Thermodynamics and Interactions

What is Thermodynamics?

Thermodynamics is the study of energy, its transformations, and its relation to matter. It is divided into several sub-disciplines, with Classical Thermodynamics focusing on macroscopic (bulk) properties of matter, independent of microscopic atomic or molecular models. Statistical Thermodynamics unifies microscopic and macroscopic approaches, providing deeper insight into the behavior of matter.

• Classical Thermodynamics: Deals with bulk properties, does not rely on atomic/molecular models.

• Statistical Thermodynamics: Integrates microscopic (molecular) and macroscopic perspectives.

• Applications: Characterizing equilibrium states, analyzing energetics of reactions, ruling out impossible processes, inter-relating observable properties, and testing models.

Additional info: Classical thermodynamics is model-independent but cannot explain phenomena at the molecular level.

Key Terminology in Thermodynamics

Types of Systems

• Open System: Exchanges both matter and energy with surroundings.

• Closed System: Exchanges energy but not matter with surroundings.

• Isolated System: Exchanges neither matter nor energy with surroundings.

Forms of Energy

• Heat (q): Energy transferred as random molecular motion.

• Work (w): Energy transferred as organized motion (e.g., mechanical work).

Fundamental Laws of Thermodynamics

Zeroth Law of Thermodynamics

Defines thermal equilibrium:

• If body A is in thermal equilibrium with body B, and B with C, then A is in thermal equilibrium with C.

First Law of Thermodynamics (Law of Energy Conservation)

• The internal energy of an isolated system is constant.

• Mathematically: where is the change in internal energy, is work done on the system, and is heat added to the system.

Second Law of Thermodynamics

• The entropy () of an isolated system increases for any spontaneous process.

• Mathematically:

Third Law of Thermodynamics

• The entropy of a perfect crystal at absolute zero temperature is zero.

• This allows entropy to have an absolute, measurable value.

Energetics of Reactions

Internal Energy ()

• Total energy contained within a system, measured in Joules (J).

• Change in internal energy:

• If , energy is lost from the system; if , energy is gained.

Notation:

• = finite change

• = infinitesimal change

• = infinitesimal change with some variables held constant

Work Involving Pressure and Volume

• Work done by a system during volume expansion at constant pressure:

• If (expansion), is negative (energy lost by the system).

Enthalpy ()

• Defined as (internal energy plus pressure-volume work).

• Change in enthalpy at constant pressure:

• Relationship between enthalpy and internal energy:

• Exothermic: (releases heat)

• Endothermic: (absorbs heat)

Heat Capacity ()

• Amount of heat required to change temperature by 1 K.

• At constant pressure:

• At constant volume:

• For solids and liquids:

• For gases: (where is moles, is the gas constant)

Spontaneity

• Spontaneous Process: Occurs naturally without external work; not necessarily fast.

• Non-Spontaneous Process: Requires work to occur; arises from a tendency toward disorder, not necessarily lower energy.

Entropy ()

• Measure of disorder or randomness; a state function.

• For reversible heat transfer:

• For irreversible processes:

Thermodynamic Equilibrium and Free Energy

Thermodynamic Equilibrium

• Represents a balance between the tendency to minimize energy and the opposing effect of thermal (Brownian) motion.

• At equilibrium, no net spontaneous change occurs ().

Gibbs Free Energy ()

• Combines enthalpy and entropy to predict spontaneity at constant temperature and pressure:

• If , the process is spontaneous.

• If , the process is non-spontaneous.

• If , the system is at equilibrium.

Example: Macrocyclic Effect

• Displacement of a tetradentate polyamine by a tetradentate macrocycle is thermodynamically favored.

• Given: kJ/mol, J/(mol·K), K.

• Calculate and :

kJ/mol kJ/mol

Additional info: This calculation demonstrates the interplay of enthalpy and entropy in determining spontaneity.

Standard Molar Entropy and Entropy Change

Standard Molar Entropy ()

• Entropy of one mole of a substance under standard conditions.

Standard Entropy Change ()

• Calculated as:

Reaction Quotient and Equilibrium Constant

Reaction Quotient ()

• For a general reaction:

• Defines the ratio of product and reactant concentrations at any stage.

Equilibrium Constant ()

• Value of at equilibrium:

• If , products dominate; if , reactants dominate; if , both are present in similar amounts.

Relationship Between , , and

• At equilibrium (, ):

Summary Table: Types of Thermodynamic Systems

Final Thought

Understanding the laws of thermodynamics is fundamental to the study of physical science, as emphasized by C.P. Snow: "Not knowing the second law of thermodynamics is like never having read a work by Shakespeare."