Problem 47 - 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

(a) Reactants: \(\mathrm{NO}_2, \mathrm{CO}\). Products: \(\mathrm{NO}, \mathrm{CO}_2\). Intermediate: \(\mathrm{NO}_3\). (b) Draw diagram with two peaks; higher for Step 1, show overall energy lower at products.

Step 1: Identify Reactants and Products

In the overall reaction \( \mathrm{NO}_{2}(\mathrm{g}) + \mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{NO}(\mathrm{g}) + \mathrm{CO}_{2}(\mathrm{g}) \), \( \mathrm{NO}_{2} \) and \( \mathrm{CO} \) are reactants, and \( \mathrm{NO} \) and \( \mathrm{CO}_{2} \) are products.

Step 2: Identify Intermediates

Intermediates are species that are formed in one step and consumed in another. \( \mathrm{NO}_{3}(\mathrm{g}) \) is produced in Step 1 and consumed in Step 2, so it is an intermediate.

Step 3: Clarify Species Roles

Combining the findings: \( \mathrm{NO}_{2} \) and \( \mathrm{CO} \) are reactants; \( \mathrm{NO}_{3} \) is an intermediate; \( \mathrm{NO} \) and \( \mathrm{CO}_{2} \) are products.

Step 4: Reaction Coordinate Diagram

To draw the reaction coordinate diagram, plot the potential energy along the vertical axis and the reaction progress along the horizontal axis. Since Step 1 is slow and endothermic, it has a higher activation energy with potential energy increase. The fast, exothermic Step 2 shows a drop in potential energy to below the starting energy, given the overall reaction is exothermic.

Step 5: Label Activation Energies and Enthalpy Change

Indicate the activation energies as peaks on the diagram for each step, with Step 1 having a taller peak. The overall enthalpy change is shown by the difference in energy between the reactants and the products, indicating a net release of energy (exothermic reaction).

Key Concepts

Reaction Coordinate Diagram

A reaction coordinate diagram is a visual way to illustrate the energy changes that occur during a chemical reaction. It shows how the potential energy of the system changes as the reaction progresses from reactants to products. The vertical axis represents potential energy, while the horizontal axis represents the reaction coordinate, which is essentially the progress of the reaction.

• Initial energy level: Corresponds to the reactants. In our reaction, this includes \( \mathrm{NO}_{2} \) and \( \mathrm{CO} \).
• Energy peaks: Indicate the activation energy of each step in the reaction mechanism. For the \( \mathrm{NO}_{2} \) and \( \mathrm{CO} \) reaction, Step 1 has the highest peak because it is slow and endothermic.
• Energy valleys: Represent the intermediate states. For example, \( \mathrm{NO}_{3} \) appears between the steps.
• Final energy level: Shows the energy level of the products, which are \( \mathrm{NO} \) and \( \mathrm{CO}_{2} \) for this reaction.

By comparing the energy heights, you can assess the activation energy needed and determine the reaction's favorability.

Activation Energy

Activation energy is the minimum amount of energy required to activate molecules to a state where they can react. It's often depicted on a reaction coordinate diagram as a peak above the energy level of the reactants. This peak represents the transition state.
For the given reaction, Step 1 is endothermic and has a higher activation energy, meaning it requires more energy for the reaction to proceed. This is because:

• Endothermic reactions absorb energy to break the bonds of the initial reactants.
• Slow steps usually involve larger energy barriers, needing more energy input to form intermediates like \( \mathrm{NO}_{3} \).

In contrast, Step 2 is exothermic and occurs quickly, reflecting a lower activation energy:

• The energy released often allows the completion of the reaction, converting \( \mathrm{NO}_{3} \) and \( \mathrm{CO} \) into final products \( \mathrm{NO}_{2} \) and \( \mathrm{CO}_{2} \).

Understanding activation energy helps predict reaction rates and determine which steps are rate-limiting.

Intermediate Species

Intermediate species in a chemical reaction are compounds formed as temporary states that account for multi-step reactions. They appear in one of the steps and are consumed in subsequent steps, never appearing in the overall reaction equation.
In the reaction between \( \mathrm{NO}_{2} \) and \( \mathrm{CO} \), \( \mathrm{NO}_{3} \) is the intermediate species. It is produced in Step 1 of the reaction mechanism and consumed in Step 2, preventing it from appearing in the overall chemical equation.
Characteristics of intermediates:

• They are crucial for understanding the detailed pathway of a reaction.
• Intermediates can often be identified by tracing the changes in formal charges or molecular structure through reaction steps.
• They enable you to piece together complex reactions into understandable sequences.

By analyzing intermediates, chemists can refine reaction mechanisms and improve reaction efficiencies.

Enthalpy Change

Enthalpy change (\( \Delta H \)) in a reaction indicates the total heat absorbed or released under constant pressure. It provides insight into whether a reaction is endothermic or exothermic.
For the reaction involving \( \mathrm{NO}_{2} \) and \( \mathrm{CO} \), the overall process is exothermic, shown by energy release:

• The overall enthalpy change is negative, reflecting a net drop in energy from reactants to products.
• In the reaction coordinate diagram, this is visualized as the products lying below the reactants in energy level, showing energy release during the process.

Steps and their respective enthalpy characteristics:

• Step 1: Endothermic, requiring energy intake to break \( \mathrm{NO}_{2} \) bonds and form \( \mathrm{NO}_{3} \).
• Step 2: Exothermic, the energy released is more than that absorbed in Step 1, indicating a net energy release overall.

Understanding enthalpy change assists in thermodynamic analysis, helping predict reaction direction and feasibility.