Problem 101 - General Chemistry: Principles and Modern Applications

Question

For a process to occur spontaneously, (a) the entropy of the system must increase; (b) the entropy of the surroundings must increase; (c) both the entropy of the system and the entropy of the surroundings must increase; (d) the net change in entropy of the system and surroundings considered together must be a positive quantity; (e) the entropy of the universe must remain constant.

Step-by-Step Solution

Answer

For a process to occur spontaneously, the net change in entropy of the system and surroundings considered together must be a positive quantity (option d). Some of the other options (a, b, c) are partially correct, while option e is incorrect.

Step 1: Understanding the Concept of Spontaneity

A spontaneous process is one which occurs by itself without any continuous external influence. These processes are influenced by changes in the system's entropy, which is a measure of the randomness or disorder of the system.

Step 2: Determining Entropy Changes

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy.

Step 3: System and Surroundings Entropy

Options (a), (b) and (c) are partially correct. It is true that for a process to be spontaneous, the entropy in the system or/and surroundings should increase. But this is not a complete statement, as it doesn't consider the system and surroundings as a whole.

Step 4: Net Change in Entropy

Option (d) now considers the system and the surroundings as a whole. It states that there should be a positive net change in entropy for a process to be spontaneous. This is a more overall description of the second law of thermodynamics.

Step 5: Entropy of The Universe

Option (e) that 'the entropy of the universe must remain constant' is incorrect. For any spontaneous process, the total entropy (system + surroundings, i.e. the universe) increases.

Key Concepts

Entropy

Entropy is a measure of disorder or randomness in a system. It is a key concept in thermodynamics to understand why some processes occur spontaneously. Each system is trying to reach a state of maximum entropy or maximum disorder.

When a process occurs, if the entropy, or disorder, of the system increases, the process is likely spontaneous. However, this increase in entropy isn't always within the system itself. It can also occur in the surroundings, or both.

So, when thinking about spontaneous processes, don't just focus on the entropy of the system. Remember that the changes in entropy for both the system and its surroundings can contribute to spontaneity.

Second Law of Thermodynamics

The Second Law of Thermodynamics is a fundamental principle in understanding entropy and spontaneity. It tells us that the total entropy of an isolated system can only increase over time. It stays constant only if the process is perfectly reversible, which is an idealization.

This law helps explain why certain processes are spontaneous. Think of it as predicting the natural direction of processes. A spontaneous process is one where the entropy of the universe increases; this means that the combined entropy of the system and its surroundings goes up.

In simple terms, because systems will naturally evolve towards a state of greater entropy or disorder, it's the driving force behind all spontaneous changes. This principle governs the natural progression towards balance and disorder within a system.

Spontaneous Processes

A spontaneous process is any process that occurs naturally without needing any external force to keep it going. Examples include heat flowing from a hot object to a cooler one and ice melting at room temperature. These happen because they result in an overall increase in the entropy of the system and surroundings together.

For a process to be spontaneous, the net change in entropy must be positive. This doesn't mean just within the system, but also including the surroundings. If a process causes a decrease in the entropy of the system, it might still be spontaneous if the increase in the surroundings' entropy makes up the difference.

Therefore, for a process to truly be spontaneous, the combined entropy of the system and its environment—essentially, the universe—must increase. Remember, spontaneous processes are nature's way to reach a state of equilibrium or balance through increased disorder.