Thermodynamics: Spontaneity, Entropy, and Gibbs Free Energy

SPONTANEOUS CHANGE

  • Definition: A spontaneous change occurs without continuous energy input from outside.

  • Once a spontaneous process begins, no further energy is needed.

  • Nonspontaneous Change: Requires continuous energy from surroundings.

  • If a change is spontaneous in one direction, it is nonspontaneous in the reverse direction.

FIRST LAW OF THERMODYNAMICS

  • Concept: Energy is conserved; it can neither be created nor destroyed, only transformed.

  • Equations:

    • Total energy of the universe: \Delta E{sys} = - \Delta E{surr}

    • \Delta E{sys} + \Delta E{surr} = \Delta E_{univ} = 0

  • This law indicates energy change in a reaction but does not guide the direction.

ENTHALPY (ΔH) AND SPONTANEITY

  • ΔH Characteristics:

    • Not predictive for spontaneity; spontaneous reactions can be exothermic (ΔH < 0) or endothermic (ΔH > 0).

  • Examples of Spontaneous Changes:

    • Exothermic: Freezing and combustion;

    • Endothermic: Melting and salt dissolving in water.

FREEDOM OF PARTICLE MOTION

  • Important for spontaneous endothermic processes:

    • Transforms from solid to liquid to gas or from solid with liquid to ions in solution, increases motion freedom.

    • More freedom of motion leads to greater entropy.

MICROSTATES AND ENTROPY

  • Microstates: Allowed energy states of particles; greater microstates correlate with higher entropy.

  • Entropy (S):

    • S = k \ln(W)

    • Where ( k ) is the Boltzmann constant: k = 1.38 \times 10^{-23} \text{ J/K} .

    • Higher entropy (more microstates) means more disorder.

ENERGY VS ENTROPY

  • Energy: Capacity to do work, constant in the universe, \Delta{E}{univ} = \Delta{E}{sys} + \Delta{E}_{surr} = 0 .

  • Entropy: Measures energy distribution at absolute temperatures, always increases in the universe, leading to \Delta S{univ} = \Delta S{sys} + \Delta S_{surr} > 0 .

SPONTANEOUS GAS EXPANSION

  • Process: When the stopcock between flasks is opened, gas fills both flasks, increasing volume and microstates, thus raising entropy.

  • Microstate Changes: The number of microstates increases; 2^n , where ( n ) is the number of particles.

REVERSIBLE PROCESS

  • A reversible process has an infinitesimal change, allowing the reactants and products to reach equilibrium.

  • Requires balancing and keeping the system at equilibrium throughout the process.

SECOND LAW OF THERMODYNAMICS

  • Real processes favor increases in the entropy of the universe (ΔS_{univ} > 0).

THIRD LAW OF THERMODYNAMICS

  • A perfect crystal at absolute zero has zero entropy:

    • S_{sys} = 0 @ 0 K

STANDARD MOLAR ENTROPY (S°)

  • Standard states: 1 atm for gases, 1 M for solutions, and pure in stable forms for solids and liquids.

FACTORS AFFECTING ENTROPY

  • Temperature: S° increases with temperature.

  • State: Entropy increases from solid to liquid to gas.

  • Formation of Solutions: Affects entropy significantly, typically increasing it.

  • Atomic Size: Larger structures have higher entropy values.

PHASE CHANGES AFFECTING ENTROPY

  • Transitions increase entropy; for instance, melting and vaporization lead to large entropy increases.

    • \Delta S^{ ext {fus}} < \Delta S^{ ext {vap}} (melting is less than vaporization).

DISSOLUTION OF SALTS

  • In salt solutions, the solute typically has higher entropy compared to solids and liquids
    e.g., the organization of water around ions impacts the overall entropy.

ENTROPY AND MOLECULAR COMPLEXITY

  • Entropy increases with molecules of greater complexity and size, influencing standard molar entropy values.

PREDICTING ENTROPY CHANGES

  • The sign of entropy change can often be inferred from changes in the number of gas moles during a reaction:

    • Positive if gas moles increase; negative if they decrease.

GIBBS FREE ENERGY (ΔG)

  • Combines enthalpy and entropy to indicate spontaneity:

  • G = H - TS

  • ΔG characteristics:

    • ΔG < 0 indicates spontaneity.

    • ΔG > 0 indicates nonspontaneity.

RELATIONSHIP BETWEEN ΔG, ΔH, and ΔS

  • Key equations:

    • ΔG^{ ext{rxn}} = ΔH^{ ext{rxn}} - TΔS^{ ext{rxn}}

    • Determine signs accordingly to evaluate reactions.

SPONTANEITY AND TEMPERATURE

  • Reactions can swap between spontaneous and nonspontaneous at various temperatures based on ΔH and ΔS relationships:

    • e.g., for endothermic reactions, the temperature at which ΔS becomes positive is crucial.

EQUILIBRIUM AND FREE ENERGY

  • At equilibrium, no net change occurs; both forward and reverse reactions are equally probable leading to ΔG_{univ} = 0 .

REDOX REACTIONS AND ELECTROCHEMISTRY

  • Redox processes involve transfer of electrons, oxidation (loss) and reduction (gain).

  • Electrochemical Cells: Voltaic cells convert chemical energy to electrical energy; electrolytic cells do the opposite.

HALF-REACTION METHOD

  • Simplifies redox reactions, separating oxidation and reduction, allowing easier balancing of charges and species.

STANDARDS AND CELL POTENTIALS

  • Standard Electrode Potentials reflect the likelihood of reactions; used to calculate overall cell potential.

  • E° reflects the potential difference between cathode and anode during spontaneity.

  • Use E° term which remains unchanged regardless of mole ratios in reaction.

NERNST EQUATION

  • Relates standard potentials, concentration, and temperature, allowing calculation of non-standard conditions versus standard potentials.

  • Adjustments made for amounts of products/reactants in equilibrium, influencing cell potential.

STOICHIOMETRY OF ELECTROLYSIS

  • Applies Faraday’s laws to compute amounts produced at electrodes based on current and time flow.

  • Charge relationship directly correlates to mass or molar weight, allowing calculations of required parameters for practical applications due to electrolysis.

IMPORTANT RELATIONSHIPS

  • ΔG^{ ext{rxn}} = - nF E_{cell} for calculations at standard state conditions.

, What is the difference between a spontaneous change and a nonspontaneous change in a thermodynamic context?