As noted in the chapter, the value of \(K_{\mathrm{eq}}\) for the reaction \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}(g)\) is \(0.0017\) at \(2027^{\circ} \mathrm{C}\) and \(2.3 \times 10^{-9}\) at \(25^{\circ} \mathrm{C}\). (a) Judging from the values of \(K_{\text {eq }}\), does this reaction shift to the left or to the right when the reaction mixture is heated? Explain your answer. (b) Is this reaction endothermic or exothermic? Explain your answer.

Le Châtelier's principle is a fundamental concept in chemical equilibrium that predicts how a system at equilibrium reacts to disturbances. If an external stress, such as a change in temperature, pressure, or concentration of one of the reactants or products, is applied to the system, the equilibrium will adjust to partially counteract the change. This behavior is a response to maintain stability.

For example, increasing the temperature of an equilibrium system where the forward reaction is endothermic will cause the system to shift towards the products to absorb the excess heat. Conversely, if it's exothermic, the system will shift towards the reactants. Similarly, increasing the pressure of a system by decreasing volume will shift the equilibrium towards the side with fewer moles of gas. Le Châtelier's principle helps us understand and predict the direction of the shift in equilibrium in response to such changes.

The equilibrium constant, denoted as Keq, is a numerical value that expresses the ratio of product concentrations to reactant concentrations for a reaction at equilibrium, each raised to the power of their coefficients in the balanced equation. It is a measure of the degree to which a chemical reaction proceeds to equilibrium at a given temperature.

Mathematically, for a reaction of the form \(aA + bB \rightleftarrows cC + dD\), the equilibrium constant is given by:
\[K_{eq} = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]
Here, the brackets represent the concentration of the chemical species at equilibrium. A large Keq signifies a high concentration of products at equilibrium, indicating the forward reaction is favored. Conversely, a small Keq indicates a high concentration of reactants and that the backward reaction is favored.

Endothermic reactions are chemical reactions that absorb heat from their environment. In an endothermic process, the energy needed to break the bonds of the reactants is greater than the energy released when new bonds are formed in the products. This results in a net absorption of energy.

Examples of endothermic reactions include the melting of ice, photosynthesis, and the reaction of barium hydroxide octahydrate with ammonium chloride. These reactions require an input of heat and are characterized by a positive change in enthalpy (\(\Delta H > 0\)). Endothermic reactions are significant in various processes such as cooking, refrigeration, and endothermic materials used in sports injury packs that absorb heat to alleviate pain.

Temperature plays a critical role in determining the direction in which a chemical reaction proceeds. Changes in temperature can shift the position of equilibrium according to Le Châtelier's principle. If a reaction is endothermic and the temperature is raised, the equilibrium will shift towards the products as the system tries to absorb the added heat. In contrast, if the reaction is exothermic, raising the temperature will shift the equilibrium towards the reactants as the system releases heat.

In the discussed reaction between nitrogen and oxygen to form nitric oxide, an increase in temperature results in an increase in the Keq value, indicating a shift towards the products. As the forward reaction is endothermic, higher temperatures favor the formation of nitric oxide, demonstrating a clear relationship between temperature and reaction direction.