Atomic Structure and Fundamental Constants

Energy Levels in the Hydrogen Atom

The energy levels of the hydrogen atom are quantized and can be calculated using the Bohr model. The following equations describe the energy of an electron in the nth energy level:

• Energy of nth level:

(for hydrogen)

• Energy difference between levels:

(for hydrogen)

• Key Terms: n is the principal quantum number; J is joules.

• Example: The energy difference between n=2 and n=1 in hydrogen can be calculated using the above formula.

SI Base Units and Constants

SI base units are the foundation of scientific measurement. Important constants for chemistry include:

• Speed of light (c):

• Planck's constant (h):

• Avogadro's number (N_A):

• Gas constant (R):

SI Base Units: kilogram (kg), meter (m), second (s), mole (mol), kelvin (K), ampere (A), candela (cd).

Conversions

• Temperature:

• Pressure:

Thermodynamics and Work

Work and Energy Relationships

Thermodynamics describes the relationships between heat, work, and energy in chemical systems.

• Work (w):

• Change in Internal Energy (\Delta E):

• Change in Enthalpy (\Delta H):

• Key Terms: q is heat, P is pressure, V is volume.

• Example: Calculating the work done by a gas expanding against a constant pressure.

Periodic Table and Electronegativity

Periodic Table of the Elements

The periodic table organizes elements by increasing atomic number and groups elements with similar chemical properties.

• Groups: Vertical columns, elements share similar valence electron configurations.

• Periods: Horizontal rows, elements have the same number of electron shells.

• Example: Alkali metals (Group 1) are highly reactive and have one valence electron.

Electronegativity Values

Electronegativity is a measure of an atom's ability to attract electrons in a chemical bond. The following table lists electronegativity values for common elements:

• Trend: Electronegativity increases across a period and decreases down a group.

• Example: Fluorine (F) is the most electronegative element.

Chemical Bonding and Lewis Structures

Lewis Structures

Lewis structures represent the arrangement of valence electrons in molecules and ions. They help predict molecular geometry, reactivity, and polarity.

• Steps to Draw Lewis Structures:

  1. Count total valence electrons for all atoms.

  2. Arrange atoms and connect with single bonds.

  3. Distribute remaining electrons to complete octets (or duets for H).

  4. Use double or triple bonds if necessary to satisfy octet rule.

• Examples:

  • NH3 (Ammonia): Central N atom with three H atoms and one lone pair.

  • CS2 (Carbon disulfide): Linear structure with double bonds between C and each S.

  • SiF4 (Silicon tetrafluoride): Central Si atom with four F atoms, each F with three lone pairs.

  • Br3- (tribromide ion): Linear structure with extra electrons to account for negative charge.

  • PF3 (Phosphorus trifluoride): Central P atom with three F atoms and one lone pair.

  • CH3F (Fluoromethane): Central C atom with three H atoms and one F atom.

  • BCl3 (Boron trichloride): Central B atom with three Cl atoms, no lone pairs on B.

Additional info: Lewis structures are essential for understanding VSEPR theory and predicting molecular shapes.

Molecular Orbitals and Bonding

Molecular Orbital Theory

Molecular orbital (MO) theory describes the formation of molecular orbitals from atomic orbitals when atoms bond. The combination of atomic orbitals can result in bonding (lower energy) or antibonding (higher energy) molecular orbitals.

• Key Terms: σ (sigma) and π (pi) orbitals.

• Bonding: Constructive overlap forms bonding orbitals; destructive overlap forms antibonding orbitals.

• Example: In O2, the molecular orbital diagram includes both σ and π bonds.

Molecular Orbitals for Diatomic Molecules

The ordering of molecular orbitals varies for different diatomic molecules. The following hints summarize the order for selected molecules:

• Example: O2 has two unpaired electrons in π* orbitals, explaining its paramagnetism.

Bonding and Antibonding Orbitals

Bonding orbitals result from constructive interference of atomic orbitals, while antibonding orbitals result from destructive interference.

• Bonding orbital: Lower energy, increases electron density between nuclei.

• Antibonding orbital: Higher energy, decreases electron density between nuclei.

• Example: The combination of two p orbitals can form both π and π* orbitals.

MO Diagrams and Electron Configuration

Molecular orbital diagrams show the relative energies and electron occupancy of molecular orbitals. Electron configuration in MO diagrams determines bond order and magnetic properties.

• Bond order:

• Example: For N2, bond order is 3, indicating a triple bond.

Summary Table: Key Equations and Constants

Additional info:

Some diagrams and Lewis structures in the file illustrate molecular geometry and electron arrangement, which are essential for understanding chemical bonding and reactivity. The periodic table and electronegativity chart are standard reference tools for General Chemistry.