Consider the reaction: $$ 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) \quad K_{\mathrm{p}}=28.4 \text { at } 298 \mathrm{~K} $$ In a reaction mixture at equilibrium, the partial pressure of NO is 108 torr and that of \(\mathrm{Br}_{2}\) is 126 torr. What is the partial pressure of NOBr in this mixture?

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. This balance of reactions means that the concentration of reactants and products remains constant over time, even though individual molecules continue to react with each other. An important factor to remember is that equilibrium does not necessarily mean that the concentrations of reactants and products are equal, but that their ratios do not change over time.

For the reaction given in our exercise, \(2 \text{NO}(g) + \text{Br}_2(g) \rightleftharpoons 2 \text{NOBr}(g)\), chemical equilibrium occurs when the rate of production of NOBr from NO and \(\text{Br}_2\) equals the rate at which NOBr decomposes back into NO and \(\text{Br}_2\). It is a dynamic process, hence, although we may not see any visible changes in a system at equilibrium, molecules are continually reacting.

Partial pressure is essentially the pressure that a single gas in a mixture of gases would exert if it occupied the entire volume on its own. It is directly proportional to the concentration of the gas in the mixture and is an important concept in the study of gases involved in chemical reactions. In the realm of chemical equilibrium involving gases, like the reaction in our exercise, the partial pressures are key to determining the position of the equilibrium.

Each gas in a reaction mixture will exert its own partial pressure, and for a system at equilibrium, these partial pressures can be plugged into the equilibrium expression to describe the state of the system. Knowing the partial pressure of each reactant and product can help us predict the direction of the reaction if conditions change, an application of Le Chatelier's principle.

The equilibrium constant, represented as \(K_c\) for concentrations or \(K_p\) for partial pressures, is a ratio that quantifies the state of equilibrium for a given chemical reaction. It is a value calculated from the concentrations or partial pressures of the reactants and products when the system is at equilibrium. For gas-phase reactions, \(K_p\) is commonly used.

\(K_p\) expresses the relationship between the partial pressures of the products and reactants raised to the power of their respective coefficients from the balanced chemical equation. In our exercise, when we establish the equilibrium expression, this fixed \(K_p\) value reflects the ratio of concentrations that the reaction will maintain at a particular temperature. It's important to note that \(K_p\) is only dependent on temperature, and any change in temperature can shift the value of \(K_p\), thus affecting the position of equilibrium.

Le Chatelier's principle tells us that if an external stress is applied to a system at equilibrium, the system adjusts in a way that minimizes the stress. This stress can result from changes in concentration, pressure, volume, or temperature. For instance, adding more reactants to a system will shift the equilibrium to produce more products, and likewise, increasing the pressure will favor the formation of the side of the reaction with fewer moles of gas.

Understanding this principle helps in predicting the behavior of a system when it's subjected to changes. In the context of the exercise where we have a chemical reaction between gaseous substances, if we were to change the partial pressure of one of the reactants, Le Chatelier's principle would predict how the system's equilibrium would shift in response to restore the equilibrium state.