Problem 62 - Chemistry: Principles and Reactions

Question

For the reaction $$\mathrm{X}+\mathrm{Y} \longrightarrow \mathrm{R}+\mathrm{Z} \quad \Delta H=+295 \mathrm{~kJ},$$ draw a reaction-energy diagram for the reaction if its activation energy is \(378 \mathrm{~kJ} .\)

Step-by-Step Solution

Answer

Question: Draw and label a reaction-energy diagram for the chemical reaction $$\mathrm{X}+\mathrm{Y} \longrightarrow \mathrm{R}+\mathrm{Z}$$ with its enthalpy change (\(\Delta H\)) equal to \(+295 \mathrm{~kJ}\) and activation energy (\(E_a\)) equal to \(378 \mathrm{~kJ}\). Answer: To draw a reaction-energy diagram for the given reaction, follow these steps: 1. Draw the axes for the reaction-energy diagram, labeling the x-axis as "Reaction Progress" and the y-axis as "Energy." 2. Indicate the initial energy state of the reactants (point A) and the final energy state of the products (point B), with B being higher on the y-axis than A due to the positive enthalpy change. 3. Mark the point representing the activation energy (point C), which is \(378 \mathrm{~kJ}\) higher on the y-axis than point A. 4. Indicate the enthalpy change (295 kJ) between A and B. 5. Connect points A, C, and B with a smooth curve to create the reaction-energy diagram, showing the energy changes during the reaction.

Step 1: Draw the axes for the reaction-energy diagram

Begin by drawing the axes for the reaction-energy diagram. Label the x-axis as "Reaction Progress" and the y-axis as "Energy".

Step 2: Indicate the initial and final energy states

On the y-axis, mark a point to represent the initial energy state of the reactants X and Y (let's call this point A). Similarly, mark a point to represent the final energy state of the products R and Z (let's call this point B). Since the enthalpy change, \(\Delta H\), is positive, the final energy state (B) will be higher on the y-axis than the initial energy state (A).

Step 3: Indicate the activation energy

The activation energy, \(E_a\), is the energy required to initiate the reaction. This can be represented by a higher energy state compared to A. Measure up from point A and mark a point \(378 \mathrm{~kJ}\) higher on the y-axis (let's call this point C). This point represents the energy level of the activated complex or transition state.

Step 4: Indicate the enthalpy change

The enthalpy change, \(\Delta H\), represents the difference in energy between the reactants and products. From the initial energy state A, measure up and mark the point that is \(295 \mathrm{~kJ}\) higher on the y-axis, which should correspond to point B.

Step 5: Connect the points to form the reaction-energy diagram

Now, connect the points A, C, and B with a smooth curve to create the reaction-energy diagram. The curve should go from the initial energy state A to the transition state C, and then back down to the final energy state B. This represents the energy changes during the reaction. You now have a complete reaction-energy diagram for the given reaction.

Key Concepts

Activation Energy

In every chemical reaction, molecules must collide with enough energy to break existing bonds and form new ones. This minimum energy required to start a reaction is known as activation energy. Activation energy is crucial for understanding how a reaction takes place because it essentially represents the obstacle that reactants must overcome for a reaction to proceed.

• The higher the activation energy, the slower the reaction, as fewer molecules will possess the necessary energy to react at a given temperature.
• Conversely, a lower activation energy means more molecules can react, leading to a faster reaction rate.

On a reaction-energy diagram, this energy is depicted as a peak that reactants must surmount. The difference between the initial energy of the reactants and the peak is the activation energy, denoted as \(E_a\). In the example provided, this energy is \(378 \ \text{kJ}\), indicating the energy threshold that reactants \(X\) and \(Y\) must meet or exceed to form \(R\) and \(Z\). By understanding and visualizing activation energy, we can better comprehend why some reactions occur rapidly while others are slow or appear not to occur at all.

Enthalpy Change

Enthalpy change, represented by \(\Delta H\), is essentially the total heat content change when a reaction occurs. It helps us understand whether the reaction releases or absorbs energy from its surroundings.

• A positive \(\Delta H\) indicates an endothermic reaction, where energy is absorbed, making the products higher in energy than the reactants.
• A negative \(\Delta H\) suggests an exothermic reaction, where energy is released, and products are lower in energy than the reactants.

In the reaction-energy diagram for the example reaction \( \mathrm{X} + \mathrm{Y} \rightarrow \mathrm{R} + \mathrm{Z} \), the enthalpy change is positive \(+295 \ \text{kJ}\), showing that the reaction absorbs energy. This means the energy level of the products is higher than that of the reactants, which is visually evident as the products are placed higher on the y-axis in the diagram. Understanding enthalpy change allows students to predict the energy flow associated with reactions, which is fundamental not only in chemistry but in broader scientific and industrial applications as well.

Chemical Reaction

A chemical reaction involves the transformation of reactants into products, resulting in substances that differ from the original substances in their chemical structure.This transformation process can be better understood by comprehending the broader energy changes within the reaction. In our example, the chemical equation \( \mathrm{X} + \mathrm{Y} \rightarrow \mathrm{R} + \mathrm{Z} \) demonstrates the conversion of reactants \(\mathrm{X}\) and \(\mathrm{Y}\) into products \(\mathrm{R}\) and \(\mathrm{Z}\).

• Reactants are the starting materials in a chemical reaction.
• Products are the new substances that result from the reaction.

The reaction-energy diagram provides an insightful visualization that complements the reaction equation, illustrating not only what the reaction is but also how it proceeds energetically. By studying both the chemical equation and its corresponding reaction-energy diagram, learners can gain a deeper understanding of the interplay between reactants and products, as well as the transition states and intermediate steps that might exist between them. This holistic view is essential for mastering the concepts behind chemical reactions and their practical applications.