$K_1, K_2$ and $K_3$ are the equilibrium constants of the following reactions $(I), (II)$ and $(III)$ respectively.
$(I) \, N_2 + 2O_2 \rightleftharpoons 2NO_2$
$(II) \, 2NO_2 \rightleftharpoons N_2 + 2O_2$
$(III) \, NO_2 \rightleftharpoons \frac{1}{2} N_2 + O_2$
The correct relation from the following is

  • A
    $K_1 = \frac{1}{K_2} = \frac{1}{K_3}$
  • B
    $K_1 = \frac{1}{K_2} = \frac{1}{(K_3)^2}$
  • C
    $K_1 = \sqrt{K_2} = K_3$
  • D
    $K_1 = \frac{1}{K_2} = K_3$

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