At \( T(\mathrm{K}) \), the equilibrium constant of \( \mathrm{A_2(g)} + \mathrm{B_2(g)} \rightleftharpoons \mathrm{C(g)} \) is \( 2.7 \times 10^{-5} \). What is the equilibrium constant for \( \frac{1}{3}\mathrm{A_2(g)} + \frac{1}{3}\mathrm{B_2(g)} \rightleftharpoons \frac{1}{3}\mathrm{C(g)} \) at the same temperature?
