Consider the following reactions in which all the reactants and products are present in gaseous state.
\( 2\,\mathrm{XY} \rightleftharpoons \mathrm{X_2} + \mathrm{Y_2};\ K_1 = 2.5 \times 10^{5} \)
\( \mathrm{XY} + \tfrac{1}{2}\mathrm{Z_2} \rightleftharpoons \mathrm{XYZ};\ K_2 = 5 \times 10^{-3} \)
The value of \( K_3 \) for the equilibrium \( \tfrac{1}{2}\mathrm{X_2} + \tfrac{1}{2}\mathrm{Y_2} + \tfrac{1}{2}\mathrm{Z_2} \rightleftharpoons \mathrm{XYZ} \) is:
