Problem 25 - A Complete Resource Book in Chemistry for JEE Main

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

Step-by-Step Solution

Answer

Option (d) is correct: Total entropy change is always positive for spontaneous processes.

Step 1: Understanding Spontaneous Processes

A spontaneous process is one that occurs naturally without the need for external energy once it has started. These processes tend to move a system towards equilibrium.

Step 2: Identifying Entropy Changes in Processes

In thermodynamics, entropy is a measure of disorder. According to the second law of thermodynamics, for any spontaneous process occurring in an isolated system, the total entropy, which combines both the system and its surroundings, tends to increase.

Step 3: Analyzing Each Option

**(a)** Entropy of the system always increases: This is not always true for the system alone; surroundings might offset the system's entropy changes. **(b)** Free energy of the system always increases: Incorrect, free energy actually decreases for spontaneous processes. **(c)** Total entropy change is always negative: Incorrect, as spontaneous reactions increase total entropy. **(d)** Total entropy change is always positive: This aligns with the second law of thermodynamics.

Step 4: Selecting the Correct Statement

From the analysis, it's clear that option **(d)** is correct. For a spontaneous process, the total entropy change is always positive, as this reflects the overall increase in disorder of the universe.

Key Concepts

Entropy

Entropy is a central concept in thermodynamics that measures disorder or randomness in a system. The notion of disorder might sound abstract, but it essentially captures the number of ways a system can be arranged. The higher the entropy, the greater the disorder.
Entropy is symbolized by the letter \( S \) and is measured in units of joules per kelvin (J/K). In simple terms, a process that increases disorder increases entropy. This concept is crucial when discussing spontaneous processes, which are natural changes that happen without needing energy input once initiated.
For example, when ice melts into water, the molecules go from an ordered crystalline structure to a more disordered liquid state, thereby increasing the entropy of the system. However, it's important to note that the total entropy change considers both the system and its surroundings, aligning with the second law of thermodynamics.

Second Law of Thermodynamics

The second law of thermodynamics states that in an isolated system, the total entropy tends to increase over time, leading to a state of equilibrium. This law implies that energy transformations are never 100% efficient, as some energy always spreads out, increasing disorder.
There are several ways to express the second law, but one of the most common is that the change in the total entropy for any spontaneous process is always positive. This concept is critical in distinguishing spontaneous processes from non-spontaneous ones, as only spontaneous ones will move a system closer to equilibrium.
The second law helps us understand why certain reactions occur naturally, like why iron rusts over time – it is moving towards a state of greater entropy. So, always remember, in any spontaneous happening, the universe's overall entropy will go up.

Free Energy

Free energy, particularly Gibbs free energy, is a useful concept for understanding whether a process is spontaneous at constant pressure and temperature. Gibbs free energy is denoted as \( G \) and combines the system's enthalpy (total heat content) and entropy into a single value.
The equation is: \[G = H - TS\]where \( G \) is the free energy, \( H \) is enthalpy, \( T \) is temperature, and \( S \) is entropy.
For a process to be spontaneous, \( \Delta G \) – the change in free energy – must be negative. This decrease in free energy means that the process can occur on its own, indicating a favorable change.
If \( \Delta G \) is zero, the system is at equilibrium and no net change will occur without external influence. Understanding how Gibbs free energy works helps in predicting chemical reactions and processes' spontaneity, essential for fields ranging from chemistry to engineering.