Official College Board AP Chemistry reference content — all equations and constants provided on the AP exam. Available on both MCQ and FRQ sections.
| Equation | Name / Quantity | Variables |
|---|---|---|
| E = hν | Photon energy | h = 6.626×10⁻³⁴ J·s; ν = frequency (Hz) |
| c = λν | Speed of light | c = 3.00×10⁸ m/s; λ = wavelength (m) |
| E = hc/λ | Photon energy (wavelength) | Combined from E=hν and c=λν |
| λ = h/mv | de Broglie wavelength | m = mass (kg); v = velocity (m/s) |
| E = −2.178×10⁻¹⁸ J (Z²/n²) | Bohr model energy | Z = atomic number; n = principal quantum number |
| ΔE = −2.178×10⁻¹⁸ J (1/n₁² − 1/n₂²) | Energy of photon emitted/absorbed | For hydrogen atom transitions |
| Equation | Name / Quantity | Notes |
|---|---|---|
| Kc = [C]^c[D]^d / [A]^a[B]^b | Equilibrium constant expression (aA + bB ⇌ cC + dD) | Pure solids and liquids excluded |
| Kp = Kc(RT)^Δn | Kp from Kc | Δn = Σ mol gas products − Σ mol gas reactants |
| Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴ at 25°C | Water dissociation constant | Always 1.0×10⁻¹⁴ at 25°C |
| Ka × Kb = Kw | Conjugate acid-base relationship | For conjugate pair |
| pH = −log[H⁺] | pH definition | [H⁺] in mol/L |
| pOH = −log[OH⁻] | pOH definition | |
| pH + pOH = 14 (at 25°C) | pH-pOH relationship | Only valid at 25°C |
| pKa = −log Ka | pKa definition | |
| pH = pKa + log([A⁻]/[HA]) | Henderson-Hasselbalch equation | Buffer systems |
| Ka = [H⁺][A⁻] / [HA] | Acid dissociation constant |
| Equation | Name / Quantity | Order / Notes |
|---|---|---|
| Rate = k[A]^m[B]^n | Rate law | m, n determined experimentally |
| [A]t = [A]₀ − kt | Zero order integrated rate law | Linear: [A] vs t; k units: M/s |
| ln[A]t = ln[A]₀ − kt | First order integrated rate law | Linear: ln[A] vs t; k units: s⁻¹ |
| 1/[A]t = 1/[A]₀ + kt | Second order integrated rate law | Linear: 1/[A] vs t; k units: M⁻¹s⁻¹ |
| t½ = [A]₀ / 2k | Half-life (zero order) | Depends on initial concentration |
| t½ = 0.693 / k = ln 2 / k | Half-life (first order) | Constant — independent of [A]₀ |
| t½ = 1 / (k[A]₀) | Half-life (second order) | Depends on initial concentration |
| k = Ae^(−Ea/RT) | Arrhenius equation | A = frequency factor; Ea = activation energy |
| ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂) | Arrhenius (two-temperature form) | R = 8.314 J/mol·K; T in Kelvin |
| Equation | Name / Quantity | Notes |
|---|---|---|
| ΔH°rxn = ΣΔHf°(products) − ΣΔHf°(reactants) | Standard enthalpy of reaction | ΔHf° for elements in standard state = 0 |
| ΔH = bonds broken − bonds formed | Enthalpy from bond energies | Approximate; use for estimating |
| q = mcΔT | Heat transfer (calorimetry) | m=mass(g); c=specific heat; ΔT=temp change |
| q = CΔT | Heat transfer (calorimeter) | C = heat capacity of calorimeter (J/K) |
| ΔH°rxn = ΔH°f products − ΔH°f reactants | Hess's Law — standard form | Can also add individual reactions |
