9.2 Atomic Theory, Ions & Molecules
Key Takeaways
- An atom's identity is set by its proton count (atomic number Z); mass number A = protons + neutrons, and isotopes of the same element differ only in neutron count.
- Electron configuration fills subshells in the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p (Aufbau principle); valence electrons determine chemical behavior.
- Cations form by loss of electrons (metals, e.g., Na → Na+); anions form by gain (nonmetals, e.g., Cl + e− → Cl−); main-group ions generally adopt a noble-gas configuration (octet).
- Periodic trends: atomic radius decreases across a period (more protons, same shell) and increases down a group (more shells); ionization energy and electronegativity increase across a period and decrease down a group.
- A molecular formula gives the actual atom count (e.g., C6H12O6); an empirical formula gives the simplest whole-number ratio (e.g., CH2O); percent composition and molar mass link them.
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:
| Isotope | Z | A | Protons | Neutrons | Use |
|---|---|---|---|---|---|
| 12C | 6 | 12 | 6 | 6 | Atomic mass standard |
| 13C | 6 | 13 | 6 | 7 | NMR reference |
| 14C | 6 | 14 | 6 | 8 | Radiocarbon dating |
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
| Trend | Across a period (→) | Down a group (↓) | Why |
|---|---|---|---|
| Atomic radius | Decreases | Increases | More protons pull same shell in; extra shells add outward |
| Ionization energy | Increases | Decreases | Tighter hold across, looser hold down |
| Electronegativity | Increases | Decreases | Same as ionization energy |
| Metallic character | Decreases | Increases | Metals on left/bottom |
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
| Group | Charge | Example |
|---|---|---|
| 1 (alkali metals) | +1 | Na+, K+ |
| 2 (alkaline earth) | +2 | Mg2+, Ca2+ |
| 13 | +3 | Al3+ |
| 15 | −3 (mostly) | N3− |
| 16 | −2 | O2−, S2− |
| 17 (halogens) | −1 | F−, Cl− |
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.
- Assume 100 g: 40.0 g C, 6.7 g H, 53.3 g O.
- Moles: C 40.0/12.01 = 3.33; H 6.7/1.008 = 6.65; O 53.3/16.00 = 3.33.
- Divide by smallest (3.33): C1H2O1 → empirical CH2O, mass 30 g/mol.
- Ratio: 180 / 30 = 6 → molecular C6H12O6 (glucose).
Polyatomic Ions to Memorize
PA-CAT stoichiometry items assume fluency with common polyatomic ions:
| Ion | Name | Ion | Name |
|---|---|---|---|
| NH4+ | ammonium | NO3− | nitrate |
| NO2− | nitrite | SO4²− | sulfate |
| SO3²− | sulfite | PO4³− | phosphate |
| OH− | hydroxide | CO3²− | carbonate |
| HCO3− | bicarbonate | CH3COO− | acetate |
| CN− | cyanide | MnO4− | permanganate |
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.
| Number | Symbol | Allowed values | Specifies |
|---|---|---|---|
| Principal | n | 1, 2, 3, … | Energy level / shell size |
| Azimuthal | l | 0 … n−1 (s=0, p=1, d=2, f=3) | Subshell shape |
| Magnetic | ml | −l … +l | Orbital orientation |
| Spin | ms | ±½ | Spin direction |
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:
| Species | Electron count | Configuration |
|---|---|---|
| O²⁻, F⁻, Ne, Na⁺, Mg²⁺, Al³⁺ | 10 | 1s² 2s² 2p⁶ |
| S²⁻, Cl⁻, Ar, K⁺, Ca²⁺ | 18 | 1s² 2s² 2p⁶ 3s² 3p⁶ |
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.
What is the ground-state electron configuration of a neutral sulfur atom (Z = 16)?
A compound contains 30.4% N and 69.6% O by mass. Its molar mass is about 92 g/mol. What is its molecular formula?