Question

A chemical reaction occurs, and \(20.7 \mathrm{~J}\) is transferred from the chemical system to its surroundings. (Assume that no work is done.) (a) What is the algebraic sign of \(\Delta T_{\text {surroundings }} ?\) (b) What is the algebraic sign of \(\Delta_{r} E_{\text {system }}\) ?

Short answer

(a) Positive (b) Negative

Step-by-step solution

Understand the Problem

We are given that 20.7 J is transferred from the system to the surroundings. We'll determine the algebraic signs for the temperature change of the surroundings and the energy change of the system.

Identify System and Surroundings

The chemical system loses 20.7 J of energy as heat, meaning the surroundings gain this energy. This implies that the heat transfer is from the system to the surroundings.

Determine Sign of Temperature Change

Since energy is transferred to the surroundings, the temperature of the surroundings increases. Therefore, the algebraic sign of \( \Delta T_{\text{surroundings}} \) is positive.

Determine Sign of Energy Change

The system loses energy, so the internal energy change of the system, \( \Delta_r E_{\text{system}} \), is negative.

Key concepts

Energy Change

Energy change is a fundamental concept when studying heat transfer during chemical reactions. In this context, energy change refers to the amount of energy lost or gained by a system as it interacts with its surroundings. When a reaction occurs, the system—composed of the reacting chemicals—can either absorb energy or release energy. In this exercise, we consider the transfer of 20.7 J of energy. Notice that the energy is leaving the chemical system and being transferred to the surroundings. This indicates an energy loss for the system, which is typically accompanied by a negative sign. The energy change of the system, denoted as \( \Delta_r E_{\text{system}} \), is thus negative because the system's internal energy decreases. Conversely, if the system were to absorb energy, \( \Delta_r E_{\text{system}} \) would be positive, indicating an increase in energy.

Temperature Change

Temperature change is directly related to heat transfer between a system and its surroundings. As energy is exchanged, it can lead to a change in temperature, which is an indicator of the system’s energetic condition.In the given exercise, energy flows from the chemical system into the surroundings. When the surroundings receive energy, their temperature typically increases, because the energy transferred manifests as increased kinetic energy of the particles composing the surroundings. Therefore, the algebraic sign of the temperature change of the surroundings, \( \Delta T_{\text{surroundings}} \), is positive.It is valuable to remember that:

• A positive \( \Delta T \) indicates a temperature increase.
• A negative \( \Delta T \) signifies a temperature decrease.

This basic idea helps in understanding how energy flow impacts temperature in various systems and reactions.

Chemical System and Surroundings

In thermodynamics, the concepts of the chemical system and surroundings are crucial in analyzing energy changes. The system is defined as the specific part of the universe being studied—typically where the chemical reaction takes place. The surroundings are everything external to the system, capable of exchanging energy with it. In our exercise, the chemical system consists of the reactants undergoing transformation. The surroundings are essentially the external environment that can absorb or supply energy. When the system loses energy, as it does by transferring 20.7 J to the surroundings, this action is termed as an exothermic process. Such a process typically results in energy being released into the surroundings, which impacts the thermal state of the environment. Understanding this interaction between system and surroundings aids in comprehending how reactions can affect their local environment. Keep in mind that:

• Energy flow from the system to the surroundings leads to a decrease in the system’s energy.
• Energy flow from the surroundings to the system results in an increase in the system’s energy

These concepts are pivotal when analyzing thermodynamic processes in various chemical reactions.