Problem 34 - A Complete Resource Book in Chemistry for JEE Main

Question

The Gibbs free energy is defined as (a) \(\mathrm{G}=\mathrm{H}-\mathrm{T} \cdot \mathrm{S}\) (b) \(\mathrm{G}=\mathrm{H}+\mathrm{T} \cdot \mathrm{S}\) (c) \(\mathrm{G}=\mathrm{E}-\mathrm{T} . \mathrm{S}\) (d) \(\mathrm{G}=\mathrm{E}+\mathrm{TS}\)

Step-by-Step Solution

Answer

The correct definition is (a) \( G = H - T \cdot S \).

Step 1: Identify Gibbs Free Energy Definition

Gibbs free energy, denoted by \( G \), is a thermodynamic quantity that measures the maximum reversible work that a system can perform. It combines enthalpy (\( H \)) and entropy (\( S \)) into one value to determine the spontaneity of a process.

Step 2: Recall the Correct Formula for Gibbs Free Energy

The Gibbs free energy is defined by the equation: \( G = H - T \cdot S \), where \( H \) is enthalpy, \( T \) is the temperature in Kelvin, and \( S \) is entropy.

Step 3: Analyze the Given Options

Compare each provided option with the correct Gibbs free energy formula. Option (a): \( G = H - T \cdot S \) matches the correct definition.Option (b): \( G = H + T \cdot S \) does not match.Option (c): \( G = E - T \cdot S \) uses energy (\( E \)) instead of enthalpy (\( H \)) and is incorrect.Option (d): \( G = E + TS \) also uses energy (\( E \)) incorrectly.

Key Concepts

Thermodynamic Quantity

Gibbs free energy is an essential thermodynamic quantity that helps predict if a chemical reaction or process will occur spontaneously.
In simpler terms, think of it as a system's energy that can do useful work. It combines two other important thermodynamic properties: enthalpy and entropy.

• Gibbs free energy, symbolized as \( G \), indicates the available energy for work in a particular process.
• Understanding the concept is crucial for predicting how and why reactions occur under constant temperature and pressure.

The term "thermodynamic" refers to the study of heat and energy transformations in systems, crucial for understanding chemical reactions and processes. Knowing \( G \) helps scientists and engineers decide whether a reaction can proceed and, if so, what conditions are needed for optimal results.

Enthalpy and Entropy

When dealing with Gibbs free energy, two other terms frequently come up: enthalpy and entropy. These are distinct yet interrelated thermodynamic quantities that help describe a system's state. Enthalpy \( (H) \) can be seen as the total heat content or "stored energy" in a system. It is concerned with the absorption or release of heat in processes at constant pressure.

• When a reaction releases heat, it is exothermic, generally resulting in a decrease in enthalpy.
• If a reaction absorbs heat, it is endothermic, usually leading to an increase in enthalpy.

Entropy \( (S) \), on the other hand, measures the degree of disorder or randomness in a system. A spontaneous change will often increase entropy, reflecting the universe's tendency towards disorder.

• High entropy represents a very disordered system, while low entropy indicates more order.
• Entropy increases as a system moves from solid to liquid to gas.

These two properties are key components of the Gibbs free energy formula: \( G = H - T \cdot S \). With \( T \) as the temperature, these terms collectively predict process spontaneity.

Spontaneity of a Process

The Gibbs free energy equation plays a critical role in determining the spontaneity of a process. At its core, spontaneity tells us if a process will occur without needing additional energy. For a process to be spontaneous, the change in Gibbs free energy \( (\Delta G) \) must be negative.

• If \( \Delta G < 0 \), the process is spontaneous and will proceed without input of external energy.
• If \( \Delta G = 0 \), the system is at equilibrium, and no net change occurs.
• If \( \Delta G > 0 \), the process is non-spontaneous; it requires energy input to occur.

This equation ties spontaneity to both energy and order changes within a system. It emphasizes that a decrease in enthalpy or increase in entropy can make a reaction more likely to happen. By weighing these factors, Gibbs free energy provides a comprehensive yardstick for process feasibility.