Problem 78 - Chemistry An Atoms First Approach

Question

Consider the following reaction: $$ \mathrm{A}_{2}+\mathrm{B}_{2} \longrightarrow 2 \mathrm{AB} \quad \Delta E=-285 \mathrm{kJ} $$ The bond energy for \(A_{2}\) is one-half the amount of the AB bond energy. The bond energy of \(\mathbf{B}_{2}=432 \mathrm{kJ} / \mathrm{mol} .\) What is the bond energy of \(\mathrm{A}_{2} ?\)

Step-by-Step Solution

Answer

The bond energy of A₂ is 49 kJ/mol.

Step 1: Write down the given information

Here are the information given in the problem: - A₂ + B₂ ⟶ 2AB, ∆E = -285 kJ - Bond energy of B₂ = 432 kJ/mol - Bond energy of A₂ = (1/2) × Bond energy of AB

Step 2: Calculate the total bond energy of the products

Assuming that the bond energy of AB is x kJ/mol, the total bond energy of products, considering the stoichiometric coefficients, will be 2x kJ.

Step 3: Calculate the total bond energy of the reactants

The bond energy of A₂ is (1/2) x, and the bond energy of B₂ is 432 kJ/mol. Therefore, the total bond energy of reactants is (1/2)x + 432 kJ.

Step 4: Apply Hess's Law

Hess's law states that the energy change for the reaction (∆E) is equal to the total bond energy of products minus the total bond energy of reactants. In this case, we have: -285 kJ = (2x kJ) - [(1/2)x + 432 kJ]

Step 5: Solve for x (bond energy of AB)

Rearrange the equation to solve for x: -285 kJ + 432 kJ = (2x kJ) - (1/2)x 147 kJ = (3/2)x x = 98 kJ/mol The bond energy of the AB molecule is 98 kJ/mol.

Step 6: Find the bond energy of A₂

Using the relationship given, we can now find the bond energy of A₂: Bond energy of A₂ = (1/2) × Bond energy of AB Bond energy of A₂ = (1/2) × 98 kJ/mol Bond energy of A₂ = 49 kJ/mol So, the bond energy of A₂ is 49 kJ/mol.

Key Concepts

Hess's Law

Hess's Law is a fundamental principle in chemistry that helps us understand energy changes in chemical reactions. It states that the total enthalpy change for a reaction is the same, regardless of the pathway taken. In simpler terms, it doesn't matter how you get from reactants to products; the energy change is constant.

In the context of our reaction, Hess's Law allows us to simplify the calculation of bond energies. We can separate the reaction into the breaking and forming of bonds, which lets us calculate the overall reaction energy. This approach is very helpful because direct measurement of bond energies isn't always feasible.

By applying Hess's Law, we can compute the required bond energies by using known bond energies and reacting substances. This helps us unravel the total energy exchanges involved in the process, providing insight into reaction energetics.

Enthalpy Change

Enthalpy change, often represented as \( \Delta H \), is the amount of heat absorbed or released during a chemical reaction. It indicates whether a reaction is endothermic or exothermic.

• If \( \Delta H \) is negative, the reaction releases heat (exothermic).
• If \( \Delta H \) is positive, the reaction absorbs heat (endothermic).

In our reaction, the enthalpy change \( \Delta E = -285 \text{ kJ} \) shows that the reaction releases 285 kJ of energy, making it exothermic. This is a vital piece of information because it tells us that the energy required to break the bonds in the reactants is less than the energy released when new bonds form in the products.

By carefully analyzing the enthalpy change, we can understand the energy dynamics at play and predict how the reaction's energetics progress. This concept serves as a cornerstone for understanding not only this particular reaction but many others in energetics studies.

Chemical Reaction Energetics

Chemical reaction energetics focuses on understanding the energy changes that occur during a chemical reaction. Energetics involves examining how energy is conserved, transferred, and transformed in the course of a reaction.

The key to comprehending reaction energetics starts with the bonds themselves. Energy is needed to break chemical bonds (endothermic) and is released when new bonds form (exothermic). Knowing the bond energies enables us to calculate the net energy change in a reaction.

• Calculate individual bond energies.
• Assess how much energy is absorbed/released.
• Determine whether the overall reaction is endothermic or exothermic.

The solution to our exercise employs these principles to determine the bond energy of \( \text{A}_2 \). By comparing the energy of products and reactants, we understand how chemical bonds influence the overall energetics of the reaction.
Understanding these energetic principles is essential for predicting reaction viability, selecting suitable reaction conditions, and designing effective industrial processes.