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 conclusion, according to Le Châtelier's principle, the equilibrium constant for the formation of NO from N2 and O2 increases with increasing temperature because the forward reaction is endothermic, consuming heat. Conversely, the equilibrium constant for the formation of NO2 from NO and O2 decreases with increasing temperature because the forward reaction is exothermic, releasing heat.

Step-by-step solution

Understand Le Châtelier's Principle

Le Châtelier's Principle states that when a system at equilibrium experiences a disturbance or change in its conditions (like concentration, temperature, or pressure), the system will adjust in such a way as to counteract the disturbance and restore the equilibrium. Heat is considered as a reactant in an endothermic reaction and a product in an exothermic reaction.

Analyze the reaction of NO formation

The formation of NO from N2 and O2 is given by the following reaction: \[N_{2} + O_{2} \rightleftharpoons 2NO\] The forward reaction is endothermic, meaning it requires heat (energy) for the reaction to proceed. Therefore, we can think of heat as a reactant, writing the reaction as: \[N_{2} + O_{2} + \Delta H_{1} \rightleftharpoons 2NO\]

Effect of increasing temperature on NO formation

According to Le Châtelier's Principle, if the temperature increases, the system will act to counteract this increase by absorbing the extra heat. In this case, the system will favor the endothermic (forward) reaction, which consumes heat. As a result, the equilibrium constant (K) for the formation of NO will increase with increasing temperature.

Analyze the reaction of NO2 formation

The formation of NO2 from NO and O2 is given by the following reaction: \[2NO + O_{2} \rightleftharpoons 2NO_{2}\] The forward reaction is exothermic, meaning it releases heat (energy) as the reaction proceeds, so we consider heat as a product: \[2NO + O_{2} \rightleftharpoons 2NO_{2} + \Delta H_{2}\]

Effect of increasing temperature on NO2 formation

According to Le Châtelier's Principle, if the temperature increases, the system again will act to counteract this increase by absorbing the extra heat. In this case, the system will favor the endothermic (reverse) reaction, which consumes heat. As a result, the equilibrium constant (K) for the formation of NO2 will decrease with increasing temperature. In conclusion, the equilibrium constant for the formation of NO increases with increasing temperature because the forward reaction is endothermic, while the equilibrium constant for the formation of NO2 decreases with increasing temperature because the forward reaction is exothermic, consistent with Le Châtelier's principle.