Problem 53 - Chemistry and Chemical Reactivity

Question

A proposed mechanism for the reaction of \(\mathrm{NO}_{2}\) and \(\mathrm{CO}\) is Step 1 Slow, endothermic $$2 \mathrm{NO}_{2}(\mathrm{g}) \longrightarrow \mathrm{NO}(\mathrm{g})+\mathrm{NO}_{3}(\mathrm{g})$$ Step 2 \(\quad\) Fast, exothermic $$\mathrm{NO}_{3}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})$$ Overall Reaction Exothermic $$\mathrm{NO}_{2}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{NO}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})$$ (a) Identify each of the following as a reactant, product, or intermediate: \(\mathrm{NO}_{2}(\mathrm{g}), \mathrm{CO}(\mathrm{g}), \mathrm{NO}_{3}(\mathrm{g}), \mathrm{CO}_{2}(\mathrm{g})\) \(\mathrm{NO}(\mathrm{g})\) (b) Draw a reaction coordinate diagram for this reaction. Indicate on this drawing the activation energy for each step and the overall reaction enthalpy.

Step-by-Step Solution

Answer

Reactants: \(\mathrm{NO}_{2}\), \(\mathrm{CO}\); Products: \(\mathrm{NO}\), \(\mathrm{CO}_{2}\); Intermediate: \(\mathrm{NO}_{3}\). Reaction is overall exothermic.

Step 1: Identify Reactants, Products, and Intermediates

1. **Reactants** are starting materials used in the overall reaction. From the overall reaction, these are \(\mathrm{NO}_{2}(\mathrm{g})\) and \(\mathrm{CO}(\mathrm{g})\). 2. **Products** are the final materials formed by the reaction. According to the overall reaction, these are \(\mathrm{NO}(\mathrm{g})\) and \(\mathrm{CO}_{2}(\mathrm{g})\).3. **Intermediates** are species that form in one step and are consumed in another step. In this mechanism, \(\mathrm{NO}_{3}(\mathrm{g})\) and \(\mathrm{NO}(\mathrm{g})\) appear in the reaction steps but not in the overall reaction.

Step 2: Draw the Reaction Coordinate Diagram

1. **Initial Energy Level:** Start by placing the initial energy at a higher level for reactants since the first step is endothermic. 2. **Step 1 (Slow, Endothermic):** Draw an upward curve representing the first step's energy increase. The difference between the peak and initial level represents the activation energy for Step 1. The energy level at the peak should be higher than the starting point. 3. **Intermediate Energy Level:** The energy of the intermediates will be at a level higher than the initial reactants due to the endothermic nature. 4. **Step 2 (Fast, Exothermic):** Draw a downward curve from the intermediate's energy level to a final lower point. This drop represents the exothermic step and the difference between initial reactant energy and final product energy shows the overall exothermic enthalpy change. 5. **Overall Enthalpy Change:** The difference between the initial reactant energy and final product energy levels represents the overall exothermic nature of the reaction.

Key Concepts

Reactants and Products

In any chemical reaction, understanding the roles of different substances is crucial. **Reactants** are the substances you start with in a chemical reaction. For the reaction of nitrogen dioxide (\(\mathrm{NO}_2\)) with carbon monoxide (\(\mathrm{CO}\)), these are the initial molecules involved. The chemistry kicks off with these two.

**Products**, however, are what you get at the end of a reaction. In this scenario, after the reaction has occurred, you end up with nitrogen monoxide (\(\mathrm{NO}\)) and carbon dioxide (\(\mathrm{CO}_2\)). These are the substances formed as the reaction concludes.

To sum up, in the overall reaction:
- Reactants: \(\mathrm{NO}_2(\mathrm{g})\) and \(\mathrm{CO}(\mathrm{g})\) - Products: \(\mathrm{NO}(\mathrm{g})\) and \(\mathrm{CO}_2(\mathrm{g})\)

Reaction Intermediates

Sometimes, a reaction doesn't just go directly from reactants to products. It might first form **intermediates**, which are temporary species formed on the way to the final products. They're kind of like a midway stop before reaching the final destination.

In the example of the \(\mathrm{NO}_2\) and \(\mathrm{CO}\) reaction, nitrogen trioxide (\(\mathrm{NO}_3\)) acts as an intermediate. It appears during the process but does not appear in the final equation. Since \(\mathrm{NO}_3\) is used up in the process, you won't see it in the end products. It's there to help along the way, speeding up or facilitating certain steps in the transition from initial to final state.

Also, in this mechanism, \(\mathrm{NO}\) is generated in the first step and then used up, fitting the description of an intermediate, even though it's also a product. Locale often changes perception!

Reaction Coordinate Diagram

A **reaction coordinate diagram** is a graphical representation of the energy changes that occur during a reaction. Imagine a graph where the horizontal axis represents the progress of the reaction, and the vertical axis shows the energy.

For our \(\mathrm{NO}_2\) and \(\mathrm{CO}\) reaction, the diagram will show two significant peaks: one for each step in the mechanism. The height of each peak indicates the energy required to pass through that step.

Here’s a quick rundown of what the diagram looks like: - Start high on the energy axis because the first step is endothermic (absorbing energy). - The first peak represents the energy barrier for the first, slow step and is higher due to its increased energy input. - After that peak, the reaction lowers slightly for the intermediates. - The second peak is smaller because the exothermic part releases energy quickly. This part slopes back down, reflecting the lower energies of the final products compared to the starting materials.

Activation Energy

**Activation energy** is like a hurdle that reactants need to jump over to become products. It's the extra energy needed for a reaction to start. Think of it as the initial push to get a ball rolling down a hill. However high this energy barrier, it determines how quickly a reaction could proceed.

In our reaction mechanism, the first step is slow, indicating it has a higher activation energy. The endothermic nature of the step means there's more energy to overcome, represented as a taller peak in the reaction coordinate diagram for this slow step.

On the other hand, the fast second step requires less activation energy, because it is aided by the energy release when molecules transform, so it's depicted as a shorter peak.

Understanding activation energy is key to controlling reaction rates. You could speed up a reaction by lowering this barrier, perhaps using a catalyst to do so without changing the initial and final energy states!

Enthalpy Change

**Enthalpy Change** represents the heat absorbed or released during a reaction occurring at constant pressure. It's denoted often as \(\Delta H\) and provides insight into whether a reaction is endothermic (absorbing heat) or exothermic (releasing heat).

In this chemical mechanism, despite the first step being endothermic, the overall reaction is exothermic. This means more energy is released in forming the products than is needed to break the bonds of the reactants. The entire reaction ends at a lower energy level than it began, releasing heat into the environment.

Differentiating steps, the **overall enthalpy change** arises from comparing the initial energy level of the reactants with the final energy level of the products. This tells us that in a completed reaction, most of the heat flows out, particularly noticeable in the creation of \(\mathrm{CO}_2\). Understanding this balance helps in predicting how favorably a reaction will proceed under given conditions.