Physical Chemistry
Physical chemistry applies the methods of physics to chemical systems. It quantifies how matter and energy behave during chemical change, and provides the theoretical underpinning for the rest of chemistry: structure (quantum theory), behaviour of gases and solutions (thermodynamics), and rates of reaction (kinetics).
The SI base unit of amount of substance: the quantity containing exactly 6.022 × 10²³ elementary entities (atoms, molecules, ions). One mole of any gas at STP occupies 22.4 L.
Gas laws
| Law | Statement | Mathematical form |
|---|---|---|
| Boyle's law | V inversely proportional to P at constant T | PV = constant |
| Charles's law | V proportional to T at constant P | V/T = constant |
| Gay-Lussac's law | P proportional to T at constant V | P/T = constant |
| Avogadro's law | V proportional to n at constant T, P | V/n = constant |
| Ideal gas equation | Combines all the above | PV = nRT |
R = 8.314 J/(mol·K) is the universal gas constant. Real gases deviate from ideal behaviour at high pressure and low temperature, when van der Waals' equation [P + a(n/V)²][V − nb] = nRT becomes more accurate.
Atomic structure and the periodic table
Modern atomic theory rests on the quantum-mechanical model: electrons occupy orbitals labelled by four quantum numbers (n, l, m, m_s) and are filled according to:
- Aufbau principle — electrons enter the lowest-energy orbital first.
- Pauli exclusion principle — no two electrons share all four quantum numbers.
- Hund's rule — degenerate orbitals are singly occupied before pairing.
The periodic table organises elements by increasing atomic number Z. Across a period, atomic radius decreases and electronegativity, ionisation energy and electron affinity generally increase. Down a group, the trend reverses.
- Standard temperature and pressure (STP): 273.15 K (0 °C), 100 kPa (IUPAC, 1982).
- 1 atm = 101.325 kPa = 760 mmHg ≈ 1.013 bar.
- The four most electronegative elements: F (3.98) > O (3.44) > N (3.04) > Cl (3.16) on the Pauling scale.
- Alkali metals (Group 1) react vigorously with water; noble gases (Group 18) are largely inert.
Chemical thermodynamics
The same four laws of thermodynamics govern chemistry. Key chemical quantities:
- Enthalpy H = U + PV. ΔH < 0 for exothermic reactions.
- Entropy S — measure of disorder. ΔS > 0 favours spontaneity.
- Gibbs free energy G = H − TS. A reaction is spontaneous at constant T, P if ΔG < 0.
Hess's law: the enthalpy change of a reaction depends only on initial and final states, not the path. This allows ΔH for any reaction to be computed from standard enthalpies of formation:
ΔH°_rxn = Σ ΔH°_f(products) − Σ ΔH°_f(reactants)
Chemical equilibrium
For a reversible reaction aA + bB ⇌ cC + dD at equilibrium, the equilibrium constant is
K_c = [C]^c [D]^d / [A]^a [B]^b
Le Chatelier's principle states that a system at equilibrium subjected to a change in concentration, temperature or pressure shifts to partially counteract the change. The relation ΔG° = −RT ln K connects thermodynamics to equilibrium.
Acid-base equilibria
| Theory | Acid | Base |
|---|---|---|
| Arrhenius | H⁺ donor | OH⁻ donor |
| Brønsted–Lowry | Proton donor | Proton acceptor |
| Lewis | Electron-pair acceptor | Electron-pair donor |
pH = −log₁₀[H⁺]. Pure water at 25 °C has [H⁺] = [OH⁻] = 10⁻⁷ M, so pH = 7. The ion product K_w = [H⁺][OH⁻] = 10⁻¹⁴ at 25 °C. For a weak acid of dissociation constant K_a, pK_a = −log K_a; pH at half-neutralisation equals pK_a (the Henderson–Hasselbalch relation).
A buffer solution resists pH change on adding small amounts of acid or base. Common laboratory buffers: acetate (pH ≈ 4.7), phosphate (pH ≈ 7.2), Tris (pH ≈ 8.3). Choose a buffer whose pK_a is close to the desired pH.
Electrochemistry
Redox reactions transfer electrons. In a galvanic cell spontaneous redox produces electrical work; in an electrolytic cell electrical work drives a non-spontaneous reaction. The cell potential at standard conditions is
E°_cell = E°_cathode − E°_anode
For non-standard concentrations, the Nernst equation applies:
E = E° − (RT/nF) ln Q
with F = 96,485 C/mol (the Faraday constant). The relation ΔG° = −nFE° links thermodynamics and electrochemistry.
Chemical kinetics
The rate of a reaction depends on concentration and temperature. For a reaction A + B → products, the rate law is r = k[A]^m[B]^n, where m and n (the orders) are determined experimentally — not from stoichiometry.
- Zero-order: [A] = [A]₀ − kt, half-life t₁/₂ = [A]₀/(2k).
- First-order: ln[A] = ln[A]₀ − kt, half-life t₁/₂ = ln 2 / k (independent of [A]₀).
- Second-order: 1/[A] = 1/[A]₀ + kt, half-life t₁/₂ = 1/(k[A]₀).
The Arrhenius equation gives the temperature dependence of the rate constant:
k = A e^(−Eₐ/RT)
where Eₐ is the activation energy and A the pre-exponential factor. A rule of thumb: rate roughly doubles for each 10 °C rise in temperature near room temperature. Catalysts lower Eₐ, accelerating both forward and reverse reactions without altering K.
These principles together make physical chemistry the language in which industrial processes (Haber, contact, chlor-alkali), biological reactions (enzymes), and atmospheric chemistry (ozone depletion, climate models) are quantitatively described.