Chapter 19: Free Energy and Thermodynamics – Study Notes

Free Energy and Thermodynamics

Introduction

This chapter explores the fundamental principles of thermodynamics, focusing on the concepts of energy, entropy, spontaneity, and free energy in chemical systems. Understanding these concepts is essential for predicting whether chemical reactions and physical processes will occur spontaneously under given conditions.

First Law of Thermodynamics

Conservation of Energy

• Definition: The first law of thermodynamics states that energy cannot be created or destroyed; it can only be transformed from one form to another.

• Application: In chemical reactions, the total energy of combustion equals the energy used for work (e.g., propelling a car) plus the energy dissipated as heat.

• Example: Burning fuel in a car: some energy moves the car, the rest is lost as heat.

The Energy Tax and Heat Tax

Energy Losses in Real Processes

• Energy Tax: Every energy transition results in a 'loss' of energy, often as heat to the surroundings.

• Second Law of Thermodynamics: To recharge a battery with 100 kJ of useful energy requires more than 100 kJ input due to unavoidable losses.

• Heat Tax: Fewer steps in energy conversion generally result in a lower total heat loss.

• Example: Heating with natural gas vs. electricity: more conversion steps mean more heat lost.

Spontaneity and Probability

Spontaneous Processes

• Spontaneous Process: Occurs without ongoing outside intervention.

• Nonspontaneous Process: Requires continuous energy input.

• Probability: Certain molecular arrangements (e.g., all O2 molecules in one corner of a room) are possible but extremely unlikely due to statistical probability.

Expansion of an Ideal Gas

Distribution of Particles

• When a valve between an ideal gas and a vacuum is opened, gas molecules spontaneously spread to fill both containers, increasing randomness (entropy).

Thermodynamics and Spontaneity

Predicting Spontaneous Change

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

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

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

• Note: Spontaneity does not indicate the speed of a process.

Reversibility of Processes

Irreversible and Reversible Processes

• Spontaneous processes are irreversible due to net energy release.

• Reversible processes can proceed back and forth between two states at equilibrium, with no net change in free energy.

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

Comparing Potential Energy

Direction of Spontaneity

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

• Systems tend to move toward lower potential energy.

Thermodynamics Versus Kinetics

Energy and Reaction Progress

• Thermodynamics: Concerns initial and final states, and whether a process is spontaneous.

• Kinetics: Concerns the speed and pathway (intermediate states) of a reaction.

Spontaneous Processes

Exothermic and Endothermic Spontaneity

• Most spontaneous processes are exothermic (release energy).

• Some spontaneous processes are endothermic (absorb energy), such as melting ice above 0°C.

Entropy

Definition and Calculation

• Entropy (S): A thermodynamic function that increases as the number of energetically equivalent ways of arranging the components increases.

• Units: J/mol·K

• Formula:

$S = k \ln W$

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

• W: Number of energetically equivalent ways a system can exist (unitless)

Calculating Entropy

Entropy Change in Phase Transitions

• For a process at constant temperature:

$\Delta S = \frac{q_{\text{rev}}}{T}$

• Example: Condensation of water vapor to liquid at 100°C, using $\Delta H_{\text{vap}}$ and temperature in Kelvin.

Microstates, Macrostates, and Probability

Statistical Interpretation of Entropy

• Microstate: A specific arrangement of particles.

• Macrostate: The overall state, defined by observable properties, which can be achieved by many microstates.

• Greater number of molecules means more microstates and higher entropy.

• Systems tend to become more homogeneous (evenly distributed).

Entropy Change in State Change

States of Matter and Entropy

• Gases have greater entropy than liquids, which have greater entropy than solids.

• Changing state (e.g., melting, vaporization) increases the number of possible microstates and thus entropy.

Entropy Changes in Chemical Reactions

Predicting Entropy Change

• $\Delta S_{\text{system}} > 0$ if the number of gaseous molecules increases in a reaction.

• $\Delta S_{\text{system}} < 0$ if the number of gaseous molecules decreases.

• Example: $\text{H}_2\text{O}(l) \rightarrow \text{H}_2\text{O}(g)$ (increase in entropy)

Factors Affecting Entropy

Comparing Substances

• Entropies of gases >> entropies of liquids > solids.

• More complex molecules have higher entropy than simpler ones.

• Weaker ionic attractions lead to higher entropy in ionic solids.

• Entropy increases when a pure liquid or solid dissolves in a solvent.

• Entropy increases when a dissolved gas escapes from solution.

Relative Standard Entropies

States, Molar Mass, Allotropes, and Complexity

• State: Gas > Liquid > Solid at the same temperature.

• Molar Mass: Larger molar mass leads to higher entropy.

• Allotropes: More rigid forms (e.g., diamond) have lower entropy than less rigid forms (e.g., graphite).

• Molecular Complexity: More complex molecules have higher entropy due to more available energy states.

Substance	S° (J/mol·K)
H2O(l)	70.0
H2O(g)	188.8
He(g)	126.2
Ne(g)	146.1
Ar(g)	154.8
Kr(g)	163.8
Xe(g)	169.4
C(s, diamond)	2.4
C(s, graphite)	5.7
CO(g)	197.7
C2H2(g)	219.3

Additional info: Table values inferred from images and standard data.