Thermodynamics: Systems, Enthalpy, Entropy, and the Laws of Thermodynamics

Thermodynamics: Systems and Surroundings

Defining the System and Surroundings

In thermodynamics, it is essential to distinguish between the system (the part of the universe under study) and the surroundings (everything else). The way energy and matter are exchanged between the system and its surroundings determines the type of system.

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

• Closed System: Can exchange energy but not matter.

• Isolated System: Cannot exchange either energy or matter.

Example: A boiling pot of water is an open system; a sealed container is a closed system; a perfectly insulated thermos is an isolated system.

The First Law of Thermodynamics and Enthalpy

Conservation of Energy

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. Energy that leaves a system is absorbed by the surroundings, and vice versa.

• Enthalpy (H): The total heat content of a system.

• Enthalpy changes reflect the energy absorbed or released during chemical reactions or physical changes.

• Types of energy include electromagnetic, heat, potential, kinetic, and chemical (e.g., molecular motion, bond stretching).

Example: The heat released when gasoline combusts in an engine is an enthalpy change.

Entropy and Spontaneity

Definition and Role of Entropy

Entropy (S) measures how energy is dispersed within a system. It is often associated with disorder, but more accurately describes the spreading out of energy.

• Entropy increases as energy becomes more spread out or randomized.

• Spontaneous processes are those where energy disperses (entropy increases).

• Disorder is a common but not always precise way to describe entropy.

Example: When ice melts, the water molecules become more disordered, and entropy increases.

Mathematical Expression of Entropy

From thermodynamics, entropy is defined as heat energy (Q) per temperature (T):

$S = \frac{Q}{T}$

For a process, the total heat energy contained in a system is $TS$, and the change in heat energy is $T\Delta S$.

Gibbs Free Energy and Spontaneity

Gibbs Free Energy Equation

The Gibbs free energy change ($\Delta G$) determines whether a process is spontaneous. It combines enthalpy and entropy changes:

$\Delta G = \Delta H - T\Delta S$

• Enthalpy term ($\Delta H$): Energy released or absorbed.

• Entropy term ($T\Delta S$): Energy dispersed at a given temperature.

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

Example: The dissolution of salt in water is spontaneous because the increase in entropy outweighs the enthalpy change.

Driving Force for a Process

• Reversible: $\Delta G$ close to 0 (system near equilibrium).

• Irreversible: $\Delta G$ very negative (far from equilibrium).

• At equilibrium: $\Delta G = 0$.

The Second Law of Thermodynamics

Entropy and Isolated Systems

The Second Law of Thermodynamics states that the entropy of an isolated system will tend to increase to a maximum value.

• Energy spontaneously spreads out if not hindered.

• Processes that increase entropy are generally favorable.

Example: Gas molecules in a container will spread out to fill the available space, increasing entropy.

Interplay of Enthalpy and Entropy

Summary Table: Enthalpy-Driven vs. Entropy-Driven Processes

The driving force for chemical and physical processes can be enthalpy-driven, entropy-driven, or a combination of both. The following table summarizes these relationships:

Process Type	Enthalpy Change ($\Delta H$)	Entropy Change ($\Delta S$)	Spontaneity ($\Delta G$)
Enthalpy-driven	Large negative	Small or negative	Spontaneous if $\Delta H$ outweighs $T\Delta S$
Entropy-driven	Small or positive	Large positive	Spontaneous if $T\Delta S$ outweighs $\Delta H$
Both	Negative	Positive	Always spontaneous
Neither	Positive	Negative	Never spontaneous

Practice: Calorimetry and Thermodynamic Quantities

Application to Combustion Reactions

Calorimetry is used to measure heat changes in chemical reactions. For the combustion of a fatty acid in a bomb calorimeter:

• For surroundings (calorimeter): $\Delta H = \text{Heat final} - \text{Heat initial}$ (positive value)

• For system (reaction): $\Delta H = \text{Heat final} - \text{Heat initial}$ (negative value)

• For system (reaction): $T\Delta S = TS_{\text{final}} - TS_{\text{initial}}$ (negative value)

Example: Measuring the heat released during combustion allows calculation of enthalpy and entropy changes for the reaction.

Key Equations

• $S = \frac{Q}{T}$

• $\Delta G = \Delta H - T\Delta S$

Additional info: The notes include diagrams and figures illustrating the dispersal of energy and the relationship between enthalpy and entropy, as well as handwritten annotations reinforcing the concepts of energy release and entropy increase during chemical processes.