When the reaction \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}(g)\) is run at \(2000^{\circ} \mathrm{C}\), appreciable amounts of reactants and product are present at equilibrium. (a) A sealed 2.00-L container at \(2000{ }^{\circ} \mathrm{C}\) is filled with \(1.00\) mole of \(\mathrm{NO}(g)\) and nothing else. At that moment, which reaction is faster, forward or reverse? Justify your answer. (b) At equilibrium, the concentration of \(\mathrm{NO}(g)\) is \(0.0683 \mathrm{M}\) and the concentration of \(\mathrm{N}_{2}(g)\) is \(0.2159 \mathrm{M}\). What is the value of \(K_{\mathrm{eq}}\) at \(2000^{\circ} \mathrm{C} ?\)

The equilibrium constant (denoted as K_eq) is a vital concept to understand when exploring chemical equilibria. It's a number that provides a quantitative measure of the position of equilibrium for a reversible reaction at a given temperature. In simple terms, the K_eq helps determine the extent to which reactants are converted into products.

The equilibrium constant is derived from the law of mass action, which states that for a balanced chemical equation, the ratio of the product of concentrations of the reaction products raised to the power of their stoichiometric coefficients to the product of concentrations of the reactants raised to the power of their stoichiometric coefficients remains constant at equilibrium. For the reaction:
N₂(g) + O₂(g) ⇌ 2NO(g),
the equilibrium constant expression is:
\[K_{eq} = \frac{[NO]^2}{[N_2][O_2]}\]
In practice, K_eq can tell us if the reactants or products are favored in an equilibrium situation. If K_eq is much greater than 1, then products are favored, and if it is much less than 1, reactants are favored. Using the equilibrium concentrations of the reactants and products, you can calculate the K_eq and determine the direction the reaction favors under specific conditions.

Closely related to the equilibrium constant is the reaction quotient (Q), which is calculated in the same way as K_eq but for any set of concentrations or partial pressures of the reactants and products, not necessarily at equilibrium. The purpose of Q is to predict the direction in which a reaction mixture will proceed to reach equilibrium.

For the given reaction, the reaction quotient would be:
\[ Q = \frac{[NO]^2}{[N_2][O_2]} \]
The comparison of Q to K_eq gives insight into the reaction's dynamics; namely, if Q < K_eq, the forward reaction is favored, and the system will shift towards the products to reach equilibrium. Conversely, if Q > K_eq, the reverse reaction is favored, and the system will shift towards the reactants. If Q = K_eq, the system is already at equilibrium, and thus, no shift is expected.

Chemical kinetics is the study of the speed or rate of a chemical reaction and the factors that affect it. Kinetics can explain why some reactions are instantaneous while others are incredibly slow. Factors like concentration, temperature, surface area, and catalysts can influence reaction rates.

Based on the initial conditions of a reaction, we can make assumptions about its kinetics. In our exercise, we determined that the initial concentration of NO was higher than at equilibrium which means initially, the reverse reaction that forms N₂ and O₂ from NO will be faster. This reflects a fundamental principle of kinetics: the rate of a reaction is often proportional to the concentrations of the reactants. Higher concentration generally leads to more collisions and therefore a faster reaction rate, until the system reaches equilibrium where the forward and reverse reactions occur at the same rate.

Le Chatelier's Principle is a qualitative tool that predicts how a change in conditions can affect the position of equilibrium for a chemical reaction. It states that when a system at equilibrium is subjected to an external change, such as pressure, temperature, or concentration changes, the system will adjust itself to counteract that change and establish a new equilibrium.

In the context of our exercise, if we were to change the conditions of the system, say by increasing the temperature, we'd expect the system to respond in a way to counteract this change. For exothermic reactions, increasing temperature shifts the equilibrium position towards the reactants, while for endothermic reactions, the equilibrium shifts towards the products. Similarly, increasing the concentration of a reactant or decreasing the concentration of a product will shift the equilibrium towards the products to reduce the change. This principle is immensely useful for predicting the outcomes of changes in a chemical process and is fundamental in the field of chemical engineering.