6.7 Gibbs Free Energy

This topic explains Gibbs free energy — a measure of the usable energy of a system. It describes how Gibbs free energy determines the spontaneity of a reaction.

Definition

Gibbs Free Energy (G): A measure of the amount of usable energy of a system at constant temperature and pressure. It is defined as the enthalpy of a system minus the product of its temperature and entropy.

Main Idea

Gibbs free energy is a measure of the amount of usable energy of a system at constant temperature and pressure. It is defined as the enthalpy of a system minus the product of its temperature and entropy. Gibbs free energy is also known as "Available energy" . It is denoted by the symbol G, after the name of its discoverer, American scientist Josiah Willard Gibbs in 1876.

Core Concept

G = H - TS

• G = Gibbs free energy
• H = Enthalpy of reaction
• T = Temperature
• S = Entropy

Gibbs free energy is a state function; it does not depend on the path followed by a reaction. Therefore, change in Gibbs free energy is given by:

Δ G^° = Δ H^° - TΔ S^°

When the reaction is carried out at constant temperature (Δ T = 0):

Δ G^° = Δ H^° - TΔ S^°

This equation is called the Gibbs-Helmholtz equation.

Detailed Explanation

What is Gibbs Free Energy?

• Gibbs free energy is a measure of the amount of usable energy of a system at constant temperature and pressure.
• It is defined as the enthalpy of a system minus the product of its temperature and entropy.

G = H - TS

• Gibbs free energy is also known as "Available energy" .
• It is denoted by the symbol G, after the name of its discoverer, American scientist Josiah Willard Gibbs in 1876.

Gibbs Free Energy as a State Function

• Gibbs free energy is a state function; it does not depend on the path followed by a reaction.
• Therefore, change in Gibbs free energy is given by:

Δ G^° = Δ H^° - TΔ S^°

- When the reaction is carried out at constant temperature (Δ T = 0):

Δ G^° = Δ H^° - TΔ S^°

• This equation is called the Gibbs-Helmholtz equation.
• Δ G^° is particularly useful in determining the spontaneity and equilibrium state of a chemical reaction.

Spontaneity and Equilibrium

The sign and magnitude of Δ G^° indicate whether the process is spontaneous or at equilibrium. There are three possibilities:

• The process is spontaneous in the forward direction.
• This also means that the system releases energy (exothermic) and tends to move to a lower energy state.

2. If Δ G^° > 0 (positive): - The process is non-spontaneous in the forward direction and requires energy (endothermic).

3. If Δ G^° = 0: - The system is in equilibrium.

Phase Transitions

Gibbs free energy is also useful for understanding phase transitions, such as from liquid to solid or gas and vice versa. Consider, for example, the melting of ice:

H₂O_(s) → H₂O_(l)

• At the melting point, Δ G^° = 0, so the solid and liquid phases are in equilibrium.
• Below the melting point, Δ G^° is negative, indicating that the solid phase is more ordered.
• Above the melting point, Δ G^° is positive, indicating that the liquid phase is more disordered.

Enthalpy and Calorie Contents of Food

• The amount of energy in a food or drink is measured in calories.
• Calories in food refer to the amount of energy stored in food, which is released through the metabolic processes in our body.
• The enthalpy change associated with these processes corresponds to the amount of energy released or absorbed during the process of digestion and metabolism.
• The energy content of food is measured in Kilocalories and is often just called calories.
• 1 Kilocalorie (kcal) is approximately equivalent to 4.184 Kilojoules (kJ) .
• This conversion factor relates the energy released during a chemical reaction to the calorie content of food.

Intermediate Level

Gibbs Free Energy

G = H - TS

Δ G^° = Δ H^° - TΔ S^°

This is the Gibbs-Helmholtz equation.

Spontaneity

Phase Transitions

• Melting point: Δ G^° = 0 (equilibrium).
• Below melting point: Δ G^° < 0 (solid stable).
• Above melting point: Δ G^° > 0 (liquid stable).

Enthalpy and Calorie Contents of Food

• Energy in food measured in calories.
• 1 kcal ≈ **4.184 kJ**.
• Relates energy released in reactions to calorie content of food.

Important Points

• 1. Gibbs free energy: G = H - TS.
• 2. Change: Δ G^° = Δ H^° - TΔ S^°.
• 3. Δ G^° < 0: Spontaneous.
• 4. Δ G^° > 0: Non-spontaneous.
• 5. Δ G^° = 0: Equilibrium.
• 6. Phase transitions: Melting point at Δ G^° = 0.
• 7. Food energy: 1 kcal ≈ 4.184 kJ.

Remember

• - Gibbs free energy: G = H - TS
• - Change: Δ G^° = Δ H^° - TΔ S^°
• - Spontaneous: Δ G^° < 0
• - Non-spontaneous: Δ G^° > 0
• - Equilibrium: Δ G^° = 0
• - Food energy: 1 kcal ≈ 4.184 kJ

Common Mistakes

• 1. Confusing Δ G^° with Δ H^°: Δ G^° includes both enthalpy and entropy.
• 2. Forgetting the sign of Δ G^°: Negative = spontaneous; Positive = non-spontaneous.
• 3. Mixing up phase transitions: At melting point, Δ G^° = 0.
• 4. Forgetting the conversion factor: 1 kcal ≈ 4.184 kJ.

Quick Revision

• Gibbs free energy: G = H - TS.
• Change: Δ G^° = Δ H^° - TΔ S^°.
• Δ G^° < 0: Spontaneous.
• Δ G^° > 0: Non-spontaneous.
• Δ G^° = 0: Equilibrium.
• Phase transitions: Melting point at Δ G^° = 0.
• Food energy: 1 kcal ≈ 4.184 kJ.

60-Second Revision

• Gibbs free energy: G = H - TS
• Change: Δ G^° = Δ H^° - TΔ S^°
• Spontaneous: Δ G^° < 0
• Non-spontaneous: Δ G^° > 0
• Equilibrium: Δ G^° = 0
• Food energy: 1 kcal ≈ 4.184 kJ

QUALITY VALIDATION

• Topic: 6.7 Gibbs Free Energy
• Chapter: 6 (Energetics)

• Source re-read: PASS
• Source scope followed: PASS
• Knowledge level matched: PASS
• Important concepts covered: PASS
• Definitions checked: PASS
• Equations checked: PASS
• Derivations checked: PASS
• Examples checked: PASS
• Unsupported knowledge added: NO
• Unnecessary repetition: NO
• Notes format maintained: PASS
• Important source content omitted: NO

• Source limitations:
• NONE

NEXT TOPIC