​ K1 and K2 are the equilibrium constants for the reactions respectively. N2(g) + O2(g) + K1 2NO(g) ​

Question

K₁ and K₂ are the equilibrium constants for the reactions respectively.

N_2(g) + O_2(g) \(\overset{K_1}{⇌}\) 2NO_(g)

2NO_(g)  + O_2(g) \(\overset{K_2}{⇌}\) 2NO_2(g)

What is the equilibrium constant for the reaction 

NO_2(g) ⇌ 1/2 N_2(g) + O_2(g)

_{\((a)\,\,\frac{1}{\sqrt{K_1K_2}}\)}

_{\((b) \,\,(K_1=K_2)^{1/2}\)}

_{\((c)\,\,\frac{1}{2K_1K_2}\)}

_{\((d)\,\,(\frac{1}{K_1K_2})^{3/2}\)}

Answer 1

_{\((a)\,\,\frac{1}{\sqrt{K_1K_2}}\)}

Let equilibrium constant for the required reaction be K.

Then,