Two gaseous equilibria $SO_{2(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons SO_{3(g)}$ and $2SO_{3(g)} \rightleftharpoons 2SO_{2(g)} + O_{2(g)}$ have equilibrium constants $K_1$ and $K_2$ respectively at $298 \ K$. Which of the following relationships between $K_1$ and $K_2$ is correct?

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