Thermochemistry, Quantum Mechanics, and Periodic Properties: Study Notes

Chapter 7: Thermochemistry

Types of Energy

Energy is the capacity to do work or produce heat. In chemistry, energy exists in several forms:

• Potential Energy: Stored energy due to position or composition.

• Chemical Energy: Energy stored within chemical bonds.

• Thermal Energy: Energy associated with the temperature of an object.

• Kinetic Energy: Energy of motion, given by the formula:

$KE = \frac{1}{2}mv^2$

Law of Conservation of Energy

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. The total energy of the universe is constant.

System and Surroundings

• System: The part of the universe being studied.

• Surroundings: Everything outside the system.

Energy transfer occurs as heat or work between system and surroundings.

Calorimetry

Calorimetry is the measurement of heat flow. It is used to determine the energy change in chemical reactions.

• Constant Pressure Calorimetry: At room pressure, no work is done by volume change.

• Constant Volume (Bomb) Calorimetry: Used for reactions where volume does not change; only heat is measured.

Heat and Temperature Change

The amount of heat transferred to or from a substance is related to its mass, specific heat, and temperature change:

$q = m \cdot C_s \cdot \Delta T$

• q: Heat (Joules)

• m: Mass (g)

• C_s: Specific heat capacity (J/g·°C)

• ΔT: Temperature change (°C)

Enthalpy (ΔH)

Enthalpy is the heat content of a system at constant pressure. The change in enthalpy ($\Delta H$) is the heat absorbed or released during a reaction at constant pressure.

Limiting Reactant and Energy Change

The limiting reactant determines the maximum amount of energy that can be converted in a chemical reaction.

Standard Enthalpy of Formation

The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states.

Example: Calculating Reaction Enthalpy

• To find the enthalpy change for a reaction, subtract the sum of the enthalpies of formation of the reactants from that of the products.

Chapter 8: The Quantum-Mechanical Model of the Atom

Electromagnetic Spectrum

The electromagnetic spectrum includes all types of electromagnetic radiation, from radio waves to gamma rays.

Frequency and Wavelength

Electromagnetic radiation is characterized by its frequency ($\nu$) and wavelength ($\lambda$). The speed of light ($c$) relates these quantities:

$c = \nu \lambda$

• c: Speed of light ($3.00 \times 10^8$ m/s)

• ν: Frequency (Hz)

• λ: Wavelength (m)

Quantization of Energy

Energy is quantized in discrete packets called quanta. The energy of a photon is given by:

$E = h \nu$

• h: Planck's constant ($6.626 \times 10^{-34}$ J·s)

• ν: Frequency (Hz)

Hydrogen Atom and Energy Levels

The energy levels of the hydrogen atom are quantized. The energy difference between levels determines the wavelength of light emitted or absorbed.

Energy of transitions in the hydrogen atom:

$E = -R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$

• $R_H$: Rydberg constant ($2.18 \times 10^{-18}$ J)

• $n_i$: Initial energy level

• $n_f$: Final energy level

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and electrons:

• Principal quantum number (n): Indicates energy level.

• Angular momentum quantum number (l): Indicates shape of orbital.

• Magnetic quantum number (m_l): Indicates orientation of orbital.

• Spin quantum number (m_s): Indicates spin direction of electron.

Shapes of Orbitals

Atomic orbitals have characteristic shapes:

• s orbitals: Spherical

• p orbitals: Dumbbell-shaped

• d orbitals: Cloverleaf-shaped

Chapter 9: Periodic Properties of the Elements

Electron Configuration and Periodic Trends

Electron configuration determines the chemical properties of elements. The periodic table reflects recurring trends in these properties.

Atomic and Ionic Radii

• Atomic radius: Distance from nucleus to outermost electron.

• Ionic radius: Size of an ion after gaining or losing electrons.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in the gas phase.

Electron Affinity

Electron affinity is the energy change when an atom gains an electron.

Metallic Character

Metallic character refers to how readily an atom loses electrons. It increases down a group and decreases across a period.

Summary Table: Periodic Trends

Property	Trend Across Period	Trend Down Group
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Generally increases	Generally decreases
Metallic Character	Decreases	Increases

Example: Sodium (Na) has a larger atomic radius and lower ionization energy than chlorine (Cl).

Additional info: Some equations and details have been expanded for clarity and completeness.