Consider this reaction: $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$ If the equilibrium partial pressures of \(\mathrm{N}_{2}, \mathrm{O}_{2}\), and NO are 0.15 atm, 0.33 atm, and 0.050 atm, respectively, at \(2200^{\circ} \mathrm{C}\), what is \(K_{P} ?\)

When dealing with gases in chemical reactions that have reached equilibrium, it's essential to understand the concept of equilibrium partial pressures. Partial pressure refers to the pressure exerted by a single gas in a mixture of gases. At equilibrium, the system has a constant ratio of products to reactants, and this ratio is described by the partial pressures of the gases involved.

For the reaction:
\[ N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \]
The equilibrium partial pressures are the pressures of each gas when the forward and reverse reactions occur at the same rate, resulting in no net change in the concentrations. The problem gives the equilibrium partial pressures of \( N_2 \), \( O_2 \), and NO as 0.15 atm, 0.33 atm, and 0.050 atm, respectively. Understanding these values allows us to calculate the equilibrium constant, which indicates the extent to which a reaction proceeds.

The equilibrium constant expression is a quantitative measure of the composition of a reaction mixture at equilibrium. It's expressed in terms of the concentrations or, in the case of gases, the partial pressures of reactants and products. For a general reaction
\[aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)\]
The equilibrium constant for pressure, \( K_P \), is written as:
\[K_P = \frac{{P_{C}^c \cdot P_{D}^d}}{{P_{A}^a \cdot P_{B}^b}}\]
where \( P_{X} \) denotes the equilibrium partial pressure of the substance X and the exponents correspond to the stoichiometric coefficients from the balanced chemical equation.

In the exercise,
\[K_P = \frac{{(P(NO))^2}}{{P(N_2) \cdot P(O_2)}}\]
By substituting the given equilibrium partial pressures into the expression and calculating, the equilibrium constant helps predict the direction of the reaction and the yields of products at a given temperature.

Le Chatelier's principle is a fundamental concept in chemical equilibrium that predicts how a system at equilibrium will respond to changes in concentration, temperature, volume, or pressure. It states that if an external stress is applied to a system at equilibrium, the system will adjust in a way that counteracts the change.

This can involve shifts in the equilibrium positions, such as:

• Adding or removing reactants or products
• Changing the volume of the system (which changes the partial pressures in the case of gases)
• Altering the temperature, which affects the equilibrium constant

For instance, if the temperature of the equilibrium system in the exercise were to increase, the principle implies that the endothermic direction will be favored to absorb the extra heat. Consequently, understanding Le Chatelier's principle helps to predict and control the yields of reactions by optimizing conditions.