At \(2200^{\circ} \mathrm{C}, K_{\mathrm{p}}=0.050\) for the reaction $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$ What is the partial pressure of \(\mathrm{NO}\) in equilibrium with \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) that were placed in a flask at initial pressures of \(0.80\) and \(0.20\) atm, respectively?

Understanding the equilibrium constant is crucial for grasping how chemical reactions reach a state of balance. The equilibrium constant, represented by the symbol K, is a number that provides a measure of where the equilibrium lies for a given chemical reaction. For gas-phase reactions, the equilibrium constant is often given as Kp, which is based on the partial pressures of gases involved.

Using the equation from the exercise, \[K_p = \frac{[NO]^2}{[N_{2}][O_{2}]}\], Kp relates to how product and reactant pressures influence the reaction's balance. A small Kp value (0.050 in this case) suggests that, at equilibrium, the reactants (N2 and O2) will predominate over the products (NO) at the specified temperature of 2200°C. In other words, there will be a higher concentration of unreacted N2 and O2 than that of NO. Understanding this concept allows students to predict the direction of the shift in a reaction when changes occur in the system.

The ICE table is a systematic approach that helps understand changes that occur as reactants move toward equilibrium to form products. ICE stands for Initial, Change, and Equilibrium, representing different stages of the reaction.

In the case of our problem, the initial pressures of N2 and O2 are given, while NO is initially not present. As the reaction proceeds towards equilibrium, the pressures of N2 and O2 decrease while that of NO increases. The changes in pressures are represented by a variable 'x' in the ICE table. This methodical layout aids in visualizing the reaction progression and simplifies the process of solving for the equilibrium constant, Kp. Students are encouraged to use this method to avoid confusion and ensure that all changes in the reactant and product concentrations are accounted for correctly when determining the equilibrium state.

Partial pressure, an essential aspect of chemical equilibrium in gaseous systems, refers to the pressure exerted by each individual gas in a mixture. According to Dalton's law, the total pressure exerted by the mixture is the sum of the partial pressures of each gas composing it. When dealing with chemical equilibria involving gases, partial pressures play a pivotal role.

In our exercise, the partial pressure of NO at equilibrium is of particular interest and is determined by the change in moles of gas 'x' during the reaction from the initial pressures of N2 and O2. Upon establishing the value of 'x', it can be substituted back into the ICE table to calculate the equilibrium partial pressures of each gas. Understanding the concept of partial pressure is instrumental in solving problems related to gas-phase equilibrium, as it intimately links to the equilibrium constant expression.