Question

For a spontaneous process, the correct statement is (a) entropy of the system always increases (b) free energy of the system always increases (c) total entropy change is always negative (d) total entropy change is always positive

Short answer

The correct answer is (d) total entropy change is always positive for a spontaneous process.

Step-by-step solution

Understanding Spontaneous Processes

A spontaneous process is one that occurs without intervention, naturally proceeding in a given direction in time. Such processes are often driven by changes in energy and entropy.

Analyzing Entropy Change

For any process, the total change in entropy ( S_{total}) is the sum of the entropy change of the system ( S_{system}) and the entropy change of the surroundings ( S_{surroundings}). Spontaneous processes in an isolated system occur with an increase in total entropy. This means that  S_{total} can never be negative for a spontaneous process. Thus,  S_{total}  0.

Evaluating System's Entropy

While sometimes the system itself may have decreasing entropy, for a spontaneous process in an isolated system, the combined system-plus-surroundings must see an increase, so the system's entropy ( S_{system}) does not always have to increase.

Considering Free Energy Change

In spontaneous processes, the free energy of the system ( G) decreases. This corresponds to the process releasing free energy which can then do work.  G is defined as  G =  H - T S, where  H is the change in enthalpy and T is temperature. Therefore, option (b) is incorrect because the free energy decreases, not increases.

Key concepts

Entropy Change

Entropy change is a key concept when examining spontaneous processes. Entropy, often symbolized as \(S\), is a measure of disorder or randomness in a system. During a spontaneous process, the total change in entropy (\( \Delta S_{total} \)) is vital to understand. It is calculated by combining the entropy change of the system (\( \Delta S_{system} \)) and the entropy change of the surroundings (\( \Delta S_{surroundings} \)). For a process to be spontaneous, especially in an isolated system, the total entropy must increase, i.e., \( \Delta S_{total} > 0 \). This increase means more disorder or randomness is created as the process occurs naturally without external influence. It's crucial to note that while the system's entropy may decrease, the total entropy still manages to increase due to contributions from the surroundings.

Free Energy

Free energy, symbolized as \(G\), is a thermodynamic quantity that helps predict whether a process is spontaneous. It's defined through the equation \( \Delta G = \Delta H - T \Delta S \), where \( \Delta H \) is the change in enthalpy, \( T \) is the temperature, and \( \Delta S \) is the entropy change. For a spontaneous process, \( \Delta G \) must be negative, indicating that the process releases free energy that can perform work.
This release signifies a decrease in the system's free energy, contrasting with entropy, which increases. While processes can proceed spontaneously with a negative \( \Delta G \), they often release heat, helping maintain the balance and driving the spontaneity through an increase in total entropy.

System and Surroundings Entropy

The concept of system and surroundings entropy provides a more in-depth understanding of entropy changes in spontaneous processes. In any reaction, the system refers to the specific part of the universe we are interested in, while the surroundings encompass everything else that can interact with the system.
Both system and surroundings contribute to the total entropy change. Even if \( \Delta S_{system} \) is negative, meaning the system becomes more ordered, \( \Delta S_{surroundings} \) can compensate with an increase large enough to make \( \Delta S_{total} \) positive. This scenario is crucial for many biological and chemical processes where heat transfer to the environment plays a significant role in achieving spontaneity.

Isolated System

An isolated system is one in which neither energy nor matter is exchanged with its surroundings. In the context of spontaneity, isolated systems are crucial because the total entropy of such a system must always increase for a spontaneous process.
Without exchanges to the external environment, any changes must result from the inherent properties and interactions within the system itself. Thus, even if energy transformations within lead to decreased internal entropy, the overall system's entropy compensates and increases, resulting in a natural, unforced progression of the process. This scenario also helps illustrate why total entropy is a more reliable measure of spontaneity compared to just system or surroundings alone.

Enthalpy and Temperature

Enthalpy, denoted as \(H\), and temperature (\(T\)) are two fundamental thermodynamic factors that play a critical role in determining a process's spontaneity. Enthalpy is the total heat content of a system, and changes in enthalpy (\( \Delta H \)) reflect the heat absorbed or released during a reaction.

• If \( \Delta H \) is negative, heat is released, often increasing the entropy of the surroundings, encouraging spontaneity.
• Temperature, on the other hand, magnifies the influence of entropy changes. As temperature increases, the entropy term \( T\Delta S \) becomes more significant, potentially driving processes that might not seem spontaneous at lower temperatures.

In essence, the balance between \( \Delta H \) and \( T\Delta S \) determines the change in free energy (\( \Delta G \)) and thus the spontaneity of the process.