Problem 62 - Chemistry The Molecular Science

Question

Draw an energy versus reaction progress diagram (similar to the one in Question 60 ) for each of the reactions whose activation energy and enthalpy change are given below. Draw arrows to represent the activation energies of the forward and reverse reaction and \(\Delta_{\mathrm{r}} H^{\circ} .\) (a) \(\Delta_{r} H^{\circ}=105 \mathrm{~kJ} \mathrm{~mol}^{-1} ; E_{\mathrm{a}}=175 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(\Delta_{r} H^{\circ}=-43 \mathrm{~kJ} \mathrm{~mol}^{-1} ; E_{\mathrm{a}}=95 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(\Delta_{r} H^{\circ}=15 \mathrm{~kJ} \mathrm{~mol}^{-1} ; E_{\mathrm{a}}=55 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-Step Solution

Answer

Diagram energy progress based on data: (a) products higher; (b) products lower; (c) products slightly higher.

Step 1: Understanding the Diagram Structure

An energy versus reaction progress diagram shows how the energy of a system changes as a reaction proceeds. Typically, the y-axis represents energy, while the x-axis represents the progress of the reaction from reactants to products.

Step 2: Identify Key Values

For each reaction, identify the enthalpy change \( \Delta_{r} H^{\circ} \) and the activation energy \( E_{a} \). The enthalpy change indicates the overall energy difference between products and reactants, while the activation energy indicates the energy barrier for the reaction.

Step 3: Draw Diagram for Reaction (a)

For reaction (a): \( \Delta_{r} H^{\circ}=105 \mathrm{~kJ} \mathrm{~mol}^{-1} \) and \( E_{a}=175 \mathrm{~kJ} \mathrm{~mol}^{-1} \). Start the diagram with reactants at a certain energy level. The peak, which represents the activated complex, is 175 kJ/mol higher. The products are at an energy level 105 kJ/mol higher than the reactants.

Step 4: Mark Arrows for Reaction (a)

Draw an arrow from the reactant to the peak representing the forward activation energy (175 kJ/mol). Add another arrow from the product level back to the peak to show reverse activation energy. Draw a double-headed arrow from the reactants to products indicating \( \Delta_{r} H^{\circ} = 105 \mathrm{~kJ} \mathrm{~mol}^{-1} \).

Step 5: Draw Diagram for Reaction (b)

For reaction (b): \( \Delta_{r} H^{\circ}=-43 \mathrm{~kJ} \mathrm{~mol}^{-1} \) and \( E_{a}=95 \mathrm{~kJ} \mathrm{~mol}^{-1} \). Here, products are at a lower energy level compared to reactants, as indicated by the negative \( \Delta_{r} H^{\circ} \). The peak energy is 95 kJ/mol above the reactants.

Step 6: Mark Arrows for Reaction (b)

Place an arrow from reactants to peak for forward \( E_{a} = 95 \mathrm{~kJ} \mathrm{~mol}^{-1} \). For reverse reaction, draw an arrow from products to the peak. Add a double-headed arrow from reactants to products showing \( \Delta_{r} H^{\circ} = -43 \mathrm{~kJ} \mathrm{~mol}^{-1} \).

Step 7: Draw Diagram for Reaction (c)

For reaction (c): \( \Delta_{r} H^{\circ}=15 \mathrm{~kJ} \mathrm{~mol}^{-1} \) and \( E_{a}=55 \mathrm{~kJ} \mathrm{~mol}^{-1} \). The products are at higher energy than reactants by 15 kJ/mol, while the peak is 55 kJ/mol above reactants.

Step 8: Mark Arrows for Reaction (c)

Draw the forward activation energy arrow from reactants to the peak (55 kJ/mol). For reverse activation energy, add an arrow from products to peak. Mark \( \Delta_{r} H^{\circ} = 15 \mathrm{~kJ} \mathrm{~mol}^{-1} \) with a double-headed arrow from reactants to products.

Key Concepts

enthalpy change

The enthalpy change, denoted as \( \Delta_{r} H^{\circ} \), is a measure of the total energy absorbed or released during a chemical reaction. It represents the difference in energy between the reactants and products. If \( \Delta_{r} H^{\circ} \) is positive, the reaction is endothermic, meaning it absorbs energy from the surroundings. Conversely, if \( \Delta_{r} H^{\circ} \) is negative, the reaction is exothermic, meaning it releases energy. This change in energy can be visualized on an energy diagram, where it is depicted as the difference in height between the reactants and products.
This concept is crucial because it helps determine whether a reaction will occur spontaneously and if it requires or produces heat. In our exercises, reaction (a) is endothermic with \( \Delta_{r} H^{\circ} = 105 \mathrm{kJ} \mathrm{mol}^{-1} \), indicating energy is absorbed, while reaction (b) is exothermic with \( \Delta_{r} H^{\circ} = -43 \mathrm{kJ} \mathrm{mol}^{-1} \), indicating energy is released. Reaction (c), with \( \Delta_{r} H^{\circ} = 15 \mathrm{kJ} \mathrm{mol}^{-1} \), is slightly endothermic.

energy diagram

An energy diagram is a visual representation of the energy changes that occur during a chemical reaction. It typically plots energy on the y-axis and the reaction progress on the x-axis. These diagrams help us understand the energetic pathway that a reaction follows.
In an energy diagram:

• The starting point on the y-axis represents the energy of the reactants.
• A peak in the diagram indicates the energy barrier, or the activated complex, that must be overcome for the reaction to proceed.
• The endpoint shows the energy level of the products.

For example, in reaction (a) of our exercise, the diagram begins at the reactants' energy level, reaches a peak to show the activation energy of 175 kJ/mol, and finishes at a higher product energy level due to the positive enthalpy change. For reaction (b), the diagram finishes lower on the y-axis due to the negative \( \Delta_{r} H^{\circ} \). Energy diagrams are invaluable tools for visualizing the thermodynamics of reactions.

reaction progress

The reaction progress in a chemical reaction refers to the movement from reactants to products over time. This is illustrated on the x-axis of an energy diagram.
As a reaction progresses:

• Reactants are converted into products by passing through a high-energy transition state.
• Initially, the reaction requires energy to overcome activation energy barriers, depicted as the peak in the energy diagram. This is essential to reach the transition state, where old bonds break and new bonds form.
• After surpassing the transition state, the system releases energy, bringing it closer to the product energy level.

In our given reactions, the reaction progress can be visualized as a journey across the energy diagram from left (reactants) to right (products). The specific enthalpy values and activation energies show the energetic changes that happen during this progress. Understanding this concept is crucial for predicting how and when reactions occur and what conditions are needed for them to proceed.