AP® Chemistry Beta
The equations and constants sheet, explained
On exam day you get a periodic table and a sheet of equations and constants. Here is what each one is for, when to reach for it, and the slips that cost points. The sheet itself is published by the College Board; this page is our own guide to using it.
Three habits that save points
- Kelvins in every gas law and every thermodynamics equation. K = °C + 273.15. The sheet gives the conversion; using °C is still one of the commonest slips.
- Match R to your units. 0.08206 L·atm/(mol·K) with pressure and volume; 8.314 J/(mol·K) with energy. Then J or kJ consistently: ΔS° usually comes in J, ΔH° in kJ.
- log is not ln. pH, pOH, pKa and Henderson-Hasselbalch use base-10 log. Only ΔG° = −RT ln K, the first-order rate law and the Nernst equation use ln.
Particles, light and charge
| Equation | What it is | When you use it | Learn it in |
|---|---|---|---|
| F ∝ q₁q₂ / r² | Coulomb's law: the attraction between two charges grows with the charges and falls with the square of the distance. | Every "why is this ionization energy, radius, lattice energy or boiling point bigger" argument. You rarely calculate with it; you compare both species' charges and distances. | Units 1, 2, 3 Periodic Trends |
| E = hν | The energy of one photon from its frequency. | Photoelectron spectroscopy, emission lines, which wavelengths can cause an electronic transition. h = 6.626 × 10⁻³⁴ J·s. | Units 1, 3 Properties of Photons |
| c = λν | Speed of light from wavelength and frequency. | Converting a wavelength (often given in nm: change it to m) to a frequency before E = hν. c = 2.998 × 10⁸ m/s. | Unit 3 Properties of Photons |
| N_A = 6.022 × 10²³ mol⁻¹ | Avogadro's number: particles in one mole. | Moving between a count of particles and moles; per-photon energy to per-mole energy. | Unit 1 Moles and Molar Mass |
Gases, liquids and solutions
| Equation | What it is | When you use it | Learn it in |
|---|---|---|---|
| PV = nRT | The ideal gas law. | Moles, molar mass or density of a gas from its pressure, volume and temperature. Temperature in kelvins, and pick the R that matches your units. | Unit 3 Ideal Gas Law |
| P₁V₁/T₁ = P₂V₂/T₂ | The combined gas law, for a fixed amount of gas. | The same gas before and after a change in conditions. Again kelvins only. | Unit 3 Ideal Gas Law |
| P_total = P_A + P_B + …; P_A = X_A × P_total | Dalton's law and mole fraction. | Gas mixtures, and gas collected over water (subtract the water's vapor pressure). | Unit 3 Ideal Gas Law |
| R = 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K) | The gas constant in two sets of units. | 0.08206 with liters and atmospheres (gas law problems); 8.314 with joules (ΔG° = −RT ln K, the Nernst equation, kinetic energy). | Units 3, 9 Ideal Gas Law |
| STP: 273.15 K and 1.0 atm; 22.4 L/mol | Standard temperature and pressure, and the molar volume of an ideal gas there. | A shortcut only at STP. At any other conditions use PV = nRT. | Unit 3 Ideal Gas Law |
| KE = ½mv² | Kinetic energy of a moving particle. | Kinetic molecular theory: at the same temperature, lighter particles move faster on average. | Unit 3 Kinetic Molecular Theory |
| M = n_solute / L of solution | Molarity. | Every solution calculation: dilution, titration, stoichiometry in solution. Liters of solution, not of solvent. | Units 3, 4 Solutions and Mixtures |
| D = m/V; molar mass = m/n | Density, and molar mass from a mass and an amount. | Identifying a gas or liquid; combined with PV = nRT for a gas's molar mass. | Units 1, 3 Ideal Gas Law |
| A = εbc | The Beer-Lambert law: absorbance from molar absorptivity, path length and concentration. | Spectrophotometry labs: a calibration line, then a concentration from an absorbance. Also kinetics labs that follow a colored species. | Units 3, 5, 7 Beer-Lambert Law |
Kinetics
| Equation | What it is | When you use it | Learn it in |
|---|---|---|---|
| ln[A]_t − ln[A]_0 = −kt | The first-order integrated rate law. | Concentration after a time, or k from data. If ln[A] against t is a straight line, the reaction is first order (slope −k). | Unit 5 Concentration Changes Over Time |
| 1/[A]_t − 1/[A]_0 = kt | The second-order integrated rate law. | If 1/[A] against t is a straight line, the reaction is second order (slope k). | Unit 5 Concentration Changes Over Time |
| t½ = 0.693/k | The half-life of a first-order reaction. | Only for first order: its half-life does not depend on concentration (radioactive decay, many decompositions). | Unit 5 Concentration Changes Over Time |
Equilibrium, acids and bases
