Problem 71 - Chemistry: Principles and Reactions

Question

For a certain reaction, \(E_{a}\) is \(135 \mathrm{~kJ}\) and \(\Delta H=45 \mathrm{~kJ}\). In the presence of a catalyst, the activation energy is \(39 \%\) of that for the uncatalyzed reaction. Draw a diagram similar to Figure \(11.11\) but instead of showing two activated complexes (two humps) show only one activated complex (i.e., only one hump) for the reaction. What is the activation energy of the uncatalyzed reverse reaction?

Step-by-Step Solution

Answer

Answer: The activation energy for the uncatalyzed reverse reaction is \(180\,\mathrm{kJ}\).

Step 1: Understand the given information

The activation energy for a certain reaction, \(E_{a}\), is \(135 \mathrm{~kJ}\). The reaction enthalpy, \(\Delta H\), is \(45 \mathrm{~kJ}\). In the presence of a catalyst, the activation energy is \(39\%\) of that for the uncatalyzed reaction. We need to find the activation energy of the uncatalyzed reverse reaction. Step 2: Calculate the activation energy of the uncatalyzed reverse reaction

Step 2: Calculate the reversed reaction's activation energy

To find the reversed reaction's activation energy, we use the formula: \(E_a^\prime=E_a+\Delta H\) Where \(E_a^\prime\) is the activation energy for the reverse reaction, \(E_a\) is the given forward reaction activation energy (135 kJ), and \(\Delta H\) is the given reaction enthalpy (45 kJ). Plug in the given values: \(E_a^\prime=135+45\) Step 3: Calculate the result

Step 3: Calculate the result

Now we can find the value of the reverse reaction's activation energy: \(E_a^\prime= 180\,\mathrm{kJ}\) Step 4: Drawing the diagram

Step 4: Drawing the diagram

Draw a diagram similar to Figure 11.11 with only one activated complex (one hump) for the reaction. The diagram should show the following: 1. The energy profile for the forward reaction (uncatalyzed): with activation energy \(E_a=135\,\mathrm{kJ}\) and reaction enthalpy \(\Delta H=45\,\mathrm{kJ}\). 2. The energy profile for the forward reaction (catalyzed): with activation energy equal to \(39\%\) of the uncatalyzed activation energy (which is \(0.39\cdot 135=52.65\,\mathrm{kJ}\)). 3. The energy profile for the reverse reaction (uncatalyzed): with activation energy \(E_a^\prime=180\,\mathrm{kJ}\). In conclusion, the activation energy for the uncatalyzed reverse reaction is \(180\,\mathrm{kJ}\).

Key Concepts

Understanding Catalyzed Reactions

To start, let's dive into what catalyzed reactions are. Simply put, a catalyst is a substance that speeds up a chemical reaction without being consumed by the reaction itself. Its presence reduces the activation energy needed for the reaction to proceed, which is the minimum energy required to initiate the chemical process.

In the exercise, the reaction's activation energy drops from 135 kJ to 52.65 kJ with the help of a catalyst. That's a dramatic reduction to just 39% of the original energy needed! This implies that the reaction can occur much faster because the energy barrier has been lowered. Catalysts are vital in many industrial processes and biological systems; they make reactions feasible that would otherwise take too long or require too much energy.

• Think of a catalyst like a shortcut on a mountainous hike—the path is less steep and much easier to travel.
• Enzymes, a type of biological catalyst, facilitate essential reactions in our bodies every day. Without them, life as we know it wouldn't be possible!

Therefore, understanding catalyzed reactions is crucial for fields ranging from medicine to environmental science.

Exploring Reaction Enthalpy

Moving on to reaction enthalpy, denoted as \(\Delta H\), which is a measure of the total heat change in a reaction. It's calculated under constant pressure and can be either positive or negative. A positive \(\Delta H\) indicates endothermic reactions, where heat is absorbed. Conversely, a negative \(\Delta H\) points to exothermic reactions, where heat is released.

In our exercise, the reaction enthalpy is positive, at 45 kJ, signifying an endothermic process. This information is key when we look at energy profiles of reactions. It tells us that the overall energy of the products is higher than that of the reactants, which is typical for reactions requiring heat absorption.

Importance of Reaction Enthalpy

Understanding \(\Delta H\) helps predict how a reaction might behave under different temperature conditions and can influence various scientific and engineering decisions. For example:

• In designing a chemical reactor, knowing the reaction enthalpy is critical for controlling the temperature and ensuring safety.
• Thermodynamic tables, filled with \(\Delta H\) values, are indispensable tools for chemists and engineers to calculate energy requirements and yields of chemical processes.

Reverse Reaction Energy Profile

Finally, let's delve into understanding the reverse reaction energy profile. Every reaction can, theoretically, proceed in the forward or backward direction. When considering the reverse reaction, it's crucial to take into account the activation energy for this backward process. For the reverse reaction to occur, the system must overcome this associated energy barrier.

According to our solutions, the activation energy for the reverse reaction (uncatalyzed) is 180 kJ. It’s higher than for the forward reaction, as we must take into account the enthalpy change. In a way, the reaction 'climbs back up' the energy hill that was descended in the forward reaction.

Diagramming the Energy Profile

A graphical representation often helps visualize this concept. The energy diagram might show a larger 'hump' to overcome in the reverse reaction, indicative of the higher activation energy. These insights are helpful in fields such as synthetic chemistry and pharmaceuticals, where controlling reaction directionality is crucial.

• Understanding the energy profile of a reverse reaction can aid in designing processes to minimize unwanted backward reactions, thus increasing yield.
• In biochemistry, manipulating the reverse reaction energy profile can alter the rates of metabolic pathways, potentially leading to new treatments for diseases.