The oxidation of \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3}\) is catalyzed by \(\mathrm{NO}_{2}\). The reaction proceeds according to: $$ \begin{array}{l} \mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{SO}_{3}(g) \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \end{array} $$ (a) Show that the two reactions can be summed to give the overall oxidation of \(\mathrm{SO}_{2}\) by \(\mathrm{O}_{2}\) to give \(\mathrm{SO}_{3}\). (b) Why do we consider \(\mathrm{NO}_{2}\) a catalyst and not an intermediate in this reaction? (c) Is this an example of homogeneous catalysis or heterogeneous catalysis?

Homogeneous catalysis is an important concept in chemistry where the catalyst and the reactants are in the same phase—typically gas or liquid. This similarity in phase allows for the catalyst to interact with the reactants more easily, which can lead to more effective and efficient reactions. For instance, in the oxidation of sulfur dioxide (\textbf{SO}\(_2\)) to sulfur trioxide (\textbf{SO}\(_3\)) using nitrogen dioxide (\textbf{NO}\(_2\)) as a catalyst, all the components are in the gas phase. This ensures that \textbf{NO}\(_2\) can effectively facilitate the reaction without being used up in the end product.

It's essential to distinguish homogeneous catalysis from heterogeneous catalysis. The latter involves the catalyst being in a different phase from the reactants, like a solid catalyst in a liquid reaction mixture. Homogeneous catalysis is widely used in industrial processes due to its advantages, which include ease of mixing and often, a higher selectivity and rate of reaction.

Understanding the chemical reaction mechanism is crucial for grasping how reactions proceed at a molecular level. It involves a step-by-step description of how reactants transition into products, which includes the breaking and forming of chemical bonds. A pivotal concept in these mechanisms is the idea of intermediates—species that are formed and consumed during the course of the reaction—versus catalysts which are regenerated at the end of the reaction.

In the case of the reaction given in our exercise, we see that \textbf{NO}\(_2\) helps convert \textbf{SO}\(_2\) into \textbf{SO}\(_3\) by first reacting with it and then being regenerated. The mechanism shows how \textbf{NO}\(_2\) temporarily becomes \textbf{NO} before being turned back into \textbf{NO}\(_2\). By examining each step, scientists can determine the most effective way to facilitate a reaction and potentially find more efficient catalysts to accomplish a desired chemical transformation.

A catalyst plays a pivotal role in chemical reactions by increasing the rate of the reaction without being permanently consumed by it. Catalysts operate by providing an alternative pathway with a lower activation energy compared to the uncatalyzed reaction. Although a catalyst is involved in the intermediate steps of a reaction, by the end of the reaction, it remains unchanged, allowing it to catalyze multiple rounds of the reaction.

In our textbook example, \textbf{NO}\(_2\) serves as a catalyst for the oxidation of \textbf{SO}\(_2\) to \textbf{SO}\(_3\). It does not appear in the overall reaction equation because it is not a reactant nor a product of the overall process. Instead, it facilitates the individual steps of the mechanism, effectively speeding up the reaction without being consumed. Catalysis is a fascinating area because of its practical benefits. It not only makes reactions faster but can also make them more selective, cost-effective, and environmentally friendly by reducing the need for excessive energy and potentially harmful by-products.