| Equation | What it is | When you use it | Learn it in |
|---|---|---|---|
| Kc = [C]^c[D]^d / ([A]^a[B]^b); Kp the same with partial pressures | The equilibrium constant for aA + bB ⇌ cC + dD. | Every equilibrium question; Q has the same form with the current values. Leave out pure solids and liquids. | Unit 7 Reaction Quotient and Equilibrium Constant |
| Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C; pH + pOH = 14.00 | The ionization of water. | Converting between [H₃O⁺] and [OH⁻], or pH and pOH, at 25 °C. | Unit 8 Introduction to Acids and Bases |
| pH = −log[H₃O⁺]; pOH = −log[OH⁻]; pKa = −log Ka | Logarithmic scales for acidity and acid strength. | Base-10 log, never ln. Keep as many decimal places as the concentration has significant figures. | Unit 8 Introduction to Acids and Bases |
| Kw = Ka × Kb; pKa + pKb = pKw | The link between a conjugate acid and base. | Getting Ka of NH₄⁺ from Kb of NH₃ (or the reverse) before a buffer or salt calculation. | Unit 8 Weak Acid and Base Equilibria |
| pH = pKa + log([A⁻]/[HA]) | The Henderson-Hasselbalch equation. | Buffer pH from the ratio of conjugate base to weak acid. At half-equivalence the ratio is 1, so pH = pKa. For a basic buffer, use the pKa of the conjugate acid. | Unit 8 Henderson-Hasselbalch Equation |
Thermodynamics and electrochemistry
| Equation | What it is | When you use it | Learn it in |
|---|---|---|---|
| q = mcΔT | Heat absorbed or released when a substance changes temperature. | Calorimetry: q of the solution, then ΔH per mole with the opposite sign. | Unit 6 Heat Capacity and Calorimetry |
| ΔH°rxn = Σ ΔH°f(products) − Σ ΔH°f(reactants) | Enthalpy of reaction from enthalpies of formation. ΔS° and ΔG° from tables work the same way. | Each value times its coefficient; an element in its standard state has ΔH°f = 0 (but not S° = 0). | Units 6, 9 Enthalpy of Formation |
| ΔG° = ΔH° − TΔS° | Gibbs free energy from enthalpy and entropy. | Whether a process is thermodynamically favored, and at what temperatures. Convert ΔS° from J to kJ first. | Unit 9 Gibbs Free Energy and Thermodynamic Favorability |
| ΔG° = −RT ln K | The link between free energy and the equilibrium constant. | K from ΔG° or the reverse. R = 8.314 J/(mol·K), so ΔG° in joules. Natural log here. | Unit 9 Free Energy and Equilibrium |
| ΔG° = −nFE° | The link between free energy and cell potential. | n is the moles of electrons transferred in the balanced equation. F = 96,485 C/mol e⁻, and 1 V = 1 J/C. | Unit 9 Cell Potential and Free Energy |
| E = E° − (RT/nF) ln Q | The Nernst equation: cell potential away from standard conditions. | Mostly reasoning: when Q < 1, E > E°; when Q > 1, E < E°; at equilibrium E = 0. | Unit 9 Cell Potential Under Nonstandard Conditions |
| I = q/t | Current is charge per time (1 A = 1 C/s). | Electrolysis: charge from current and time, then moles of electrons with F, then moles of metal from the half-reaction. | Unit 9 Electrolysis and Faraday's Law |
What is not on the sheet
The exam gives you these values in the question, or expects you to reason without them. None of them is printed on the sheet.
- A table of standard reduction potentials. Any E° you need is given in the question. Learn how to use one: the more positive E° is the cathode, and E°cell = E°(cathode) − E°(anode), never multiplied by a coefficient. Cell Potential and Free Energy
- Solubility rules. A question that needs to know whether a salt dissolves tells you, or gives a Ksp. Worth knowing anyway: sodium, potassium and ammonium salts, and all nitrates, dissolve. Net Ionic Equations
- The Arrhenius equation. How k depends on temperature is tested as reasoning with the collision model and energy distributions, not as a calculation. Collision Model
- The zero-order integrated rate law. [A]_t = [A]_0 − kt. For a zero-order reaction [A] against t is a straight line with slope −k, and the half-life shortens as the reaction goes. Concentration Changes Over Time
- Strong acids and bases. Learn the common strong acids (HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄) and strong bases (group 1 hydroxides, and Ca, Sr, Ba hydroxides). pH and pOH of Strong Acids and Bases
- Formal charge, bond angles and electron configurations. None of the structure rules are on the sheet. Formal charge = valence electrons − (nonbonding electrons + ½ bonding electrons). Resonance and Formal Charge
The sheet also lists unit symbols, conversions (1 atm = 760 mm Hg = 760 torr; 1 V = 1 J/C; 1 A = 1 C/s) and the metric prefixes from giga to pico.
Practice with it
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