Thermochemistry: Energy, Chemical Reactions, and Thermodynamics

Thermochemistry

Introduction to Thermochemistry

Thermochemistry is the study of the energy changes, particularly heat, that occur during chemical reactions and physical transformations. It is a branch of thermodynamics focused on the transfer of energy as heat and work in chemical processes.

• Energy transfer occurs in all chemical reactions.

• Example reaction: $C_2H_2(g) + 5O_2(g) \rightarrow 4CO_2(g) + 2H_2O(g)$, $\Delta H = -2219\;\text{kJ}$

• Thermodynamics studies the effects of work, heat, and energy on a system, often with large-scale responses that can be observed and measured.

The Nature of Energy

Definition and Conservation of Energy

Energy is the quantitative property that must be transferred to an object to perform work or to heat the object. The Law of Conservation of Energy (First Law of Thermodynamics) states that energy can neither be created nor destroyed, only transformed.

• Energy (E): Ability to do work or transfer heat.

• Work (w): Energy used to move an object against a force. $W = F \cdot d$

• Energy Units:

  • Joule (J): SI unit, $1\;\text{J} = 1\;\text{kg} \cdot \text{m}^2/\text{s}^2$

  • Calorie (cal): $1\;\text{cal} = 4.184\;\text{J}$

  • Dietary Calorie (Cal): $1\;\text{Cal} = 1000\;\text{cal} = 1\;\text{kcal}$

Forms and Types of Energy

Kinetic and Potential Energy

Energy exists in various forms, primarily as kinetic and potential energy.

• Kinetic Energy ($E_k$): Energy of motion.

  • $E_k = \frac{1}{2}mv^2$

  • Thermal energy (microscopic kinetic energy): $E_{thermal} = N \cdot f \cdot \frac{1}{2}kT$

• Potential Energy ($E_p$): Energy stored due to position or arrangement.

  • Gravitational: $E_p = mgh$

  • Chemical: Energy stored in chemical bonds

  • Electrostatic: $E = k \frac{Q_1 Q_2}{r}$

• Other forms: motion, thermal, electric, radiant, sound, mechanical, chemical, nuclear, gravitational, solar.

Attraction Between Ions

Electrostatic Interactions and Energy Changes

Electrostatic attraction occurs between oppositely charged ions. Energy is released when chemical bonds are formed and consumed when bonds are broken.

• Bond formation: Releases energy

• Bond breakage: Consumes energy

• Electrostatic energy equation: $E = k \frac{Q_1 Q_2}{r}$

Laws of Thermodynamics

The First Law of Thermodynamics

The first law states that energy can be converted from one form to another, but it cannot be created or destroyed. The change in internal energy ($\Delta E$) of a system is equal to the heat ($q$) added to the system plus the work ($w$) done on the system.

• Equation: $\Delta E = q + w$

• Implication: When energy enters or leaves a system (as work, heat, or matter), the system's internal energy changes.

Energy, Temperature, and Heating

Thermal Energy and Temperature

Temperature is a measure of the thermal energy of a sample. Thermal energy is the energy due to the motion of particles (atoms, molecules, ions).

• Thermal energy: $E_{thermal} = N \cdot f \cdot \frac{1}{2}kT$

• Higher temperature ($T$) means faster particle motion and higher thermal energy.

• Heat is transferred due to a temperature difference, flowing from hotter to cooler objects until thermal equilibrium is reached.

Systems, Surroundings, and Internal Energy

Definitions and Relationships

In thermodynamics, the universe is divided into the system (the part under study) and the surroundings (everything else).

• System: The part of the universe under study (e.g., chemicals in a flask).

• Surroundings: The rest of the universe (e.g., the classroom).

• Universe: System + Surroundings

Types of Systems

• Open System: Can exchange heat and mass with surroundings.

• Closed System: Can exchange heat but not mass with surroundings.

• Isolated System: Cannot exchange heat or mass with surroundings.

Internal Energy ($U$)

Internal energy is the total energy contained within a system, including both kinetic and potential energy at the microscopic level.

• Depends on temperature, type of material, and amount of material.

• Change in internal energy: $\Delta U = U_f - U_i$

• In a closed system: $\Delta U = q + w$

State Functions

Definition and Examples

A state function is a property whose value depends only on the current state of the system, not on the path taken to reach that state.

• Examples: Internal energy ($U$), pressure ($P$), volume ($V$), temperature ($T$), enthalpy ($H$), entropy ($S$), Gibbs free energy ($G$).

• Change in state function: $\Delta E = E_f - E_i$

Visualization of Thermodynamic Changes

Energy Transfer as Heat and Work

Energy can be transferred between a system and its surroundings as heat or work, or both simultaneously.

• Heat transfer: $\Delta E = q$ (if only heat is transferred)

• Work transfer: $\Delta E = w$ (if only work is transferred)

• Both: $\Delta E = q + w$

Laws of Thermodynamics—Recap

First, Second, and Third Laws

• First Law: $\Delta U = q + w$ (energy conservation)

• Second Law: In a closed system, processes tend to occur that increase the total entropy ($S$) of the system. ($\Delta S > 0$ is favored in a closed system)

• Third Law: A system's entropy approaches a constant value as the temperature approaches absolute zero. ($S \rightarrow 0$ at $0\;\text{K}$)

Internal Energy (U) Recapitulation

Definitions and Context

Internal energy is a state function representing the energy of a system due to its temperature, type, and amount of material. It is used in thermodynamic calculations and is essential for understanding energy changes in chemical reactions.

• IUPAC: Internal energy is the sum of all kinetic and potential energies of the particles in a system.

• Wiki: Internal energy is the energy necessary to bring a system to its current state from a reference state.

Internal Energy of a Molecule—Quantized Internal Energy

Quantized Energy Levels

The internal energy of a molecule is quantized and can be expressed as the sum of electronic, vibrational, and rotational energies.

• $E_{int} = E_{elec} + E_{vib} + E_{rot}$

• Each term represents the energy associated with electronic, vibrational, and rotational states, respectively.

Type of System	Heat Exchange	Mass Exchange	Example
Open	Yes	Yes	Boiling water in an open pot
Closed	Yes	No	Sealed flask
Isolated	No	No	Thermos bottle

Example: Calculating the change in internal energy for a reaction using $\Delta U = q + w$.

Additional info: Some definitions and equations have been expanded for clarity and completeness. The quantized internal energy section is included for reference and future study, as indicated in the original notes.