Consider the equilibrium \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\). (a) What happens to the partial pressure of \(\mathrm{SO}_{3}\) when the partial pressure of \(\mathrm{SO}_{2}\) is decreased? (b) If the partial pressure of \(\mathrm{SO}_{2}\) is increased, what happens to the partial pressure of \(\mathrm{O}_{2}\) ?

Chemical equilibrium occurs when a chemical reaction and its reverse process proceed at the same rate, leading to no overall change in the amounts of the reactants and products. This state is dynamic, meaning that the molecules continue to react, but because the reaction rates in both directions are equal, the concentrations remain constant over time.

In the context of the exercise concerning the reaction \(2\text{SO}_{2}(\text{g}) + \text{O}_{2}(\text{g}) \rightleftharpoons 2\text{SO}_{3}(\text{g})\), the system reaches equilibrium when the rate at which the reactants turn into the products (sulfur dioxide and oxygen forming sulfur trioxide) is equal to the rate at which the products decompose back into reactants.

Understanding this concept is crucial for interpreting the changes in partial pressures as described in the exercise solution. It provides a baseline to predict how the system readjusts to maintain that finely balanced state when subjected to external changes.

Partial pressure is the pressure that a single gas component in a mixture of gases would exert if it alone occupied the entire volume. It's a way to describe the contribution of individual gas species to the total pressure of the mixture.

In the equilibrium scenario presented, the partial pressures of \(\text{SO}_{2}\), \(\text{O}_{2}\), and \(\text{SO}_{3}\) come into play significantly. For instance, if the problem asks what happens to the partial pressure of \(\text{SO}_{3}\) when \(\text{SO}_{2}\)'s partial pressure decreases, it implies that we're looking at how the individual gas's behavior impacts the overall system. The understanding of partial pressures is key to predicting changes in equilibrium conditions, such as those prompted in the exercise, and it's an important concept in chemical thermodynamics.

An equilibrium shift is the movement of a reaction mixture's composition towards the products or reactants side in response to an external stress, as described by Le Chatelier's Principle. When a chemical system at equilibrium experiences a change in concentration, temperature, volume, or pressure, the system will adjust accordingly to minimize that change and restore a new equilibrium state.

In the exercise, decreasing the partial pressure of \(\text{SO}_{2}\) causes the equilibrium to shift to the left, increasing its production and decreasing \(\text{SO}_{3}\)'s partial pressure as the system seeks to counteract the disturbance. Conversely, increasing \(\text{SO}_{2}\)'s partial pressure would cause the equilibrium to shift to the right, using more \(\text{O}_{2}\) and resulting in its partial pressure decreasing. This demonstrates how equilibrium can dynamically adjust to changes, a central concept when predicting the behavior of chemical systems.