WEB Nitrogen dioxide can decompose to nitrogen oxide and oxygen. $$2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$$ \(K\) is \(0.87\) at a certain temperature. A 5.0-L flask at equilibrium is determined to have a total pressure of \(1.25\) atm and oxygen to have a partial pressure of \(0.515\) atm. Calculate \(P_{\mathrm{NO}}\) and \(P_{\mathrm{NO}}\), at equilibrium.

One of the fundamental principles in chemistry is the concept of chemical equilibrium. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, leading to a constant composition of the reaction mixture over time. The quantification of this state for a particular reaction is expressed as the equilibrium constant, denoted by the symbol K.

For the reaction involving nitrogen dioxide (NO₂) decomposing to nitrogen oxide (NO) and oxygen (O₂), the equilibrium constant expression considers the concentrations, or in the case of gases, the partial pressures of the reactants and products. It is given by the formula: $$K = \frac{P_{NO}^2 \times P_{O_2}}{P_{NO_2}^2}$$
where (P_{NO}), (P_{O_2}), and (P_{NO_2}) are the partial pressures of nitrogen oxide, oxygen, and nitrogen dioxide, respectively. The superscript 2 reflects the stoichiometry of the reaction as indicated by the balanced chemical equation. When evaluating the equilibrium state of a reaction, the equilibrium constant provides a ratio that relates the concentrations (or partial pressures) of products to reactants.

The partial pressures of gases are a crucial aspect of understanding chemical equilibria in gaseous systems. Each gas in a mixture exerts a certain amount of pressure, which is referred to as its partial pressure. The total pressure of the system is the sum of all partial pressures.

In a chemistry problem where you are asked to calculate individual partial pressures at equilibrium, such as in the given nitrogen dioxide decomposition reaction, you would typically assign a variable to the unknown partial pressures and relate them to known values and conditions, such as total pressure. In this scenario, the total pressure inside the flask is known, and the problem involves finding the partial pressures of (NO) and (NO₂).

To approach this task, a system of equations may be set up based on the stoichiometric relationships given in the balanced reaction equation. The calculated partial pressures, aside from being an essential part of finding the equilibrium constant, also offer insights into the extent of reaction and the concentrations of various species at equilibrium.

Le Chatelier's principle is a qualitative tool that predicts how a change in conditions can affect the position of equilibrium. When a system at equilibrium is disturbed, it will respond in such a way as to counteract the change and achieve a new equilibrium state. This principle helps to understand the behavior of reactions in response to external stresses, such as changes in concentration, pressure, and temperature.

For instance, increasing the pressure on our reaction system would shift the equilibrium toward the side with fewer gas molecules, which in the case of the nitrogen dioxide decomposition reaction would be the side with the (NO₂). Conversely, reducing the partial pressure of (O₂) would shift the equilibrium towards the production of more (O₂) to counteract the change. Understanding Le Chatelier's principle is not only essential for predicting the behaviour of reactions but also for manipulation of conditions to control product concentrations in industrial chemical processes.

By applying Le Chatelier's principle to various scenarios, students can develop an intuitive sense of how systems at equilibrium respond to dynamic changes, reinforcing a foundational concept in chemical thermodynamics.