CHM111: Third Law of Thermodynamics

Gibbs Free Energy and Thermodynamics

  • Understanding Gibbs Free Energy

    • What does it mean when Gibbs free energy (G) is equal to zero?
    • Indicates a system at equilibrium.

  • Humor in Learning

    • Student empowerment by relating scientific concepts humorously. Suggest students text loved ones using scientific terms (like 'Gibbs') to see their reaction.

  • Gibbs Free Energy Calculation:

    • Gibbs free energy is calculated similarly to entropy, using the equation:
      ΔG=∑G<em>products−∑G</em>reactants\Delta G = \sum G<em>{products} - \sum G</em>{reactants}
    • Also uses similar procedures as enthalpy and entropy.

Third Law of Thermodynamics

  • Exploring Gibbs at Absolute Zero:
    • At absolute zero (0 K), the temperature factor in Gibbs equation becomes zero.
    • Hence, the Gibbs free energy becomes equal to:
      G=FNDG = FND
    • No energy production occurs at this state, as no reactions take place at perfect crystalline arrangements.

Standard Conditions for Phases of Matter

  • Characteristics of Different Phases:
    • Solids:
    • Must be pure crystalline solids with no impurities.
    • Liquids:
    • Must be pure, with no mixtures or solutions.
    • Gases:
    • Must be at standard pressure (1 atm) to be considered at standard conditions.
    • Solutions:
    • Must be a defined concentration, typically 1 molarity (mol/L).

Understanding Standard Gibbs Energies

  • Elements at Standard State:

    • Natural diatomic gases such as $H2$ or $O2$ have a Gibbs free energy of zero at standard conditions.
    • Such elements haven't undergone any reaction to change their state, hence they remain as defined.

  • Calculating Gibbs Free Energy for Pure Substances:

    • Pure elements have Gibbs free energy of zero, but compounds like sodium chloride (NaCl) will have non-zero Gibbs free energy based on their molecular structure.

Gibbs and Equilibrium

  • Gibbs Free Energy Relation to Q and K:
    • Standard Gibbs free energy relates to the non-standard Gibbs as follows:
      ΔG=−RTln⁡(Q)\Delta G = -RT \ln(Q)
    • Where Q represents the reaction quotient.
    • If the reaction is at equilibrium, then $Q = K$ and:
    • ΔG=0\Delta G = 0
    • Gibbs free energy less than zero indicates spontaneous reactions that favor products, and greater than zero indicates non-spontaneous reactions favoring reactants.

Implications of Gibbs Free Energy on Reactions

  • Understanding Spontaneity:

    • Spontaneous reactions:
    • Gibbs < 0
    • Favors products.
    • Non-spontaneous reactions:
    • Gibbs > 0
    • Favors reactants.

  • Equilibrium Conditions:

    • Within equilibrium, rates of reaction remain equal but do not imply equal quantities of products and reactants.

Calculation of Gibbs Free Energy in Reactions

  • Example Calculation:

    • Equation for Gibbs Calculation:
      ΔG=−RTln⁡(K)\Delta G = -RT \ln(K)
    • Where:
    • R = 8.314 J/(mol K)
    • T = Temperature in Kelvin
    • K = Equilibrium constant for the reaction

  • Conversion of Units in Problems:

    • The importance of unit consistency when performing Gibbs calculations, particularly between joules and kilojoules.

Practical Application and Graphing

  • Understanding Graphs for Gibbs Free Energy:

    • Application of Gibbs equations and rearranging them to derive linear relationships useful for graphing.
    • Example: Graphing the relationship of Gibbs energy versus temperature.

  • Equilibrium Constant Relationship:

    • Setting up experiments based on K values and temperature changes helps predict the behaviors of reactions and their spontaneity.

Review Problems

  • Jumbo Review Problem:

    • Will consolidate knowledge gained on Gibbs free energy, enthalpy, and entropic transformations.
    • Reinforces the understanding of spontaneity and equilibrium as reactions are manipulated.

  • Exam Tips:

    • Pay attention to signs when applying thermodynamic equations. Orders of variables are critical to avoid common pitfalls in calculations.
    • When closed systems and standard conditions are referenced, ensure clarity on what constitutes a pure substance and how it affects Gibbs free energy results.

Conclusion

  • Recap on Gibbs Free Energy:
    • Essential for understanding chemical equilibrium and thermodynamic spontaneity.
    • Understanding these principles aids in predicting chemical behavior and energy exchange efficiently.