Question

Explain how the entropy of the surroundings of a reaction is related to the enthalpy of the reaction.

Short answer

The entropy of the surroundings, ΔS_surroundings, is inversely proportional to the enthalpy change of the system, ΔH_system, and directly proportional to the inverse of the temperature, at constant temperature (ΔS_surroundings = -ΔH_system/T).

Step-by-step solution

Understanding the Concepts of Entropy and Enthalpy

Entropy is a measure of the disorder or randomness of a system. Enthalpy is a measure of the total energy of a system, including internal energy and the energy required to make room for it by displacing its environment and establishing its volume and pressure. The relationship between entropy and enthalpy is governed by the second law of thermodynamics.

Relating Entropy Change of the Surroundings to the Enthalpy Change of the System

According to the second law of thermodynamics, the total entropy change of the universe, which includes the system and its surroundings, must increase for a spontaneous process. The change in entropy of the surroundings (ΔS_surroundings) is often related to the enthalpy change of the system (ΔH_system) at a constant temperature by the formula: ΔS_surroundings = -ΔH_system/T, where T is the temperature in Kelvin.

Interpreting the Equation

If a reaction releases heat (ΔH_system < 0), it means that the surroundings are gaining that heat. Therefore, the entropy of the surroundings increases. Conversely, if the reaction absorbs heat (ΔH_system > 0), the surroundings lose heat, causing a decrease in the entropy of the surroundings.

Key concepts

Entropy Change of Surroundings

Entropy isn't just a concept confined to the system under study; it extends to the surroundings where the process occurs. The entropy change of the surroundings (ΔS_surroundings) is intrinsically connected to the heat exchange between the system and its environment. Heat transfer is a form of energy dispersal and this dispersion manifests as a change in entropy.

For example, if a chemical reaction releases heat to its surroundings—what chemists call an exothermic process—this energy release increases the randomness or disorder of the surrounding molecules, subsequently increasing the surrounding's entropy (ΔS_surroundings > 0). Conversely, an endothermic reaction, which absorbs energy, leads to a decrease in the entropy of the surroundings (ΔS_surroundings < 0) as energy is drawn into the system, making the surroundings more ordered.

Enthalpy Change of System

Delving into the nature of enthalpy change of a system (ΔH_system), we find it's a measure reflecting the total heat content within a system—often considered under constant pressure. Enthalpy change can be thought of as the system's ability to release or absorb heat energy during a reaction or process.

When the system undergoes a chemical reaction, the change in enthalpy denotes whether the process is consuming energy (ΔH_system > 0), thereby being endothermic, or releasing energy (ΔH_system < 0) as an exothermic process. This change isn't isolated—it directly impacts the entropy of the surroundings as energy flows in or out, underpinning the symbiotic relationship between enthalpy of a system and entropy of its surroundings.

Second Law of Thermodynamics

The second law of thermodynamics serves as a fundamental principle in understanding spontaneous processes. It asserts that the total entropy of an isolated system can never decrease over time. Moreover, it states that entropy tends to increase to a maximum, propelling the system towards equilibrium.

This law helps us understand that for any spontaneous process, the change in the entropy of the universe (which includes both the system and the surroundings) must be positive (ΔS_universe > 0). It is this principle that governs the relationship between entropy and enthalpy changes in a system, providing a basis for predicting the direction of a chemical reaction or process.

Spontaneous Processes Thermodynamics

In thermodynamics, a spontaneous process is one that occurs without needing to be driven by an external energy source. Spontaneity in a process isn't about the speed of the reaction, but about its thermodynamic favorability.

A key indicator of such processes is the sign of the Gibbs free energy change (ΔG), which combines the system's enthalpy and entropy changes. The rule of thumb is that for a process to be spontaneous at constant temperature and pressure, the change in Gibbs free energy must be negative (ΔG < 0). This condition aligns with the second law of thermodynamics, enforcing that spontaneous processes must be energetically favorable and lead to an increase in the overall entropy of the universe.