Nitrogen and oxygen react at high temperatures. (a) Write the expression for the equilibrium constant \(\left(K_{c}\right)\) for the reversible reaction \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad \Delta H=181 \mathrm{kJ}\) (b) What will happen to the concentrations of \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{NO}\) at equilibrium if more \(\mathrm{O}_{2}\) is added? (c) What will happen to the concentrations of \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{NO}\) at equilibrium if \(\mathrm{N}_{2}\) is removed? (d) What will happen to the concentrations of \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and NO at equilibrium if NO is added? (e) What will happen to the concentrations of \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{NO}\) at equilibrium if the volume of the reaction vessel is decreased? (f) What will happen to the concentrations of \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{NO}\) at equilibrium if the temperature of the system is increased?

The equilibrium constant expression is a mathematical representation of a chemical reaction at equilibrium. It relates the concentrations of the products and reactants in a balanced chemical equation and is denoted by the symbol \(K_c\). In a generic form, the equilibrium constant for a reaction \(aA + bB \rightleftharpoons cC + dD\) can be written as \(K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}\), where the square brackets denote the molar concentrations of the substances, and the letters \(a\), \(b\), \(c\), and \(d\) represent the stoichiometric coefficients from the balanced equation. For the given reaction \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\), the equilibrium constant expression is \(K_c = \frac{[NO]^2}{[N_2][O_2]}\). This expression is crucial as it provides valuable insight into the extent of the reaction and whether a system has reached equilibrium. In teaching this concept, it is essential to emphasize the direct connection between the balanced chemical equation and the equilibrium constant expression.

Understanding the equilibrium constant expression allows for the prediction of how changes to the system's conditions will affect the concentrations of reactants and products, using a related concept known as the reaction quotient (\(Q\)). If \(Q < K_c\), the reaction will proceed in the forward direction to reach equilibrium. If \(Q > K_c\), the reaction shifts in the reverse direction until equilibrium is achieved.

Le Chatelier's principle is named after the French chemist Henri Louis Le Chatelier, and it provides a qualitative prediction of how a system at equilibrium will respond to changes in concentration, pressure, or temperature. Simply put, when a stress is applied to a system at equilibrium, the system will adjust in such a way as to counteract that stress and establish a new state of equilibrium. This is pivotal for understanding the behavior of chemical reactions under various conditions.

For instance, if additional \(O_2\) is added to the reaction mixture, Le Chatelier's principle predicts that the equilibrium will shift to the right, favoring the formation of more \(NO\) to alleviate the increase in \(O_2\)'s concentration. Conversely, removing \(N_2\) will result in an equilibrium shift to the left, compensating for the lowered \(N_2\) concentration by producing more of it from the reaction products. These shifts will continue until the system re-establishes equilibrium. It is crucial to provide clear examples to show how equilibrium shifts in response to different kinds of stresses applied to the system.

The reaction quotient, denoted by \(Q\), is a snapshot of a reaction's status at a given moment and is defined by an expression that has the same form as the equilibrium constant expression but can be evaluated at any time, not just at equilibrium. The comparison between \(Q\) and the equilibrium constant \(K_c\) indicates the direction the reaction will proceed to achieve equilibrium. If \(Q < K_c\), the reaction will tend to produce more products, shifting to the right. If \(Q > K_c\), there are more products than at equilibrium relative to reactants, and the reaction will shift to the left, creating more reactants.

For the reaction \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\), if you were to measure the concentrations of \(N_2\), \(O_2\), and \(NO\) before the system reaches equilibrium and calculate \(Q\), you could predict which way the reaction would shift to reach equilibrium. This concept has practical implications in industrial processes, where maintaining the desired yield of a product often requires monitoring and adjusting reaction conditions.

Endothermic reactions are chemical reactions that absorb heat from their surroundings. This thermodynamic behavior is denoted by a positive change in enthalpy (\(\Delta H\)). In the reaction \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\), with \(\Delta H = 181 \mathrm{kJ}\), the positive sign indicates that it is an endothermic process. According to Le Chatelier's principle, increasing the temperature adds energy to the system, thereby favoring the endothermic forward reaction and shifting the equilibrium towards the products, increasing the concentration of \(NO\).

It is essential for students to understand that endothermic reactions require energy input, making them sensitive to temperature changes. For teaching purposes, connecting the concepts of Le Chatelier's principle and enthalpy changes deeply enriches students' comprehension of how temperature influences chemical equilibrium and why exothermic reactions behave oppositely to endothermic ones.