The equilibrium constant $(K_c)$ for the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2 NO_{(g)}$ at temperature $T$ is $4 \times 10^{-4}$. The value of $K_c$ for the reaction $NO_{(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + \frac{1}{2} O_{2(g)}$ at the same temperature is:

  • A
    $0.02$
  • B
    $2.5 \times 10^2$
  • C
    $4 \times 10^{-4}$
  • D
    $50$

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