Question

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.

Short answer

In accordance with Le Châtelier's principle, the equilibrium constant for the formation of NO from N2 and O2 increases with increasing temperature because the reaction is endothermic; it absorbs heat, causing the equilibrium to shift toward the direction that absorbs heat, favoring the formation of NO. On the other hand, the equilibrium constant for the formation of NO2 from NO and O2 decreases with increasing temperature since the reaction is exothermic; it releases heat, causing the equilibrium to shift toward the direction that also absorbs heat, which is opposite to the formation of NO2.

Step-by-step solution

Recall Le Châtelier's Principle

Le Châtelier's principle states that when a stress (change) is applied to a system at equilibrium, the equilibrium will shift to counteract the change (to restore equilibrium). The equilibrium constant (K) depends on temperature, so considering changes in temperature is crucial for this question.

Identify the system in question (reactions)

There are two reactions in question: 1. \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\) 2. \(2NO(g)\ +\ O_2(g)\ \rightleftharpoons\ 2NO_2(g)\)

Determine the exothermic or endothermic nature of the reactions

The first reaction, \(N_2(g)\ +\ O_2(g) \rightleftharpoons\ 2NO(g)\) is endothermic (absorbs heat) because it requires energy to break the strong N≡N and O=O bonds present in the diatomic molecules. The second reaction, \(2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)\) is exothermic (releases heat) because it forms strong double bonds (N=O) in the nitrogen dioxide molecule, releasing energy in the process.

Apply Le Châtelier's Principle to temperature changes for each reaction

We'll now apply Le Châtelier's principle to the two reactions, focusing on how changes in temperature affect the equilibrium constants. 1. For the endothermic reaction \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\), increasing the temperature adds heat to the system. According to Le Châtelier's principle, the equilibrium will shift in the direction that absorbs the added heat, favoring the formation of NO. This will increase the equilibrium constant, K. 2. For the exothermic reaction \(2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)\), increasing the temperature adds heat to the system. According to Le Châtelier's principle, the equilibrium will shift in the direction that absorbs the added heat, which is the reverse direction (opposite of NO2 formation). This will decrease the equilibrium constant, K.

Conclusion

Based on Le Châtelier's principle, the equilibrium constant for the formation of NO from N2 and O2 increases with increasing temperature because the reaction is endothermic and absorbs heat. In contrast, the equilibrium constant for the formation of NO2 from NO and O2 decreases with increasing temperature because the reaction is exothermic and releases heat.