Question

Gas \(A_{2}\) reacts with gas \(B_{2}\) to form gas AB at a constant temperature. The bond energy of \(A B\) is much greater than that of either reactant. What can be said about the sign of \(\Delta H ? \Delta S_{\mathrm{surr}} ?\) \(\Delta S\)? Explain how potential energy changes for this process. Explain how random kinetic energy changes during the process.

Short answer

In the reaction where gas A₂ reacts with gas B₂ to form gas AB, ΔH is negative as it is an exothermic reaction, releasing energy. ΔSsurr is positive because the released heat increases the entropy of the surroundings. However, ΔS will be negative as the number of gaseous particles decreases, reducing the system's entropy. The potential energy decreases during the reaction due to the formation of stronger AB bonds, and the random kinetic energy increases because of the heat transfer, leading to higher particle motion and randomness.

Step-by-step solution

Analyze the bond energy information

Since the bond energy of AB is much greater than that of either reactant, we can infer that the formation of the AB bond is energetically favorable. This means that energy is released when the AB bond is formed.

Determine the sign of ΔH

As energy is released during the formation of the AB bond, the reaction is exothermic. Therefore, the enthalpy change, ΔH, would be negative.

Determine the sign of ΔS_surr

An exothermic reaction, like the one described, releases heat into the surroundings, increasing the randomness (entropy) of the surroundings. Thus, the entropy change of the surroundings, ΔSsurr, would be positive.

Determine the sign of ΔS

In this reaction, two gaseous reactants (A₂ and B₂) combine to form one gaseous product (AB). As the number of gaseous particles decreases, the randomness (entropy) of the system decreases. Therefore, the entropy change, ΔS, would be negative.

Explain the change in potential energy

The potential energy decreases during the reaction, since energy is released when the more stable AB bond is formed. The potential energy largely resides in the chemical bonds; so, when stronger bonds are formed, the potential energy is lowered.

Explain the change in random kinetic energy

The random kinetic energy, associated with the motion of particles, increases during the reaction. As the reaction is exothermic, heat is released into the surroundings. This heat transfer increases the kinetic energy and the motion of the particles in the system and surroundings, leading to a higher degree of randomness. In conclusion, the given reaction has a negative ΔH, a positive ΔSsurr, and a negative ΔS. The potential energy decreases, and the random kinetic energy increases during the process.

Key concepts

Bond Energy

Bond energy is a crucial concept in thermodynamics as it represents the energy required to break a bond between two atoms. For this reaction, we consider the bond energy between gases \(A_{2}\) and \(B_{2}\) forming gas AB. The fact that the bond energy of AB is much greater than that of the reactants indicates a more stable product formation. This high bond energy signifies that AB bonds are strong, requiring substantial energy to break.
When stronger bonds form from weaker ones, energy is released, making the process energetically favorable. This release of energy reflects on the system, often seen in exothermic reactions where heat disperses to the surroundings as a result of bond formation.

Enthalpy Change

Enthalpy change, often represented as \(\Delta H\), is a measure of heat energy change at constant pressure. In this exercise, the process of forming gas AB from \(A_2\) and \(B_2\) is exothermic, meaning it releases heat. Therefore, the enthalpy change \(\Delta H\) is negative.
A negative \(\Delta H\) signifies that the energy content of the products is lower than that of the reactants. This drop underscores the release of energy in forming the stronger AB bonds, contributing to the stability of the product. The release of heat to the surroundings plays a key role in dictating the flow of energy in chemical reactions.

Entropy Change

Entropy change, denoted as \(\Delta S\), indicates the measure of disorder or randomness in a system. During the reaction of gases \(A_{2}\) and \(B_{2}\) to form AB, the total number of gas molecules decreases. This reduction implies lesser freedom for the molecules to move, reducing randomness.
Consequently, the entropy change of the system \(\Delta S\) is negative. In physics and chemistry, it's known that reactions producing fewer moles of gas generally decrease system entropy. However, since the reaction is exothermic, the entropy of the surroundings \(\Delta S_{surr}\) increases.

Potential Energy

Potential energy in chemical reactions is largely tied to the energy stored in chemical bonds. In this specific reaction, the potential energy decreases as \(A_{2}\) and \(B_{2}\) form AB. As stronger bonds form in the product (gas AB), the potential energy stored in these bonds lowers.
This decrease in potential energy occurs because AB bonds are more stable and require less energy to maintain compared to the original weaker bonds. Therefore, forming stronger chemical bonds releases energy, signifying a drop in the system's potential energy, and is a defining feature of exothermic reactions.

Kinetic Energy

Kinetic energy generally refers to the energy of motion, related to the velocity of particles. In this exercise, the exothermic nature of the reaction causes a release of heat into the surroundings. This release enhances the movement of molecules both in the system and the surroundings.
Therefore, as the reaction proceeds, the kinetic energy of particles within the system increases, leading to greater particle movement and higher temperatures. This heightened molecular activity contributes to increased random kinetic energy, which relates to an increase in the system's temperature and contributes to surrounding disorder via heat transfer.