An equilibrium mixture at a specific temperature is found to consist of $1.2 \times 10^{-3} \mathrm{mol} / \mathrm{LHCl}$ , $3.8 \times 10^{-4} \mathrm{mol} / \mathrm{L} \mathrm{O}_{2}, 5.8 \times 10^{-2} \mathrm{mol} / \mathrm{L} \mathrm{H}_{2} \mathrm{O},$ and $5.8 \times 10^{-2} \mathrm{mol} / \mathrm{L} \mathrm{Cl}_{2}$ according to the following:
$\quad 4 \mathrm{HCl}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{Cl}_{2}(g)$
Determine the value of the equilibrium constant for this system.