Kinetics, Atomic Structure, Periodicity, and Bonding

Core Review

Chemical Kinetics

Rate Law: For a reaction aA + bB → products, the rate law is determined experimentally:

rate = k[A]^m[B]^n

k = rate constant; m and n = reaction orders (NOT the stoichiometric coefficients a and b, unless the step is elementary). Overall order = m + n.

Determining order from data: Compare two experiments where one reactant concentration changes while others are held constant. If doubling [A] doubles the rate, m = 1 (first order). If doubling [A] quadruples the rate, m = 2 (second order). If doubling [A] has no effect, m = 0 (zero order).

Worked Example: For A + B → C, when [A] doubles and [B] constant, rate doubles → first order in A. When [B] doubles and [A] constant, rate quadruples → second order in B. Rate = k[A][B]²; overall order = 3.

Activation Energy (E_a): The minimum energy required for a reaction to occur. The Arrhenius equation relates k to T:

k = A·e^(−E_a/RT)        or        ln k = ln A − E_a/(RT)

Higher T → larger k → faster rate. Larger E_a → smaller k → slower rate.

Catalysts: Lower E_a by providing an alternative pathway. Catalysts do NOT change ΔH, ΔG, or K — they only lower E_a, equally for forward and reverse reactions, accelerating both.

Reaction coordinate diagrams: Plot energy vs. reaction progress. Peak = transition state (E_a). Difference between reactants and products = ΔH.

Atomic Structure

• Protons (p⁺): mass ≈ 1 amu, charge +1, located in nucleus, defines atomic number (Z).
• Neutrons (n⁰): mass ≈ 1 amu, charge 0, nucleus. Isotopes differ in neutron number.
• Electrons (e⁻): mass ≈ 1/1836 amu, charge −1, electron cloud. In a neutral atom, #e⁻ = #p⁺.

Isotopes: Same Z (protons), different number of neutrons, different mass number. ¹²C (6p, 6n), ¹³C (6p, 7n), ¹⁴C (6p, 8n).

Quantum Numbers

Each electron is described by four quantum numbers:

1. n (principal): energy level/shell. n = 1, 2, 3, ... Larger n = higher energy, larger orbital.
2. l (angular momentum, azimuthal): subshell shape. l = 0, 1, 2, ..., n−1. l = 0 (s), 1 (p), 2 (d), 3 (f).
3. m_l (magnetic): orbital orientation. Values: −l to +l (e.g., l=1 → m_l = −1, 0, +1 for three p orbitals).
4. m_s (spin): electron spin. +½ or −½.

Pauli Exclusion Principle: no two electrons in an atom can have the same four quantum numbers.

Electron Configurations

Aufbau Principle: Fill lowest energy orbitals first. Order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p...

Hund's Rule: Within a subshell, each orbital gets one electron before any orbital gets a second (all with parallel spins).

Notable exceptions: Cr: [Ar]4s¹3d⁵ (not 4s²3d⁴); Cu: [Ar]4s¹3d¹⁰ (not 4s²3d⁹). Half-filled and fully-filled d subshells are unusually stable.

Periodic Trends

Across a period (left → right): Nuclear charge (Z_eff) increases while shielding is roughly constant. Down a group (top → bottom): Principal quantum number n increases; valence electrons farther from nucleus.

Key exceptions: O has lower IE than N (N's half-filled p³ is stable). Noble gases have the highest IE in each period. Group 2 has higher IE than Group 3 (s² stability).

Chemical Bonding

Ionic bonding: Metal + nonmetal; electron transfer; forms crystalline lattice. ΔEN > 1.7 (approximate). High MP, brittle, conducts when molten/dissolved.

Covalent bonding: Nonmetal + nonmetal; electron sharing. Can be nonpolar (ΔEN ≈ 0, equal sharing) or polar (ΔEN > 0, unequal sharing → bond dipole).

Polar covalent threshold: 0.3 < ΔEN < 1.7. The greater the ΔEN, the more polar the bond.

Lewis Structures

1. Count total valence electrons.
2. Draw skeleton with least electronegative atom as central (never H as central).
3. Connect atoms with single bonds; subtract 2e⁻ per bond.
4. Distribute remaining electrons as lone pairs, satisfying octets (start with outer atoms, then central).
5. If central atom lacks octet, form multiple bonds.

Formal charge: FC = valence e⁻ − (lone pair e⁻ + ½ bonding e⁻). The best Lewis structure minimizes formal charges, with negative FC on the more electronegative atom.

Resonance: When multiple valid Lewis structures differ only in electron placement (not atom positions), the true structure is a resonance hybrid — a weighted average. Delocalized electrons (as in benzene, carbonate) are more stable.

VSEPR Theory

Valence Shell Electron Pair Repulsion: electron groups (bonds + lone pairs) repel and arrange to maximize separation.

Memorize these geometries:

Lone pairs occupy more space than bonding pairs, compressing bond angles.

Molecular Polarity

A molecule is polar if:

1. It has polar bonds (ΔEN > 0), AND
2. The bond dipoles do NOT cancel due to molecular symmetry.

CO₂ has polar C=O bonds but is linear → dipoles cancel → nonpolar. H₂O has polar O–H bonds and is bent → dipoles do NOT cancel → polar. CH₄ is tetrahedral and symmetric → nonpolar. NH₃ is trigonal pyramidal → polar. BF₃ is trigonal planar and symmetric → nonpolar.

Key Equations

Common Traps

• Using coefficients as reaction orders (only valid if the step is known to be elementary).
• Confusing electron geometry with molecular geometry (lone pairs affect molecular geometry name and angles).
• Writing 4s after 3d for transition metal cations — when ionizing, remove 4s electrons before 3d.
• Thinking all molecules with polar bonds are polar (symmetry cancels dipoles in CO₂, CF₄, BF₃).
• Ionization energy anomalies: Group 3 lower than Group 2; Group 16 lower than Group 15.