General Chemistry Study Notes: Atomic Structure, Periodic Trends, Chemical Bonding, and Lattice Energy

Atomic Structure and Electron Configuration

Ground State Electron Configuration

The ground state electron configuration of an atom describes the arrangement of electrons in the lowest energy orbitals. This configuration follows the Aufbau principle, Pauli exclusion principle, and Hund's rule.

• Aufbau Principle: Electrons fill orbitals starting with the lowest energy first.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

• Hund's Rule: Electrons occupy degenerate orbitals singly before pairing.

• Example: The ground state electron configuration for Rhodium (Rh) is [Kr]4d85s1.

Valence Electrons

Valence electrons are the electrons in the outermost shell of an atom and are responsible for chemical bonding.

• Alkaline earth metals (Group 2) have 2 valence electrons.

• Example: Magnesium (Mg) has 2 valence electrons.

Periodic Trends

Ionization Energy (IE)

Ionization energy is the energy required to remove an electron from a gaseous atom or ion.

• IE increases across a period (left to right) and decreases down a group.

• Order of increasing IE: N < As < F

Atomic Radius

Atomic radius is the distance from the nucleus to the outermost electron shell.

• Atomic radius decreases across a period and increases down a group.

• Example: Sodium has a larger atomic radius than potassium (False).

Electron Affinity

Electron affinity is the energy change when an electron is added to a neutral atom.

• Generally becomes more negative across a period.

• Example: Fluorine has a more negative electron affinity than oxygen.

Chemical Bonding

Lewis Structures

Lewis structures represent the arrangement of electrons in molecules, showing bonds and lone pairs.

• Best Lewis structure for BeF2 has Be in the center with two single bonds to F atoms.

• Example: BeF2: F–Be–F

Bond Energy and Enthalpy Calculations

Bond energy is the energy required to break one mole of a bond in a molecule. It is used to estimate reaction enthalpy ($\Delta H_{rxn}$).

• $\Delta H_{rxn} = \sum \text{Bond energies of bonds broken} - \sum \text{Bond energies of bonds formed}$

• Example Table:

Bond	Energy (kJ/mol)
Br–Br	193
C≡C	837
C–C	347
C–Br	276

Molecular Geometry and Polarity

Molecular geometry describes the three-dimensional arrangement of atoms in a molecule. Polarity depends on the difference in electronegativity and molecular shape.

• Examples of polar molecules: CO, COS, SeBr2

• Nonpolar: XeO3

Hybridization

Hybridization is the mixing of atomic orbitals to form new hybrid orbitals suitable for bonding.

• sp, sp2, sp3 are common types.

• Example: In HCN, the central carbon is sp hybridized.

Sigma (σ) and Pi (π) Bonds

Sigma (σ) bonds are formed by the head-on overlap of orbitals, while pi (π) bonds are formed by the side-on overlap.

• Single bonds are always sigma bonds.

• Double and triple bonds contain one sigma and one or two pi bonds.

Quantum Numbers and Electronic Configuration

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them:

• n: Principal quantum number (energy level)

• l: Angular momentum quantum number (orbital shape)

• ml: Magnetic quantum number (orientation)

• ms: Spin quantum number (+1/2 or -1/2)

• Example: n = 2, l = 1, ml = -2 is not allowed (ml must be between -l and +l).

Short and Full Electron Configurations

Electron configurations can be written in short (noble gas) or full notation.

• Example: K: [Ar]4s1; Au: [Xe]4f145d106s1

Lattice Energy and Born-Haber Cycle

Lattice Energy

Lattice energy is the energy released when ions combine to form a crystalline solid. It can be calculated using the Born-Haber cycle.

• Born-Haber Cycle: A thermochemical cycle that relates lattice energy to other measurable quantities.

• Equation: $E = \frac{KQ_1Q_2}{r}$

• Example Table:

Step	ΔH (kJ)
Ca(s) → Ca(g)	193
Ca(g) → Ca2+(g) + 2e-	590
O2(g) → 2O(g)	498
O(g) + 2e- → O2-(g)	-141
Ca2+(g) + O2-(g) → CaO(s)	-635

Useful Constants and Equations

Physical Constants

• 1 cal = 4.184 J

• R = 0.08206 L·atm·mol-1·K-1

• c = 3.00 × 108 m/s

• h = 6.626 × 10-34 J·s

• RH = 1.097 × 107 m-1

• B = 2.18 × 10-18 J

• π = 3.1416

Key Equations

• Temperature conversions:

  • $^\circ C = \frac{^\circ F - 32.0}{1.80}$

  • $^\circ F = (1.80 \times ^\circ C) + 32.0$

• Kinetic energy: $KE = \frac{1}{2}mv^2$

• Potential energy: $PE = mgh$

• Change in energy: $\Delta E = w + q$

• Pressure: $P = \frac{zRT}{V}$

• Ideal gas law: $\left(\frac{P + a\left(\frac{n}{V}\right)^2}{V - nb}\right) = nRT$

• Energy of a photon: $E = h\nu$

• de Broglie wavelength: $\lambda = \frac{h}{mv}$

• Energy levels of hydrogen: $E_n = -\frac{Z^2R_H}{n^2}$

Definitions of Key Terms

• Ground electronic state: The lowest energy state of an atom or molecule, with electrons in the lowest possible orbitals.

• Degenerate: Orbitals or energy levels that have the same energy.

• Lattice energy: The energy released when gaseous ions form an ionic solid.

• Polar covalent bond: A covalent bond in which electrons are shared unequally, resulting in partial charges.

• Hybrid orbital: An orbital formed by the combination of two or more atomic orbitals on the same atom.

• Sigma (σ) bond: A covalent bond formed by the direct overlap of orbitals along the axis connecting two nuclei.

Additional info: Some explanations and examples have been expanded for clarity and completeness.