Explain, using Le Châtelier's principle, why the equilibrium constant for the formation of \(\mathrm{NO}\) from \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) increases with increasing temperature, whereas the equilibrium constant for the formation of \(\mathrm{NO}_{2}\) from \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) decreases with increasing temperature.

First, let's write down the balanced chemical equations for the formation of NO from N2 and O2, and the formation of NO2 from NO and O2: 1. Formation of NO: \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\) 2. Formation of NO2: \(2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)\) Now that we know the reactions, we can analyze them using Le Châtelier's principle.

Le Châtelier's principle states that if a system at equilibrium experiences a change in temperature, pressure, or concentration, the system will adjust to counteract the change and restore equilibrium. In the current exercise, the focus is on the change in temperature. The key point to keep in mind is that an increase in temperature favors the endothermic reaction, while a decrease in temperature favors the exothermic reaction.

The formation of NO from N2 and O2 is an endothermic process, meaning it absorbs heat from the surroundings: \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\) , ΔH > 0 (Endothermic) The formation of NO2 from NO and O2 is an exothermic process, meaning it releases heat to the surroundings: \(2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)\) , ΔH < 0 (Exothermic) Now we will use this information and Le Châtelier's principle to explain why the equilibrium constant for these reactions changes as the temperature increases.

When the temperature increases: 1. For the endothermic reaction (formation of NO), the equilibrium will shift towards the products to counteract the increased temperature. Therefore, the equilibrium constant will increase: \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\) , Kc increases as temperature increases. 2. For the exothermic reaction (formation of NO2), the equilibrium will shift towards the reactants to counteract the increased temperature. Therefore, the equilibrium constant will decrease: \(2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)\) , Kc decreases as temperature increases. These changes in equilibrium constants with temperature can be explained using Le Châtelier's principle: An endothermic reaction will shift towards products with increasing temperature, while an exothermic reaction will shift towards reactants with increasing temperature.