Question

The reaction of \(\mathrm{G}_{2}\) with \(\mathrm{E}_{2}\) to form \(2 \mathrm{EG}\) is exothermic, and the reaction of \(\mathrm{G}_{2}\) with \(\mathrm{X}_{2}\) to form \(2 \mathrm{XG}\) is endothermic. The activation energy of the exothermic reaction is greater than that of the endothermic reaction. Sketch the potential-energy profile diagrams for these two reactions on the same graph.

Short answer

Sketch shows higher activation energy for exothermic reaction with lower product energy than endothermic.

Step-by-step solution

Understand Reaction Types

The reaction of \(\mathrm{G}_{2}\) with \(\mathrm{E}_{2}\) is exothermic, meaning that it releases energy, while the reaction of \(\mathrm{G}_{2}\) with \(\mathrm{X}_{2}\) is endothermic, meaning it absorbs energy. This implies that the products of the exothermic reaction have lower potential energy than the reactants, while the products of the endothermic reaction have higher potential energy than the reactants.

Exothermic Reaction Profile

Begin by sketching a potential energy profile for the exothermic reaction. Start with the reactants at a certain energy level. Draw a curve that rises to a peak (representing the activation energy) and then drops to a lower energy level for the products, showing that energy is released.

Endothermic Reaction Profile

For the endothermic reaction, sketch a curve starting at the reactants' energy level. The curve rises to a peak, representing the activation energy, and then continues to a higher energy level for the products, indicating that the reaction absorbs energy.

Compare Activation Energies

Since the activation energy of the exothermic reaction is greater than that of the endothermic reaction, the peak of the exothermic reaction curve should be higher than the peak of the endothermic reaction curve. Adjust the height of the peaks in your sketches accordingly.

Label and Finalize Diagram

Ensure both reactions are clearly labeled on the graph. The y-axis represents potential energy, and the x-axis represents the reaction coordinate. Label the starting and ending points of each reaction, and make sure the energy differences are evident from the graph.

Key concepts

Exothermic Reaction

In an exothermic reaction, energy is released into the surroundings as heat. This type of reaction usually feels hot to the touch because it gives off warmth. As a rule of thumb, the total potential energy of the products is lower than that of the reactants. This energy difference is what is released during the reaction.

For example, when \( \mathrm{G}_{2} \) reacts with \( \mathrm{E}_{2} \) to form \( 2\mathrm{EG} \), the overall reaction releases energy. On a potential energy diagram, the curve for this reaction starts at a certain level for the reactants, rises to a peak due to the activation energy, and then falls to a lower energy level for the products. This step-down visualizes the energy release.

Endothermic Reaction

An endothermic reaction requires an input of energy from the surroundings. This kind of reaction typically feels cold as it absorbs heat. During this process, the potential energy of the products is higher than that of the reactants.

In the case of \( \mathrm{G}_{2} \) and \( \mathrm{X}_{2} \), forming \( 2\mathrm{XG} \), energy is absorbed. A potential energy diagram of this reaction starts with the energy level of the reactants, rises through a peak due to activation energy, and ends at a higher energy level for the products. This upward shift indicates the absorption of energy.

Activation Energy

Activation energy is the minimum amount of energy needed for a reaction to occur. It is represented as the peak on the potential energy diagram.

In an exothermic reaction, even though energy is released, input is needed to reach the transition state. The potential energy peak is the activation energy. In this scenario, the activation energy for the exothermic reaction is higher than that of the endothermic reaction. This can be visualized as a taller peak on the diagram for \( \mathrm{G}_{2} \) and \( \mathrm{E}_{2} \) compared to that for \( \mathrm{G}_{2} \) and \( \mathrm{X}_{2} \).

Activation energy essentially serves as a barrier that must be overcome for reactants to transform into products.

Reaction Coordinate

The reaction coordinate represents the progress of a reaction from reactants to products. You can think of it as a journey along the x-axis of a potential energy diagram.

This axis shows how potential energy changes as the reaction advances.

• At the start of the axis, you have the reactants.
• As you move along, you reach the peak indicating the activation energy needed.
• Finally, you end with the products.

The reaction coordinate helps us visualize how energy levels shift during the reaction. It effectively links every point on a potential energy diagram to a specific stage of the chemical reaction.