Thermodynamics: Energy, Heat, Work, and Spontaneity in Chemical Systems

Thermodynamics Overview

Introduction to Thermodynamics

Thermodynamics is the branch of chemistry that studies the transformation of energy, particularly how energy is transferred as heat and work in chemical systems. It provides the framework for understanding how and why chemical reactions occur, and how energy changes affect matter.

Topic 4A: Work and Heat

System and Surroundings

In thermodynamics, the universe is divided into the system (the part under study, such as a reaction mixture) and the surroundings (everything else). Energy can be transferred between the system and its surroundings as heat or work.

• System: The portion of the universe chosen for study.

• Surroundings: Everything outside the system.

Types of Systems

Systems are classified based on their ability to exchange energy and matter with their surroundings:

System	Energy Transfer	Matter Transfer
Open	Yes	Yes
Closed	Yes	No
Isolated	No	No

Energy: Kinetic and Potential

• Kinetic Energy (KE): Energy of motion. $E_K = \frac{1}{2}mv^2$

• Potential Energy (PE): Energy due to position in a field of force. $E_P = mgh$ (gravitational)

• Total Internal Energy (U): $U = E_K + E_P$

Work and Heat

• Work (w): Energy used to move an object. $w = F \times d$

• Heat (q): Energy transferred due to temperature difference.

Pressure-Volume Work

• When a gas expands or contracts against an external pressure, work is done: $w = -P_{ext} \Delta V$

• Expansion: $\Delta V > 0$, $w < 0$ (system does work on surroundings)

• Compression: $\Delta V < 0$, $w > 0$ (surroundings do work on system)

Topic 4B: Internal Energy

First Law of Thermodynamics

The first law of thermodynamics states that energy cannot be created or destroyed, only transformed. The change in internal energy ($\Delta U$) of a system is given by:

• $\Delta U = U_{final} - U_{initial}$

• $\Delta U = q + w$

State and Path Functions

• State functions: Depend only on the initial and final states (e.g., U, H, S, G).

• Path functions: Depend on the process taken (e.g., q, w).

Topic 4C: Enthalpy

Definition and Measurement

Enthalpy (H) is a state function defined as $H = U + PV$. The change in enthalpy ($\Delta H$) at constant pressure equals the heat transferred: $\Delta H = q_p$.

• Exothermic: $\Delta H < 0$ (heat released)

• Endothermic: $\Delta H > 0$ (heat absorbed)

Topic 4D: Thermochemistry

Enthalpy of Reaction and Hess's Law

• Enthalpy of reaction ($\Delta H_{rxn}$): $\Delta H = \sum H_{products} - \sum H_{reactants}$

• Hess's Law: The enthalpy change for a reaction is the sum of the enthalpy changes for each step.

Standard Enthalpy of Formation

• $\Delta H_f^\circ$ is the enthalpy change when 1 mole of a compound forms from its elements in their standard states.

• For elements in their standard states, $\Delta H_f^\circ = 0$.

Topic 4E: Contributions to Enthalpy

Bond Enthalpy

• Bond enthalpy: Energy required to break a chemical bond.

• Bond breaking is endothermic; bond formation is exothermic.

• $\Delta H_{rxn} = \sum \text{Bond energies broken} - \sum \text{Bond energies formed}$

Topic 4F: Entropy

Definition and Quantification

Entropy (S) is a measure of disorder or randomness. It is a state function and increases with temperature, volume, and phase changes (solid → liquid → gas).

• $\Delta S = nR \ln \frac{V_2}{V_1}$ (volume change)

• $\Delta S = C \ln \frac{T_2}{T_1}$ (temperature change)

• $\Delta S_{phase} = \frac{\Delta H_{phase}}{T_{transition}}$ (phase change)

Second and Third Laws of Thermodynamics

• Second Law: The entropy of an isolated system increases in any spontaneous process.

• Third Law: The entropy of a perfect crystal at 0 K is zero.

Topic 4G: Molecular Interpretation of Entropy

Boltzmann Formula

• $S = k \ln W$

• Where $k$ is Boltzmann's constant and $W$ is the number of microstates.

Topic 4H: Absolute Entropies

Standard Molar Entropy

• Standard molar entropy ($S^\circ$) is the entropy of 1 mole of a substance at 1 bar and 298 K.

• Large, complex molecules have higher $S^\circ$ than small, simple ones.

Topic 4I: Global Changes in Entropy

Total Entropy Change

• $\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings}$

• For a process at constant pressure: $\Delta S_{surroundings} = -\frac{\Delta H_{system}}{T}$

• A process is spontaneous if $\Delta S_{total} > 0$.

Topic 4J: Gibbs Free Energy

Definition and Spontaneity

Gibbs free energy (G) is a state function that predicts spontaneity at constant temperature and pressure.

• $G = H - TS$

• $\Delta G = \Delta H - T\Delta S$

• If $\Delta G < 0$, the process is spontaneous.

• If $\Delta G > 0$, the process is nonspontaneous.

• If $\Delta G = 0$, the system is at equilibrium.

Temperature Dependence

• Spontaneity depends on both $\Delta H$ and $\Delta S$ and the temperature.

• At equilibrium: $\Delta G = 0$

Tables and Data

Specific and Molar Heat Capacities

Substance	Specific Heat Capacity (J/g·K)	Molar Heat Capacity (J/mol·K)
Aluminum	0.897	24.2
Graphite	0.685	8.23
Iron	0.449	25.1
Copper	0.385	24.5
Gold	0.129	25.6
Water (liquid)	4.184	75.4
Water (ice)	2.06	37.1

Varieties of Work

Type of Work	Equation	Units
Expansion	$-P_{ex} \Delta V$	Pa·m³
Extension	$f \Delta l$	N·m
Raising a weight	$mg \Delta h$	kg·m²·s⁻²
Electrical	$\phi \Delta q$	V·C
Surface expansion	$\gamma \Delta A$	N·m⁻¹·m²

Summary

Thermodynamics provides the essential principles for understanding energy changes in chemical reactions, the direction of spontaneous change, and the relationship between heat, work, and entropy. Mastery of these concepts is fundamental for further study in chemistry and related sciences.