Ch. 19: Free Energy and Thermodynamics – Study Notes

Free Energy and Thermodynamics

Introduction

This chapter explores the fundamental principles of thermodynamics, focusing on how energy, entropy, and free energy determine the direction and spontaneity of chemical reactions. Understanding these concepts allows us to predict whether a reaction will occur naturally or require external intervention.

Predicting the Direction of Chemical Change

Spontaneity in Chemical Reactions

• Spontaneous processes occur without ongoing outside intervention (e.g., ice melting, rust forming).

• Nonspontaneous processes require continuous energy input (e.g., water electrolysis).

• The key question: What determines if a reaction happens by itself?

Main Ideas in Thermodynamics

Core Concepts

• Laws of Thermodynamics: Describe how energy is conserved and distributed.

• Entropy (S): Measures disorder and randomness in a system.

• Gibbs Free Energy (ΔG): Predicts whether a reaction is spontaneous.

A Tale of Two Reactions

Examples of Spontaneous Processes

• Ice melting: Endothermic and spontaneous.

• Hand warmer reaction: Exothermic and spontaneous. Example reaction: $4Fe(s) + 3O_2(g) \rightarrow 2Fe_2O_3(s) + \text{energy}$

• Both absorption and release of energy can result in spontaneous processes.

First Law of Thermodynamics

Energy Conservation

• Energy cannot be created or destroyed; it can only be converted from one form to another.

• Example: The total energy from combustion equals the energy used for work and the energy lost as heat.

Spontaneous and Nonspontaneous Processes

Thermodynamic Favorability

• Thermodynamics predicts if a process will occur under given conditions.

• Spontaneity is determined by comparing the chemical potential energy before and after the reaction.

• If the system has less potential energy after the reaction, it is thermodynamically favorable.

• Spontaneity does not indicate the speed of a reaction.

Comparing Potential Energy

Mechanical vs. Chemical Potential

• Mechanical potential energy predicts movement in physical systems.

• Chemical potential energy predicts the direction of chemical change.

• The direction of spontaneity is determined by comparing the system's potential energy at the start and end.

Diamond to Graphite Conversion

Thermodynamic Stability

• Graphite is more stable than diamond; thus, diamond spontaneously converts to graphite.

• This process is extremely slow, so diamonds remain intact over human lifetimes.

Kinetics vs. Thermodynamics

Distinguishing Spontaneity and Rate

• Spontaneity refers to whether a reaction can occur naturally.

• Rate (kinetics) refers to how fast a reaction occurs.

• Do not confuse a spontaneous reaction with a fast reaction.

Entropy and the Second Law of Thermodynamics

Spontaneous Processes and Energy Release

• Spontaneous processes often release energy from the system (exothermic, $\Delta H < 0$).

• Some spontaneous processes absorb energy (endothermic, $\Delta H > 0$), such as ice melting.

Entropy in Physical Changes

Examples of Increasing Entropy

• Melting ice: Particles gain freedom of movement, increasing randomness and entropy.

• Water evaporation: Molecules become more disordered, further increasing entropy.

• Salt dissolving in water: Ions and molecules become more randomly arranged, increasing entropy.

Entropy: Definition and Calculation

Boltzmann's Equation

• Entropy (S): A thermodynamic function that increases with the number of energetically equivalent ways to arrange a system.

• Mathematically: $S = K \ln W$ where $K = 1.38 \times 10^{-23} \text{ J/K}$ (Boltzmann constant), $W$ = number of microstates.

• Entropy is a state function: $\Delta S = S_{\text{final}} - S_{\text{initial}}$

The Second Law of Thermodynamics

Entropy of the Universe

• For any spontaneous process, the entropy of the universe increases.

• Mathematically: $\Delta S_{\text{universe}} > 0$

• Processes that increase the universe's entropy occur spontaneously.

Macrostates and Microstates

Definitions

• Macrostate: Defined by measurable conditions (pressure, volume, temperature).

• Microstate: The specific arrangement of particles and energy at an instant.

• $W$ is the number of possible microstates for a macrostate.

Microstates and Probability

Expansion of an Ideal Gas

• Energetically equivalent states exist for gas expansion.

• Some states (macrostates) are more probable due to more possible microstates.

• Higher entropy corresponds to higher probability and greater energy dispersal.

Entropy Changes Associated with State Changes

State Transitions and Entropy

• Entropy increases as matter changes from solid to liquid to gas: $S_{\text{solid}} < S_{\text{liquid}} < S_{\text{gas}}$

• Gases have more macrostates and microstates than liquids or solids.

Predicting the Sign of Entropy Change (ΔS)

General Rules

• Entropy increases ($\Delta S > 0$) for:

  • Solid to liquid transition

  • Solid to gas transition

  • Liquid to gas transition

  • Increase in number of moles of gas during a reaction

• Entropy decreases ($\Delta S < 0$) for the reverse processes.

Examples and Practice Problems

Example: Entropy Change in Water

• Condensation of water on a cold glass: Entropy decreases.

• Melting of ice or boiling of water: Entropy increases.

Example: Predicting ΔS

• $H_2O(g) \rightarrow H_2O(l)$: $\Delta S$ is negative (gas to liquid).

• Solid CO2 sublimes: $\Delta S$ is positive (solid to gas).

• $2N_2O(g) \rightarrow 2N_2(g) + O_2(g)$: $\Delta S$ is positive (increase in moles of gas).

Practice Problem

• Identify the process in which entropy decreases:

  • An increase in the number of moles of gas during a reaction: Entropy increases.

  • Phase transition from gas to liquid: Entropy decreases.

  • Phase transition from solid to gas: Entropy increases.

  • Phase transition from solid to liquid: Entropy increases.

  • Phase transition from liquid to gas: Entropy increases.

Summary Table: Entropy Change in State Transitions

Process	ΔS (Sign)	Explanation
Solid → Liquid	Positive	Increased molecular freedom
Solid → Gas	Positive	Much greater disorder
Liquid → Gas	Positive	Increased randomness
Gas → Liquid	Negative	Decreased randomness
Liquid → Solid	Negative	Decreased molecular freedom

Additional info: These notes expand on the original slides by providing definitions, equations, and context for entropy, spontaneity, and thermodynamic laws, ensuring a self-contained study guide for exam preparation.