Gibbs Free Energy

Introduction to Gibbs Free Energy

• Definition of Gibbs Free Energy (G):
  • Denotes the maximum reversible work a system can perform at constant temperature and pressure.
  • Energy available for chemical transformations excluding expansion work.

Predicting Reaction Outcomes

• Conditions Indicated by ΔG:
  • Negative ΔG: Reaction is spontaneous.
  • Zero ΔG: Reaction is at equilibrium.
  • Positive ΔG: Reaction is non-spontaneous.

Formula Overview

• Formula: $\Delta G = \Delta H - T \Delta S$
  • ΔG: Change in Gibbs Free Energy
  • ΔH: Change in enthalpy (heat content)
  • T: Absolute temperature (Kelvin)
  • ΔS: Change in entropy (measure of disorder)

Worked Examples

Example Calculation

Given:

• Reaction at 298 K
• ΔH = -10 kJ/mol
• ΔS = -50 J/mol·K

Let's calculate the change in Gibbs Free Energy:

1. First, convert ΔH to joules: ΔH = -10,000 J/mol
2. Apply the formula $\Delta G = \Delta H - T \Delta S$:
   • $\Delta G = -10,000 - 298 \times (-50)$
   • $\Delta G = -10,000 + 14,900$
   • $\Delta G = 4,900 \text{ J/mol}$

Interpretation: Since ΔG > 0, the reaction is non-spontaneous.

Understanding Reaction Spontaneity

Criteria for Spontaneity

Temperature's Role (T)

• Influence on $\Delta G$: Temperature can impact the spontaneity of a reaction using the equation $\Delta G = \Delta H - T \Delta S$.

Misconceptions

Speed vs. Spontaneity

• Gibbs Free Energy ($\Delta G < 0$) signifies if a reaction is possible, but not its speed.

Enthalpy ($\Delta H$)

Processes:

• Endothermic:
  • Absorbs heat ($\Delta H > 0$).
  • Example: Melting of ice, requiring heat absorption for the solid-to-liquid transition.
• Exothermic:
  • Releases heat ($\Delta H < 0$).
  • Example: Combustion of a fuel, releasing energy in the form of heat.

Entropy ($\Delta S$)

Examples:

• Phase Changes:
  • Moving from solid $\rightarrow$ liquid $\rightarrow$ gas increases $\Delta S$.
  • Example: Water transitioning from ice to steam, reflecting increasing disorder.
• Dissolution:
  • Salt dissolving in water causes an increase in $\Delta S$, indicating increased randomness as ions separate.

Practice Problems

• Example 1:

  • Assess conditions for reactions spontaneous at low temperatures.
    • Given:
      • $\Delta H = 50 \text{ kJ/mol}$
      • $\Delta S = 0.15 \text{ kJ/(mol K)}$
    • Calculate:
      • $T_1 = 500 \text{ K}$
      • $\Delta G = 50 - 500 \times 0.15 = 50 - 75 = -25 \text{ kJ/mol}$ (Spontaneous)
      • $T_2 = 300 \text{ K}$
      • $\Delta G = 50 - 300 \times 0.15 = 50 - 45 = 5 \text{ kJ/mol}$ (Non-spontaneous)

• Example 2:

  • Demonstrate non-spontaneous reactions at varying temperatures.
    • Given:
      • $\Delta H = 75 \text{ kJ/mol}$
      • $\Delta S = -0.1 \text{ kJ/(mol K)}$
    • Analysis:
      • At any temperature: $\Delta G = 75 - T \times (-0.1) = 75 + 0.1T$
      • Since both terms are positive, $\Delta G$ will always be positive
      • Therefore, the reaction is non-spontaneous at all temperatures

Visual Aids

Annotated Diagrams

• Phase Change Diagram:
  • Purpose: Showcases how entropy and enthalpy vary during transitions like melting and boiling.
  • Annotations:
    • X-axis: Reflects temperature variations.
    • Y-axis: Indicates entropy and enthalpy changes.
  • Real-World Examples:
    • Boiling Water: Demonstrates increased entropy as water converts to steam.
    • Melting Ice: Exhibits entropy change as solid transitions to liquid.

• Graphs for Entropy, Enthalpy, and Gibbs Free Energy:
  • Description: Outlines the interaction between $\Delta S$, $\Delta H$, and $\Delta G$.

Addressing Misconceptions

Misconceptions

• "Entropy equals chaos":
  • infoNote

    Correction: Entropy is a metric, not chaos; it measures disorder.

• "Spontaneity means fast":
  • infoNote

    Correction: Spontaneity signifies thermodynamic favourability, not speed.

• "Negative $\Delta G$ equals rapid reaction":
  • infoNote

    Correction: A negative $\Delta G$ indicates potential onset, not reaction speed.

Importance of Catalyst

• Catalyst Significance:
  • Vital in both academic study and industrial applications.
  • Example: Enzymes act as biological catalysts, critical for accelerating metabolic reactions.

Exam Tips

• Spontaneity vs. Speed: Avoid confusing speed with spontaneity. Catalysts expedite reactions but do not alter Gibbs Free Energy.