Thermodynamics and Spontaneous Changes: Entropy, Free Energy, and Equilibrium

Chapter 18: Thermodynamics

Introduction to Thermodynamics

Thermodynamics is the study of energy changes that accompany physical and chemical processes. It helps predict whether a reaction will occur spontaneously and how energy is transferred.

• Enthalpy (H): The heat content of a system at constant pressure.

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

• Spontaneity: Determines if a process can occur without outside intervention.

Key Concepts in Thermodynamics

• System and Surroundings: The system is the part of the universe under study; everything else is the surroundings.

• State Functions: Properties that depend only on the state of the system, not the path taken (e.g., H, S, G).

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

Enthalpy and Entropy Changes

• Enthalpy Change ($\Delta H$): The heat absorbed or released during a reaction at constant pressure.

• Entropy Change ($\Delta S$): The change in disorder; positive $\Delta S$ means increased disorder.

• Standard Entropy ($S^\circ$): Entropy of a substance at 1 atm and 25°C.

Calculating Entropy Changes

• Phase Changes: Entropy increases when a substance changes from solid to liquid to gas.

• Mixing: Mixing substances generally increases entropy.

• Volume and Pressure Changes: Increasing volume or decreasing pressure increases entropy.

• Temperature Changes: Higher temperature increases entropy.

Formulas for Entropy Change

• $\Delta S = S_{final} - S_{initial}$

• $\Delta S_{rxn} = \sum S^\circ_{products} - \sum S^\circ_{reactants}$

Chapter 19: Spontaneous Changes

Spontaneity and Free Energy

Spontaneous processes occur without outside intervention. The direction of spontaneity is determined by changes in enthalpy and entropy.

• Gibbs Free Energy ($G$): A thermodynamic quantity that combines enthalpy and entropy to predict spontaneity.

• Formula: $\Delta G = \Delta H - T\Delta S$

• Spontaneous Process: $\Delta G < 0$

• Nonspontaneous Process: $\Delta G > 0$

• Equilibrium: $\Delta G = 0$

Factors Affecting Spontaneity

• Enthalpy ($\Delta H$): Exothermic reactions ($\Delta H < 0$) tend to be spontaneous.

• Entropy ($\Delta S$): Increased disorder ($\Delta S > 0$) favors spontaneity.

• Temperature ($T$): Higher temperatures can make endothermic reactions spontaneous if $\Delta S$ is positive.

Calculating Free Energy Changes

• Standard Free Energy Change ($\Delta G^\circ$): Calculated under standard conditions (1 atm, 25°C).

• Formula: $\Delta G^\circ = \sum \Delta G^\circ_{f,products} - \sum \Delta G^\circ_{f,reactants}$

• Relationship to Equilibrium Constant ($K$): $\Delta G^\circ = -RT \ln K$

Examples and Applications

• Phase Changes: Melting, vaporization, and sublimation increase entropy.

• Mixing Solutions: Mixing increases entropy due to increased disorder.

• Volume and Pressure: Expanding gases increases entropy.

• Temperature: Raising temperature increases entropy and can affect spontaneity.

Tabular Summary: Effects on Entropy

Process	Effect on Entropy ($\Delta S$)
Solid to Liquid	Increase
Liquid to Gas	Increase
Mixing Substances	Increase
Increasing Volume	Increase
Increasing Temperature	Increase
Decreasing Pressure	Increase

Calculating Entropy and Free Energy for Reactions

• Use standard entropy and free energy values from tables.

• Apply formulas for $\Delta S_{rxn}$ and $\Delta G_{rxn}$.

• For temperature dependence: $\Delta G = \Delta H - T\Delta S$

Rule of Thumb for Spontaneity

• If $\Delta H < 0$ and $\Delta S > 0$, reaction is always spontaneous.

• If $\Delta H > 0$ and $\Delta S < 0$, reaction is never spontaneous.

• If both $\Delta H$ and $\Delta S$ are positive or negative, spontaneity depends on temperature.

Standard States and Reference Points

• Standard state for a substance is its pure form at 1 atm and 25°C.

• Elements in their standard state have $\Delta G^\circ_f = 0$.

Summary Table: Spontaneity Based on $\Delta H$ and $\Delta S$

$\Delta H$	$\Delta S$	Spontaneity
< 0	> 0	Always spontaneous
> 0	< 0	Never spontaneous
< 0	< 0	Spontaneous at low T
> 0	> 0	Spontaneous at high T

Additional info:

• Entropy and free energy concepts are essential for understanding chemical equilibrium and predicting reaction direction.

• Standard tables of $S^\circ$, $\Delta H^\circ$, and $\Delta G^\circ$ are used for calculations.

• Temperature plays a critical role in determining spontaneity when $\Delta H$ and $\Delta S$ have the same sign.