| ΔS°rxn = ΣS°(products) − ΣS°(reactants) | Standard entropy change | S° always positive; gas > liquid > solid |
| ΔG° = ΔH° − TΔS° | Standard Gibbs free energy | T in Kelvin; ΔG°<0 means spontaneous |
| ΔG° = −RT ln K | ΔG° and equilibrium constant | R=8.314 J/mol·K; T in Kelvin |
| ΔG = ΔG° + RT ln Q | Gibbs free energy (non-standard) | Q = reaction quotient |
| ΔG° = −nFE°cell | ΔG° from electrochemistry | n = mol electrons; F = 96,485 C/mol |
| Equation | Name / Quantity | Notes |
|---|---|---|
| E°cell = E°cathode − E°anode | Standard cell potential | E° values from standard reduction potential table |
| ΔG° = −nFE°cell | Gibbs free energy from E° | n = moles of electrons transferred |
| E°cell = (RT/nF) ln K | E° and equilibrium constant | At 25°C: E° = (0.0592/n) log K |
| E = E° − (RT/nF) ln Q | Nernst equation | At 25°C: E = E° − (0.0592/n) log Q |
| E = E° − (0.0592/n) log Q | Nernst equation at 25°C | Simplified for AP exam use |
| q = It | Charge from current and time | q=coulombs; I=amperes; t=seconds |
| n = q/F = It/F | Moles of electrons (electrolysis) | F = 96,485 C/mol |
| Equation | Name / Quantity | Notes |
|---|---|---|
| PV = nRT | Ideal gas law | R=0.08206 L·atm/mol·K or 8.314 J/mol·K |
| P₁V₁/T₁ = P₂V₂/T₂ | Combined gas law | T must be in Kelvin |
| Ptotal = P₁ + P₂ + P₃ + … | Dalton's law of partial pressures | For non-reacting gas mixtures |
| Pa = Xa × Ptotal | Partial pressure from mole fraction | Xa = mole fraction of gas a |
| r₁/r₂ = √(M₂/M₁) | Graham's law of effusion/diffusion | Lighter gas effuses faster |
| KE_avg = ³⁄₂ RT | Average kinetic energy per mole | Depends only on temperature (KMT) |
| u_rms = √(3RT/M) | Root-mean-square speed | M = molar mass in kg/mol; T in Kelvin |
| (P + n²a/V²)(V − nb) = nRT | Van der Waals equation | a = intermolecular attraction; b = molecular volume |
| Equation | Name / Quantity | Notes |
|---|---|---|
| M = n/V | Molarity | n=moles; V=litres of solution |
| m = n_solute / kg_solvent | Molality | Used in colligative property calculations |
| χ = n_a / n_total | Mole fraction | Dimensionless |
| M₁V₁ = M₂V₂ | Dilution equation | Moles of solute = constant |
| ΔTb = iKb m | Boiling point elevation | i=van't Hoff factor; Kb=0.512°C·kg/mol for water |
| ΔTf = iKf m | Freezing point depression | Kf=1.86°C·kg/mol for water |
| π = iMRT | Osmotic pressure | π in atm; R=0.08206 L·atm/mol·K |
| P_solution = χ_solvent × P°_solvent | Raoult's law (vapour pressure lowering) | χ_solvent = mole fraction of pure solvent |
| A = εbc | Beer-Lambert law | ε=molar absorptivity; b=path length; c=concentration |
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| giga | G | 10⁹ | 1 GJ = 10⁹ J |
| mega | M | 10⁶ | 1 MHz = 10⁶ Hz |
| kilo | k | 10³ | 1 kg = 10³ g |
| deci | d | 10⁻¹ | 1 dm = 0.1 m |
| centi | c | 10⁻² | 1 cm = 0.01 m |
| milli | m | 10⁻³ | 1 mL = 0.001 L |
| micro | μ | 10⁻⁶ | 1 μg = 10⁻⁶ g |
| nano | n | 10⁻⁹ | 1 nm = 10⁻⁹ m |
| pico | p | 10⁻¹² | 1 pm = 10⁻¹² m |