Chemical Thermodynamics and Entropy: Core Concepts and Applications

Chemical Thermodynamics

Introduction to Chemical Thermodynamics

Chemical thermodynamics is the study of energy changes, particularly heat and work, that accompany chemical reactions and physical changes. It helps predict whether a reaction will occur spontaneously and how much energy is involved.

• Thermodynamics deals with the transfer and transformation of energy in matter.

• System: The part of the universe under study (e.g., a reaction vessel).

• Surroundings: Everything outside the system.

• Universe: System + surroundings.

Example: The reaction of sodium with water releases heat and hydrogen gas, demonstrating energy transfer between system and surroundings.

Heat and Temperature

Heat is the transfer of energy due to a temperature difference. Temperature is a measure of the average kinetic energy of particles in a substance.

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

• Temperature (T): Indicates the direction of heat flow; measured in Kelvin (K), Celsius (°C), or Fahrenheit (°F).

Formula:

$\Delta T = T_{final} - T_{initial}$

System, Surroundings, and Universe

Thermodynamic analysis requires defining the system and its boundaries:

• Open system: Can exchange both matter and energy with surroundings.

• Closed system: Can exchange energy but not matter.

• Isolated system: Cannot exchange matter or energy.

Units of Energy

The SI unit of energy is the joule (J). Another common unit is the calorie (cal).

• 1 cal = 4.184 J

• 1 J = 1 kg·m2/s2

Change in a Quantity (ΔX)

Changes in thermodynamic quantities are denoted by the Greek letter delta (Δ):

• $\Delta X = X_{final} - X_{initial}$

• For temperature: $\Delta T = T_{final} - T_{initial}$

• For volume: $\Delta V = V_{final} - V_{initial}$

The First Law of Thermodynamics

Internal Energy and Its Change

The internal energy (U) of a system is the sum of all kinetic and potential energies of its particles. The first law states that energy cannot be created or destroyed, only transferred or transformed.

• $\Delta U = q + w$

• q = heat absorbed by the system

• w = work done on the system

Work (w): For gases, work is often due to volume changes at constant pressure:

$w = -P_{ext} \Delta V$

Heat Capacity and Specific Heat

Heat capacity (C) is the amount of heat required to raise the temperature of an object by 1 K (or 1 °C). Specific heat capacity (c) is the heat required to raise the temperature of 1 g of a substance by 1 K.

• $q = C \Delta T$

• $q = m c \Delta T$

Example Table: Specific Heats of Selected Substances at 25°C

Substance	Specific Heat (J/g·K)
Water (l)	4.18
Aluminum (s)	0.90
Iron (s)	0.45
Copper (s)	0.39
Gold (s)	0.13

Enthalpy (H)

Definition and Calculation

Enthalpy is a thermodynamic quantity equivalent to the total heat content of a system at constant pressure. The change in enthalpy (ΔH) is the heat absorbed or released at constant pressure.

• $\Delta H = \Delta U + P \Delta V$

• At constant pressure: $\Delta H = q_p$

Standard Enthalpy Changes

Standard enthalpy change (ΔH°) refers to the enthalpy change when all reactants and products are in their standard states (1 bar, 25°C).

• Standard enthalpy of formation (ΔHf°): Enthalpy change when 1 mole of a compound forms from its elements in their standard states.

Example Table: Standard Enthalpies of Formation at 25°C

Substance	ΔHf° (kJ/mol)
H2O(l)	-285.8
CO2(g)	-393.5
CH4(g)	-74.8
NaCl(s)	-411.2

Hess's Law

Hess's law states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. This allows calculation of enthalpy changes for reactions that are difficult to measure directly.

• $\Delta H_{reaction} = \sum \Delta H_{products} - \sum \Delta H_{reactants}$

Bond Enthalpies

Bond enthalpy is the energy required to break one mole of a particular type of bond in a gaseous molecule. It is used to estimate the enthalpy change of reactions involving bond breaking and formation.

• $\Delta H_{reaction} = \sum D_{bonds\,broken} - \sum D_{bonds\,formed}$

Example Table: Average Bond Enthalpies at 25°C

Bond	Bond Enthalpy (kJ/mol)
H–H	436
C–H	413
O=O	498
C=O	799

Entropy (S) and the Second Law of Thermodynamics

Entropy and Probability

Entropy is a measure of the disorder or randomness of a system. The second law of thermodynamics states that the total entropy of the universe always increases in a spontaneous process.

• Higher entropy = more disorder, more possible microstates.

• Spontaneous processes increase the entropy of the universe.

Formula:

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

Factors Affecting Entropy

• Physical state: Entropy increases from solid to liquid to gas.

• Number of particles: More particles = higher entropy.

• Temperature: Higher temperature = higher entropy.

• Volume: Greater volume = higher entropy for gases.

Example: The entropy change for the reaction $2Na(s) + Cl_2(g) \rightarrow 2NaCl(s)$ is negative because two reactants (one gas) form a single solid product, decreasing disorder.

Summary Table: Key Thermodynamic Quantities

Quantity	Symbol	Definition	Units
Internal Energy	U	Total energy of a system	J
Enthalpy	H	Heat content at constant pressure	J
Entropy	S	Disorder/randomness	J/K
Gibbs Free Energy	G	Energy available to do work	J

Additional info: These notes cover the core concepts of chemical thermodynamics and entropy, including definitions, laws, calculations, and applications relevant to a General Chemistry college course.