Consider the reaction $$ \begin{aligned} 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) & \\ \Delta H^{\circ}=&-198.2 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ Comment on the changes in the concentrations of \(\mathrm{SO}_{2}, \mathrm{O}_{2},\) and \(\mathrm{SO}_{3}\) at equilibrium if we were to \((\mathrm{a})\) increase the temperature, (b) increase the pressure, (c) increase \(\mathrm{SO}_{2},\) (d) add a catalyst, (e) add helium at constant volume.

In a chemical reaction, when the rate of the forward reaction equals the rate of the reverse reaction, it is said to be at a chemical equilibrium. The concentrations of reactants and products remain constant, but reactions are still occurring. For example, in the synthesis of sulfur trioxide (SO_3) from sulfur dioxide (SO_2) and oxygen (O_2), the system achieves equilibrium when the formation rate of SO_3 equals its decomposition rate back into SO_2 and O_2.

Equilibrium does not mean the reactants and products are present in equal amounts, but their ratios do not change over time. This balance can be depicted using an equilibrium constant, K, which is specific to each reaction and conditions such as temperature.

Temperature changes can significantly impact chemical equilibrium, as exemplified by Le Châtelier’s Principle. An increase in temperature typically favors the endothermic direction—the direction that absorbs heat—while a decrease in temperature favors the exothermic direction—the direction that releases heat. In the reaction of SO_2 with O_2 to form SO_3, the process is exothermic, releasing heat. Raising the temperature shifts the equilibrium toward the reactants, SO_2 and O_2, while reducing the amount of SO_3, thereby demonstrating the principle's application.

Lowering the temperature would have the opposite effect, driving the equilibrium toward the formation of more SO_3. This is because the system counteracts the temperature decrease by favoring the reaction that produces heat.

Pressure changes can also influence chemical equilibrium, especially in reactions involving gases. An increase in pressure causes the system to adjust so as to minimize the pressure, generally by favoring the side of the reaction with fewer gas molecules. For a reaction like 2SO_2(g) + O_2(g) \(\rightleftharpoons\) 2SO_3(g) where the reactants total three moles of gas, and the products total two moles, an increase in pressure would shift the equilibrium toward the product side (SO_3) with fewer gas molecules. Conversely, decreasing the pressure would favor the side with more gas molecules, SO_2 and O_2, thus pushing the equilibrium towards the reactants.

Catalysts are substances that speed up chemical reactions without being consumed in the process. They work by lowering the activation energy of both the forward and reverse reactions. However, they do not affect the equilibrium position or the concentrations of the reactants and products at equilibrium. Instead, they allow the system to reach equilibrium more rapidly. In the context of the given reaction, the addition of a catalyst would not affect the levels of SO_2, O_2, or SO_3. It would simply mean that the equilibrium state is achieved faster, which is valuable in industrial processes where time and efficiency are crucial.

When an inert gas like helium is added to a reaction mixture at constant volume, the total pressure increases, but the partial pressures of the reacting gases remain unchanged. This is because inert gases do not react with the substances in the mixture. As Le Châtelier’s Principle would suggest, no shift in equilibrium occurs since there is no change in the concentrations of the reactants or products. Therefore, in the production of sulfur trioxide from sulfur dioxide and oxygen, adding helium would not alter the equilibrium concentrations of SO_2, O_2, and SO_3.