.1$

Hence, the correct option C is i.e., 0.1.