Problem 41 - Chemistry and Chemical Reactivity

Question

The reaction of \(\mathrm{H}_{2}\) molecules with \(\mathrm{F}\) atoms $$\mathrm{H}_{2}(\mathrm{g})+\mathrm{F}(\mathrm{g}) \rightarrow \mathrm{HF}(\mathrm{g})+\mathrm{H}(\mathrm{g})$$ has an activation energy of \(8 \mathrm{kJ} / \mathrm{mol}\) and an enthalpy change of \(-133 \mathrm{kJ} / \mathrm{mol} .\) Draw a diagram similar to Figure 15.13 for this process. Indicate the activation energy and enthalpy change on this diagram.

Step-by-Step Solution

Answer

Draw an energy diagram with activation energy as a peak and enthalpy change as a drop from reactants to products.

Step 1: Identify Key Variables

The reaction in question is \( \mathrm{H}_{2}(\mathrm{g})+\mathrm{F}(\mathrm{g}) \rightarrow \mathrm{HF}(\mathrm{g})+\mathrm{H}(\mathrm{g}) \). We're given the activation energy \( E_a = 8 \text{kJ/mol} \) and the enthalpy change \( \Delta H = -133 \text{kJ/mol} \).

Step 2: Draw the Energy Profile Diagram

Draw an energy profile diagram with the y-axis representing the energy of the system, while the x-axis represents the reaction progress from reactants to products.

Step 3: Mark Initial Energy Level

On the diagram, start by marking an initial energy level for the reactants, which are \( \mathrm{H}_{2}(\mathrm{g}) \) and \( \mathrm{F}(\mathrm{g}) \).

Step 4: Indicate the Transition State and Activation Energy

Draw a peak above the initial energy level to denote the transition state. The height difference from the initial energy level to the peak represents the activation energy. Mark this difference as \( 8 \text{kJ/mol} \).

Step 5: Mark Final Energy Level

Below the initial energy level, draw the final energy level for the products \( \mathrm{HF}(\mathrm{g}) \) and \( \mathrm{H}(\mathrm{g}) \), which is lower due to the negative enthalpy change.

Step 6: Indicate Enthalpy Change

Draw a vertical arrow from the energy level of the reactants down to the energy level of the products. Label this with the enthalpy change \( \Delta H = -133 \text{kJ/mol} \).

Step 7: Label the Diagram Clearly

Ensure that each element on the diagram such as the reactants, products, transition state, activation energy, and enthalpy change are clearly labeled.

Key Concepts

Activation Energy

In any chemical reaction, activation energy is the energy needed to start the process. Think of it like a hill that reactants must climb before they can be transformed into products. For the given reaction of \[\mathrm{H}_{2}( ext{g})+\mathrm{F}( ext{g}) \rightarrow \mathrm{HF}( ext{g})+\mathrm{H}( ext{g}),\]we know the activation energy is 8 kJ/mol.
This small amount of energy is crucial, as it helps break the initial bonds in the reactants.
This is why sometimes a spark or heat is needed to get a reaction going. Here's what you need to remember about activation energy:

• It’s always positive because energy input is required to reach the transition state.
• In an energy diagram, it's the difference in energy between the reactants and the peak of the curve, which represents the transition state.
• It affects the reaction rate—the higher the activation energy, the slower the reaction, as more energy is needed to start the process.

This concept is fundamental in understanding how chemical reactions occur and how quickly they proceed.

Enthalpy Change

Enthalpy change, symbolized as \( \Delta H \), indicates the total heat change in a reaction.
For our reaction, the enthalpy change is \(-133 \text{kJ/mol}\).
This negative value suggests that the reaction releases energy as heat—it’s an exothermic process. Here's why enthalpy change is important:

• Exothermic reactions (negative \( \Delta H \)) release heat, causing the surrounding temperature to rise.
• Endothermic reactions (positive \( \Delta H \)) absorb heat, leading to a cooler environment.
• In the energy diagram, it's the difference between the energy level of reactants and products.

When plotting on an energy diagram, you'll notice the products lie lower than the reactants.
This visual drop represents the loss of energy, consistent with our calculated enthalpy change.
The concept of enthalpy is essential in predicting whether a reaction will be spontaneous and, if so, how it impacts the surroundings.

Transition State

The transition state refers to the highest energy point along the reaction pathway.
In the energy diagram, it's shown as the peak at the top of the curve.
It's a temporary, unstable arrangement of atoms that occurs when bonds in the reactants are breaking and new bonds are forming to create the products. Key aspects of the transition state include:

• It resembles neither reactants nor products but is a hybrid of both.
• In diagrams, the transition state is always at the top of the energy barrier that reactants must overcome.
• It is very short-lived, existing only for an instant before the products are formed.

Understanding the transition state helps in grasping why the activation energy is necessary.
The energy needed to reach this peak allows the reaction to proceed.
Identifying the transition state is important because it defines the critical point in the reaction where the old bonds are at their weakest and most susceptible to breaking.