9.2 Atomic Theory, Ions & Molecules

Atomic Structure

Quick Answer: An atom consists of a dense nucleus of protons (charge +1, mass ~1 u) and neutrons (neutral, mass ~1 u), surrounded by electrons (charge −1, mass ~1/1836 u) in orbitals. The atomic number (Z) equals the proton count and defines the element; the mass number (A) equals protons plus neutrons.

Isotopes

Isotopes are atoms of the same element (same Z) with different neutron counts. Carbon's common isotopes:

The weighted average of isotope masses gives the element's atomic mass on the periodic table. A neutral atom has #electrons = #protons; an ion differs only in electron count.

Electron Configuration

Electrons fill subshells by the Aufbau principle (lowest energy first), obeying the Pauli exclusion principle (max 2 e− per orbital, opposite spins) and Hund's rule (maximize unpaired electrons in degenerate orbitals).

Filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p.

Subshell capacities: s holds 2, p holds 6, d holds 10, f holds 14.

Examples

• Oxygen (Z = 8): 1s² 2s² 2p⁴ — 6 valence electrons (2s² 2p⁴).
• Sodium (Z = 11): 1s² 2s² 2p⁶ 3s¹ — 1 valence electron; loses it to form Na+.
• Chlorine (Z = 17): 1s² 2s² 2p⁶ 3s² 3p⁵ — 7 valence electrons; gains one to form Cl−.
• Iron (Z = 26): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶; the transition-metal exception is that Fe can lose both 4s and a 3d electron to give Fe2+ (3d⁶) or Fe3+ (3d⁵, half-filled, extra stability).

Valence Electrons Drive Chemistry

For main-group elements, valence electrons = those in the outermost s and p subshells. The group number (1–8 for main groups using the A notation) equals the valence count. Group 1 has 1, Group 2 has 2, Group 13 has 3, … Group 17 has 7, Group 18 has 8 (full octet).

Periodic Trends

Exceptions: Group 13's first ionization energy is slightly lower than Group 2's (filled vs half-filled subshell effects), and oxygen's is slightly lower than nitrogen's (paired-electron repulsion in 2p⁴).

Ion Formation

Ions form to reach a stable (usually noble-gas) electron configuration.

• Cations (positive): metals lose electrons. Na (3s¹) → Na+ (Ne core). Mg (3s²) → Mg2+ (Ne core). Al → Al3+.
• Anions (negative): nonmetals gain electrons. Cl (3s² 3p⁵) + e− → Cl− (Ar core). O + 2 e− → O2−.
• Transition metals often form multiple oxidation states (Fe2+/Fe3+, Cu+/Cu2+).

Predicting Charges for Main-Group Ions

Molecular and Empirical Formulas

A molecular formula gives the actual number of each atom in a molecule; an empirical formula gives the simplest whole-number ratio.

• Benzene: molecular C6H6, empirical CH.
• Glucose: molecular C6H12O6, empirical CH2O.
• Hydrogen peroxide: molecular H2O2, empirical HO.

Worked Example: Empirical → Molecular

A compound is 40.0% C, 6.7% H, 53.3% O by mass. Its molar mass is 180 g/mol. Find the molecular formula.

1. Assume 100 g: 40.0 g C, 6.7 g H, 53.3 g O.
2. Moles: C 40.0/12.01 = 3.33; H 6.7/1.008 = 6.65; O 53.3/16.00 = 3.33.
3. Divide by smallest (3.33): C1H2O1 → empirical CH2O, mass 30 g/mol.
4. Ratio: 180 / 30 = 6 → molecular C6H12O6 (glucose).

Polyatomic Ions to Memorize

PA-CAT stoichiometry items assume fluency with common polyatomic ions:

Many of these (acetate, bicarbonate, phosphate) appear in the biochemical context the PA-CAT favors — recognizing them speeds up balancing and acid-base items alike.

Quantum Numbers and Isoelectronic Species

Electron configuration tells you which subshells are occupied; the four quantum numbers specify one orbital and the electron in it. PA-CAT items that ask "how many electrons can share n = 3, l = 2" are quantum-number counting questions.

Counting rule: the number of orbitals in a subshell is 2l + 1, each holding 2 electrons, so a subshell holds 2(2l + 1) electrons — s: 2, p: 6, d: 10, f: 14. For n = 3, l = 2 (the 3d subshell): 5 orbitals, 10 electrons maximum.

Isoelectronic Species

Ions and atoms with the same electron count share chemistry the PA-CAT probes. Know these series:

Within an isoelectronic series, the species with more protons pulls the electron cloud tighter — ionic radius shrinks as Z rises: O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺. This links quantum-number mastery back to the periodic-trend questions elsewhere on the exam.