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For the reaction N2(g) + O2(g)2 NO(g), Kc = 4.08×104 at 2000 K. What is the value of Kc at 2000 K for the reaction NO(g)½ N2(g) + ½ O2(g)?
The given reaction is N2(g) + O2(g)2 NO(g), Kc = 4.08×104
Reversing the reaction gives the proper reactants and products for the target reaction, but with the wrong stoichiometry. Reversing the reaction also means that the new equilibrium constant is the inverse of the original equilibrium constant.
2 NO(g) N2(g) + O2(g) Kc = 1/4.08×104 = 2.45×103
To obtain the correct stoichiometry for the target reaction, all of the stochiometric coefficients are multiplied by ½. This means that the new equilibrium constant is the square root of the old equilibrium constant.
NO(g) ½ N2(g) + ½ O2(g) Kc = (2.45×103)½ = 49.5