Chapter 19: Free Energy and Thermodynamics – Terms, Definitions, Tables, and Formulas

Chapter 19: Free Energy and Thermodynamics

19.1 Cold Coffee and Dead Universes

This section introduces the laws of thermodynamics, which govern energy changes and the direction of spontaneous processes in chemistry.

• First Law of Thermodynamics: Energy cannot be created or destroyed.

• Second Law of Thermodynamics: Energy tends to disperse or spread out rather than concentrate.

19.2 Spontaneous and Nonspontaneous Processes

Thermodynamics studies energy and its transformations, providing a fundamental basis for predicting whether a process will occur spontaneously.

• Spontaneous Process: Occurs naturally without ongoing outside intervention.

• Nonspontaneous Process: Occurs only with continuous external influence.

• Thermodynamic Favorability: Determined based on the laws of thermodynamics, especially the dispersal of energy and matter.

• Relationship: The balance between the First Law (conservation of energy) and the Second Law (entropy increase) determines spontaneity.

19.3 Entropy and the Second Law of Thermodynamics

Entropy is a central concept in thermodynamics, quantifying the dispersal of energy and matter.

• Entropy (S): A measure of energy dispersal or randomness in a system.

• Second Law of Thermodynamics: For any spontaneous process, the total entropy of the universe increases.

• Mathematical Expression: $\Delta S_{univ} = \Delta S_{system} + \Delta S_{surroundings} > 0$

• Boltzmann Equation: Relates entropy to the number of microstates (W): $S = k \ln W$

  • k = Boltzmann constant = $1.38 \times 10^{-23}$ J/K

• Microstate: A specific arrangement of energy among particles in a system.

• State Function: A property that depends only on the current state, not on the path taken to reach that state.

19.4 Entropy Changes Associated with State Changes

Entropy changes can be calculated for physical changes such as melting, vaporization, and sublimation.

• System: The substance being measured in thermodynamics.

• Surroundings: Everything else that exchanges energy with the system.

• General Equation for Entropy Change: $\Delta S = \dfrac{q_{rev}}{T}$ (at constant temperature)

  • $q_{rev}$ = heat of a reversible process

  • T = temperature in Kelvin

• Example (Gas Expansion): $\Delta S = nR \ln \dfrac{V_f}{V_i}$

  • n = moles of gas

  • R = gas constant

  • $V_f$, $V_i$ = final and initial volumes

Reversible vs. Irreversible Processes

• Reversible Process: Can reverse direction upon an infinitesimally small change in some property.

• Irreversible Process: Cannot return to their original state without significant changes in energy or conditions.

Table: Heats of Vaporization of Several Liquids at Their Boiling Points and at 25°C

Liquid	Chemical Formula	ΔHvap (kJ/mol)	ΔSvap (J/mol·K)
Water	H2O	40.7	109
Ethanol	C2H5OH	38.6	109
Benzene	C6H6	30.8	87
Ammonia	NH3	23.3	97

19.5 Heat Transfer and Changes in the Entropy of the Surroundings

• Entropy Change of Surroundings: $\Delta S_{surr} = -\dfrac{q_{sys}}{T}$

• Spontaneous Reaction: $\Delta S_{univ} > 0$

19.6 Gibbs Free Energy

Gibbs free energy combines enthalpy and entropy to predict spontaneity at constant temperature and pressure.

• Gibbs Free Energy Change: $\Delta G = \Delta H - T\Delta S$

• Spontaneity: A negative $\Delta G$ indicates a spontaneous process.

Table: The Effect of ΔH, ΔS, and T on Spontaneity

ΔH	ΔS	Spontaneity at Low T	Spontaneity at High T	Example
-	+	Spontaneous	Spontaneous	Combustion of H2
+	-	Nonspontaneous	Nonspontaneous	Decomposition of H2O
-	-	Spontaneous	Nonspontaneous	Freezing of water
+	+	Nonspontaneous	Spontaneous	Melting of ice

19.7 Entropy Changes in Chemical Reactions: Calculating ΔS°rxn

• Standard State: The pure gas at 1 atm, pure solid or liquid, or 1 M solution at a specified temperature (usually 25°C).

• Standard Entropy Change for a Reaction: $\Delta S^{\circ}_{rxn} = \sum n S^{\circ}_{products} - \sum n S^{\circ}_{reactants}$

• Factors Affecting Entropy:

  1. State (gas > liquid > solid)

  2. Molar mass (higher molar mass, higher entropy)

  3. Allotropes (different forms of the same element have different entropies)

  4. Molecular complexity (more complex molecules, higher entropy)

  5. Extent of dissolution (dissolved substances have higher entropy)

Table: Standard Molar Entropy Values (S°, J/mol·K) for Selected Substances at 298 K

Substance	S° (J/mol·K)	Substance	S° (J/mol·K)
H2(g)	130.6	NaCl(s)	72.1
O2(g)	205.0	H2O(l)	69.9
CO2(g)	213.7	CaCO3(s)	92.9
CH4(g)	186.3	Ca(OH)2(s)	83.4

19.8 Free Energy Changes in Chemical Reactions: Calculating ΔG°rxn

• Calculation at 25°C: $\Delta G^{\circ}_{rxn} = \Delta H^{\circ}_{rxn} - T\Delta S^{\circ}_{rxn}$

• Standard Free Energy Change for a Reaction: $\Delta G^{\circ}_{rxn} = \sum n \Delta G^{\circ}_{f,products} - \sum n \Delta G^{\circ}_{f,reactants}$

Table: Standard Molar Free Energies of Formation (ΔG°f, kJ/mol) for Selected Substances at 298 K

Substance	ΔG°f (kJ/mol)	Substance	ΔG°f (kJ/mol)
H2O(l)	-237.1	CO2(g)	-394.4
O2(g)	0	NaCl(s)	-384.1
CH4(g)	-50.8	CaCO3(s)	-1128.8

19.9 Free Energy Changes for Nonstandard States: The Relationship between ΔG°rxn and ΔGrxn

• Nonstandard Conditions: $\Delta G = \Delta G^{\circ} + RT \ln Q$

  • R = 8.314 J/(mol·K)

  • T = temperature in Kelvin

  • Q = reaction quotient

19.10 Free Energy and Equilibrium: Relating ΔG°rxn to the Equilibrium Constant (K)

• Relationship: $\Delta G^{\circ} = -RT \ln K$

• When K > 1: $\Delta G^{\circ} < 0$ (reaction is spontaneous in the forward direction)

• When K < 1: $\Delta G^{\circ} > 0$ (reaction is spontaneous in the reverse direction)

• Temperature Dependence (Two-Point Form): $\ln \left( \dfrac{K_2}{K_1} \right) = -\dfrac{\Delta H^{\circ}_{rxn}}{R} \left( \dfrac{1}{T_2} - \dfrac{1}{T_1} \right)$

Summary of Key Calculations and Concepts

• Identify spontaneous and nonspontaneous processes.

• Analyze systems and surroundings for entropy change.

• Calculate the entropy change for a change in state.

• Calculate entropy changes using standard entropy values and the universe.

• Calculate reaction spontaneity using Gibbs free energy change.

• Analyze reaction spontaneity using standard Gibbs free energy changes.

• Calculate ΔG°rxn using free energies of formation.

• Calculate ΔGrxn for a stepwise reaction.

• Calculate ΔGrxn for nonstandard conditions.

• Perform ΔG°rxn calculations using equilibrium constants (K).