In the synthesis of gaseous methanol from carbon monoxide gas and hydrogen gas, the following equilibrium concentrations were determined at 483 K: [CO(g)] = 0.0911 M, [H₂(g)] = 0.0822 M, and 3[CH₃OH(g)] = 0.00892 M. Calculate the equilibrium constant and Δ_rG° for the reaction CO(g) + 2 H₂(g) → CH₃OH(g).