Problem 35 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statement is true for \(\Delta G\) ? (a) it is always proportional to \(\Delta \mathrm{H}\) (b) it may be less than or greater than or equal to \(\Delta \mathrm{H}\) (c) it is always greater than \(\Delta \mathrm{H}\) (d) it is always less than \(\Delta \mathrm{H}\)

Step-by-Step Solution

Answer

(b) it may be less than or greater than or equal to \( \Delta H \).

Step 1: Understanding Gibbs Free Energy

In thermodynamics, Gibbs Free Energy (\( \Delta G \)) is an important concept that helps predict whether a process will occur spontaneously. It is related to enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)) through the equation \( \Delta G = \Delta H - T\Delta S \), where \( T \) is the temperature in Kelvin.

Step 2: Analyzing the Relationship

To determine how \( \Delta G \) compares to \( \Delta H \), analyze the equation \( \Delta G = \Delta H - T\Delta S \). Since \( T\Delta S \) can take on positive, negative, or zero values, the specific relationship between \( \Delta G \) and \( \Delta H \) varies.

Step 3: Considering Different Scenarios

- When \( T\Delta S \) is positive, \( \Delta G \) can be less than \( \Delta H \).- When \( T\Delta S \) is negative, \( \Delta G \) can be greater than \( \Delta H \).- When \( T\Delta S \) is zero, \( \Delta G = \Delta H \).

Step 4: Conclusion

Considering these possibilities, \( \Delta G \) may be less than, greater than, or equal to \( \Delta H \) depending on the value of \( T\Delta S \).

Key Concepts

Thermodynamics

Thermodynamics is the branch of physics that studies the relationships between heat, work, temperature, and energy. It provides a framework to understand how energy is transferred in processes and systems. In simple terms, it tells us how different forms of energy interact and transform within a system. Basic principles involve key laws, including the conservation of energy, which states that energy cannot be created or destroyed, only transformed.

• First Law of Thermodynamics: This is essentially the law of energy conservation. It implies that the total energy of an isolated system remains constant.
• Second Law of Thermodynamics: This introduces the concept of entropy. It states that the total entropy of an isolated system can never decrease over time.

Both laws are crucial in understanding how Gibbs Free Energy functions in processes.

Enthalpy

Enthalpy, symbolized as \( \Delta H \), is a measure of the total energy of a thermodynamic system. It combines the system's internal energy with the product of its pressure and volume. Simply put, it's the heat content of a system under constant pressure.

• If \( \Delta H \) is positive, the system absorbs heat, indicating an endothermic reaction.
• If \( \Delta H \) is negative, the system releases heat, indicating an exothermic reaction.

Understanding enthalpy is vital in predicting how energy changes influence chemical reactions. It ties directly into Gibbs Free Energy, impacting spontaneity along with entropy.

Entropy

Entropy, denoted as \( \Delta S \), measures the disorder or randomness in a system. The higher the entropy, the greater the disorder and energy dispersal.

• High entropy signals a high level of unpredictability and dispersion of energy.
• Entropy is crucial as it helps predict the direction of natural processes.

In any spontaneous process, the entropy of the universe tends to increase. This concept is fundamental in predicting spontaneity, especially when considering Gibbs Free Energy.

Spontaneity

Spontaneity in thermodynamics refers to whether a process can occur on its own without any input of energy from outside the system. The key to determining spontaneity lies in calculating the Gibbs Free Energy \( \Delta G \).

• If \( \Delta G \) is negative, the process is spontaneous.
• If \( \Delta G \) is positive, the process is non-spontaneous.
• If \( \Delta G \) is zero, the system is at equilibrium.

By evaluating \( \Delta G \), we can predict a system's behavior and energy requirements under constant temperature and pressure.

Thermodynamic Equations

Thermodynamic equations provide the mathematical framework for understanding energy changes. A fundamental equation in thermodynamics is the Gibbs Free Energy equation: \[\Delta G = \Delta H - T\Delta S\]In this equation, \( \Delta G \) determines spontaneity, \( \Delta H \) represents the heat exchange, and \( T\Delta S \) accounts for temperature and entropy changes.

• By manipulating the equation, you can identify the influencing factors on spontaneity.
• It helps in predicting whether a reaction or change in state will occur naturally.

Understanding this simple yet powerful equation is crucial for grasping the principles of thermodynamics and their applications in real-world processes.