Question

Two atomic gases will react to form a diatomic gas: \(A+B \rightarrow A B\). Suppose you perform this reaction with 1 mole each of \(A\) and \(B\) in a thermally isolated chamber, so no heat is exchanged with the environment. Will the temperature of the system increase or decrease?

Short answer

Answer: The temperature of the system will increase as a result of the reaction between the two atomic gases A and B to form the diatomic gas AB, when performed in a thermally isolated chamber.

Step-by-step solution

Compare the potential energy of the reactants and products

In this reaction, two atomic gases A and B combine to form a diatomic gas AB. Initially, the potential energy of the system is due to the interaction between the atoms of A and the atoms of B. After the reaction, the potential energy is due to the interaction between the A and B atoms within each AB molecule. The key point is to consider the potential energy change during the reaction. If the potential energy decreases (becomes more negative) after the reaction, this means that energy is released, and the kinetic energy of the system increases, leading to an increase in temperature. Conversely, if the potential energy increases (becomes less negative) after the reaction, this means that energy is absorbed, and the kinetic energy of the system decreases, leading to a decrease in temperature.

Identify the potential energy change

In our case, since A and B are combining to form AB, the potential energy after the reaction is more negative (lower) than before the reaction. This is because stronger bonds are formed between A and B atoms in the AB molecule, resulting in a decrease in potential energy.

Determine the change in temperature

Since the potential energy of the system decreases (becomes more negative) during the reaction, it means that energy is released. The energy released increases the kinetic energy of the system, leading to an increase in temperature. Therefore, the temperature of the system will increase as a result of the reaction between the two atomic gases A and B to form the diatomic gas AB, when performed in a thermally isolated chamber.

Key concepts

Potential Energy Change in Chemical Reactions

Imagine you have two separate atoms, let's call them Atom A and Atom B. Alone, they have a certain amount of stored energy due to their position and arrangement, known as potential energy. During a chemical reaction, like our example where atomic gases A and B react to form a diatomic gas AB, there is a change in this potential energy.

Why does this matter? Well, when Atom A and Atom B join together, they form a bond. Bonds are like energetic promises atoms make to each other; stable bonds mean a happier, more energetically favorable relationship. In most chemical reactions, forming bonds releases energy — this is because more stable bonds require less energy to maintain. The energy that gets released was once potential energy.

Thus, during the reaction, the potential energy decreases as the bond forms, resulting in the release of energy. This is crucial in understanding how reactions lead to changes in the other forms of energy, such as kinetic energy, and consequently, the temperature of the system.

Kinetic Energy in Reactions

The released energy from the potential energy change doesn't just disappear; it transforms. It often becomes kinetic energy, which is the energy associated with motion. In the molecular world, increased kinetic energy means increased movement of the particles — they start to move faster.

In our example reaction, as the potential energy decreases, the kinetic energy of the molecules within the system increases. Think of it like a group of students getting out of class; the bell (the bond formation) releases them, and they speed up as they leave (increase in kinetic energy).

It's crucial to remember that temperature is a measure of the average kinetic energy of the molecules in a substance. When the kinetic energy increases because of a reaction like this, it directly leads to a rise in temperature, as the particles are moving more vigorously.

Temperature Change in Reactions

What happens to temperature when a chemical reaction occurs? This depends on whether the reaction releases or absorbs energy. In exothermic reactions, where potential energy is lost and kinetic energy increases, the temperature of the substance goes up. For our specific scenario, since the final product AB has a stronger bond than the separate atoms A and B, it is a more stable, lower energy state.

Since the chamber is thermally isolated, meaning no heat escapes, all the energy that was in potential form turns into the movement of the molecules, heating up the system. It's similar to a closed room where a dance party starts spontaneously — the room gets warmer as more people dance (molecules move).

In summary, since the potential energy decreases due to bond formation, the kinetic energy must increase to keep the energy balance. With no heat loss, the temperature of the system rises. This offers a direct insight into how energy transformations are responsible for temperature changes during chemical reactions.