Problem 51 - Chemistry and Chemical Reactivity

Question

A proposed mechanism for the reaction of \(\mathrm{NO}_{2}\) and \(\mathrm{CO}\) is Step 1: Slow, endothermic $$ 2 \mathrm{NO}_{2}(\mathrm{g}) \rightarrow \mathrm{NO}(\mathrm{g})+\mathrm{NO}_{3}(\mathrm{g}) $$ Step 2: Fast, exothermic $$ \mathrm{NO}_{3}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) $$ Overall Reaction: Exothermic $$ \mathrm{NO}_{2}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{NO}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) $$ (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 enthalpy change.

Step-by-Step Solution

Answer

NO₂ and CO are reactants. NO₃ is an intermediate. CO₂ and NO are products. Draw a diagram with two peaks, higher for the endothermic step.

Step 1: Identifying Reactants and Products

First, we need to identify the substances involved in the reaction mechanisms provided and classify each as reactants, products, or intermediates. Reactants appear at the start of the sequence of reactions, intermediates are products in one step and reactants in another, and final products appear at the end of all steps. For the given mechanisms, - \(\text{NO}_{2}\) and \(\text{CO}\) appear as reactants in the overall reaction.- \(\text{NO}_{3}\) is formed in the first step and consumed in the second, making it an intermediate.- \(\text{CO}_{2}\) and \(\text{NO}\) are the final products of the overall reaction.

Step 2: Reaction Coordinate Diagram Setup

To draw the reaction coordinate diagram, we plot the progress of the reaction on the x-axis against the energy on the y-axis. Each step of the reaction from reactants to products is represented by a peak (which represents the transition state) and a valley (which represents the intermediate or final product). Since Step 1 is slow and endothermic, it has a higher peak than Step 2, which is fast and exothermic.

Step 3: Activation Energy and Enthalpy Change

In the reaction coordinate diagram, the activation energy for each step is the height of the peak above the respective starting point of that step (reactants or intermediates). The enthalpy change (\(\Delta H\)) for each step is the difference in energy between the starting point and the ending point. For the overall reaction, the total \(\Delta H\) is the difference in energy between the start of the first step (step 1 reactants) and the end of the second step (step 2 products). Since the overall reaction is exothermic, the products are at a lower energy level compared to the reactants.

Key Concepts

Intermediates in Chemical Reactions

In chemical reactions, intermediates play a crucial role, acting as temporary substances that appear and disappear as the reaction progresses. They are neither starting materials nor final products but bridge the gap between them. Intermediates are vital for understanding the overall flow and mechanism of the reaction. In the context of the given mechanism involving nitrogen dioxide (\(\text{NO}_2\)) and carbon monoxide (\(\text{CO}\)), the intermediate is the nitrate radical (\(\text{NO}_3\)).
- In the first step, \(\text{NO}_3\) is produced as \(\text{NO}_2\) molecules react with each other.
- This makes \(\text{NO}_3\) an intermediate, because it is consumed in the following step, where it reacts with \(\text{CO}\) to form carbon dioxide (\(\text{CO}_2\)) and regenerate \(\text{NO}_2\).
Intermediates often have a short existence and are formed and consumed within the reaction steps. Understanding these intermediates is important because they affect overall reaction rates and pathways, influencing how quickly products are formed or how the reaction might be catalyzed or inhibited.

Reaction Coordinate Diagrams

Reaction coordinate diagrams provide a visual representation of how the energy of a system changes throughout the course of a reaction. On these diagrams, the y-axis represents the potential energy, while the x-axis represents the "reaction coordinate," or the progress of the reaction from reactants to products.
- Each reaction step is shown as a curve that rises to a peak and then falls again, corresponding to the transition state and the completion of that step, respectively.
For the given two-step reaction mechanism, the diagram would show two curves: - The first, higher curve represents step 1, which is slow and endothermic, indicating a larger input of energy to progress through the reaction. - The second, lower curve corresponds to step 2, which occurs quickly and releases energy, depicted as an exothermic transition where the energy of products is lower than that of the intermediates.
The overall slope of the reaction coordinate diagram indicates whether the entire process is exothermic or endothermic, which in this case is exothermic, shown by the fact that the final product's energy is lower than the initial reactants' energy.

Activation Energy

Activation energy is a key concept in understanding chemical reactions. It refers to the minimum amount of energy required to initiate a reaction. In a reaction coordinate diagram, the activation energy is represented by the peak of each step. It's the energy barrier that must be overcome for the reactants to be transformed into intermediates (in Step 1) or into products (in Step 2).
- In our reaction mechanism, the slow, endothermic first step has a higher activation energy compared to the fast, exothermic second step. This high activation energy mirrors the energy required for the initial \(\text{NO}_2\) molecules to break apart and form \(\text{NO}_3\).
- Conversely, the second step's lower activation energy makes it faster, as \(\text{NO}_3\) quickly reacts with \(\text{CO}\) to form \(\text{CO}_2\) and complete the reaction sequence.
Understanding activation energy is essential for controlling reaction speeds and optimizing conditions in chemical processes. It helps chemists manipulate reactions for desired outcomes, whether that's speeding up a beneficial reaction or slowing down an unwanted one.