Question

The oxidation of \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3}\) is catalyzed by \(\mathrm{NO}_{2}\). Thereaction proceeds as follows: $$ \begin{aligned} &\mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{SO}_{3}(g) \\ &2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \end{aligned} $$ (a) Show that the two reactions can be summed to give the overall oxidation of \(\mathrm{SO}_{2}\) by \(\mathrm{O}_{2}\) to give \(\mathrm{SO}_{3}\). (Hint: The top reaction must be multiplied by a factor so the \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) cancel out.) (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?

Short answer

The overall reaction for the oxidation of \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3}\) is \(2\mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2\mathrm{SO}_{3}(g)\). \(\mathrm{NO}_{2}\) is considered a catalyst because it increases the reaction rate without being consumed in the overall reaction. This is an example of homogeneous catalysis since the catalyst and reactants are all in the gaseous phase.

Step-by-step solution

Combining the Reactions to Get the Overall Reaction

We are given the following two reactions: \( \mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{SO}_{3}(g) \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \) To cancel out \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\), we will multiply the first reaction by 2 and then add it to the second reaction: \( 2[\mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{SO}_{3}(g)] \\ \) This gives us: \( 2 \mathrm{NO}_{2}(g) + 2\mathrm{SO}_{2}(g) \longrightarrow 2\mathrm{NO}(g)+ 2\mathrm{SO}_{3}(g) \) Now we add this to the second reaction: \( (2 \mathrm{NO}_{2}(g) + 2\mathrm{SO}_{2}(g)) + (2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)) \longrightarrow (2\mathrm{NO}(g)+ 2\mathrm{SO}_{3}(g)) + (2 \mathrm{NO}_{2}(g)) \) After canceling out the common terms, we get the overall reaction: \( 2\mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2\mathrm{SO}_{3}(g) \)

Explaining Why \(\mathrm{NO}_{2}\) is a Catalyst

A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the reaction. An intermediate is a species formed in one step of a reaction then consumed in another step. In our case, \(\mathrm{NO}_{2}\) is present at the beginning of the first reaction and formed at the end of the second reaction. As it is not consumed throughout the entire process, we consider \(\mathrm{NO}_{2}\) as a catalyst.

Identifying the Type of Catalysis

There are two types of catalysis: homogeneous and heterogeneous. Homogeneous catalysis occurs when the catalyst and reactants are in the same phase (e.g., both are in the gaseous phase), while heterogeneous catalysis occurs when the catalyst and reactants are in different phases. In our case, all the reactants and the catalyst, \(\mathrm{NO}_{2}\), are in the gaseous phase. Therefore, this is an example of homogeneous catalysis.

Key concepts

Oxidation

Oxidation is a crucial part of many chemical reactions and refers to the process where a substance loses electrons. In the context of the given reactions, the oxidation process involves the conversion of sulfur dioxide (\(\mathrm{SO}_{2}\)) into sulfur trioxide (\(\mathrm{SO}_{3}\)). This conversion happens through an increase in the oxidation state of sulfur, essentially involving the addition of oxygen atoms to \(\mathrm{SO}_{2}\).
The overall reaction represents the oxidation of sulfur dioxide, where it gains oxygen atoms from the oxygen molecule \(\mathrm{O}_{2}\). This reaction is represented by the equation:

• 2\(\mathrm{SO}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2\mathrm{SO}_{3}(g)\)

This equation highlights the role of oxygen in the oxidation process.
In oxidation reactions, the substance that loses electrons is oxidized, here being \(\mathrm{SO}_{2}\), transforming into \(\mathrm{SO}_{3}\). Understanding oxidation helps in grasping how substances transform during chemical reactions.

Reaction Mechanism

A reaction mechanism describes the step-by-step process by which a chemical reaction occurs. Each step of the reaction can involve the breaking and forming of bonds to reach the final products. In this exercise, the transformation from \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3}\) catalyzed by \(\mathrm{NO}_{2}\) is a multi-step process.
Initially, \(\mathrm{NO}_{2}\) reacts with \(\mathrm{SO}_{2}\) to produce \(\mathrm{NO}\) and \(\mathrm{SO}_{3}\). Then, \(\mathrm{NO}\) quickly reacts with \(\mathrm{O}_{2}\) to regenerate \(\mathrm{NO}_{2}\). The overall mechanism can be summarized as:

• \(\mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \rightarrow \mathrm{NO}(g)+\mathrm{SO}_{3}(g)\)
• \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\)

Combining these two steps and cancelling out the intermediates results in the overall oxidation reaction. Understanding each step of these mechanisms is crucial, as they explain how reactants convert into products through different stages.

Chemical Kinetics

Chemical kinetics is the field that studies the speed or rate of chemical reactions and the factors that affect these rates. For the oxidation of \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3},\) the presence of \(\mathrm{NO}_{2}\) affects the kinetics significantly. As a catalyst, \(\mathrm{NO}_{2}\) provides an alternate pathway with a lower activation energy for the reaction.
This lower activation energy means that the reaction can proceed faster than it would without the catalyst. It doesn’t alter the equilibrium of the reaction but merely increases the rate at which equilibrium is reached. Key factors affecting chemical kinetics include:

• Concentration of reactants
• Temperature
• Presence of a catalyst (such as \(\mathrm{NO}_{2}\) in this case)

These factors play a vital role in the efficiency and speed of chemical reactions in both laboratory and industrial settings.

Homogeneous Catalysis

Homogeneous catalysis occurs when the catalyst is in the same phase as the reactants. In our reaction, both the reactants and the catalyst \(\mathrm{NO}_{2}\) are gases. This setup of all species in the gaseous phase exemplifies homogeneous catalysis.
In this type of catalysis, the catalyst and reactants freely mix, allowing the reaction to occur uniformly through the medium. The homogeneous catalyst (\(\mathrm{NO}_{2}\)) facilitates the reaction between \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\).
The advantages of homogeneous catalysis include:

• Ease of mixing and interaction between catalyst and reactants
• Uniform reactions throughout the medium
• Simplicity in controlling reaction conditions

However, separating the catalyst from the products can sometimes be challenging, which is a consideration in process design. Homogeneous catalysis is vital in processes where uniformity and consistency are key requirements.