Unit 9

Chapter 17: Spontaneity, Entropy, and Free Energy

Section 17.1: Spontaneous Processes and Entropy

• Thermodynamics vs. Kinetics

  • Rate of a reaction depends on the pathway from reactants to products.

  • Thermodynamics determines the spontaneity of reactions based on reactant and product properties.

• Spontaneous Processes

  • A spontaneous process occurs without outside intervention; it can happen rapidly or slowly.

  • Examples include:

    • Radioactive decay

    • Rusting

    • Ice melting (at 1 atm and >0°C)

    • Formation of graphite from diamond.

• Energy Definitions

  • Internal Energy (E): ΔE = q + w (where q = heat, w = work)

  • Enthalpy (H): Determines heat energy in reactions.

    • ΔH > 0: Endothermic reaction

    • ΔH < 0: Exothermic reaction

Understanding Entropy

• What is Entropy?

  • Entropy (S) measures disorder in a system.

  • Second Law of Thermodynamics: In a spontaneous process, there is always an increase in the entropy of the universe.

  • If S > 0, disorder is increasing; if S < 0, disorder is decreasing.

Example Analysis

• Consider a gas in a 4.0 L bulb at 32°C connected to a 20.0 L evacuated bulb:

  • Expected Behavior: The gas will spontaneously expand into the larger space when the valve is opened.

  • When gas expands, ΔH, ΔE, q, and w are all equal to zero, making entropy the driving force of the process.

Characteristics of Entropy

• Driving Force: An increase in entropy is the driving force for spontaneous processes.

• Positional Entropy

  • Gases expand into a vacuum leading to a uniform distribution, as this state corresponds to the highest positional probability.

  • Entropy order: S_solid < S_liquid << S_gas.

Predictions of Entropy Changes

• Predict the signs of ΔS for the following:

  • Evaporation of alcohol: +

  • Freezing of water: -

  • Compressing an ideal gas at constant temperature: -

  • Heating an ideal gas at constant pressure: +

  • Dissolving NaCl in water: +.

Second Law of Thermodynamics

• Entropy of the universe is always increasing, even if the total energy remains constant:

  • ΔSuniverse = ΔS_system + ΔS_surroundings.

Heat Flow and Surrounding Entropy

• ΔS_surroundings (ΔS_surr) depends on heat flow:

  • Heat flows into the system → ΔS_surr is negative.

  • Heat flows out of the system → ΔS_surr is positive.

  • Magnitude of ΔS_surr also depends on temperature, with effects being more pronounced in colder environments.

Effects of Temperature on Spontaneity

• Spontaneity depends on both enthalpy and entropy changes:

  • ΔSuniverse will be favorable if both ΔS_surr is positive and ΔS_system is positive.

Free Energy Concepts

• Definition of Gibbs Free Energy (G):

  • G = H - TS.

  • If G < 0, the reaction is spontaneous (releases energy).

  • If G > 0, the reaction is non-spontaneous (absorbs energy).

  • If G = 0, the system is at equilibrium.

Free Energy Calculations

• Example: Vaporization at boiling point:

  • Signs of changes: w = -; q = +; ΔH = +; ΔS = +; ΔS_surr = -; ΔG = 0.

Changes in Free Energy and Chemical Reactions

• Standard Free Energy Change (ΔG°):

  • ΔG° = ΔH° - TΔS° for reactions in standard states.

Third Law of Thermodynamics

• Entropy of a perfect crystal at 0 K is zero, and entropy increases with temperature.

Entropy Changes in Chemical Reactions

• Calculation of ΔS° using standard entropy values, noting Hess's Law parallels.

Free Energy and Work

• Maximum useful work obtainable is equal to ΔG.

• All real processes tend to degrade energy—irreversible pathways lead to energy waste.