AP Chemistry Formula Sheet — Every Formula & Equation You Need
This formula sheet collects every key AP Chemistry formula in one place, organised by AP unit, so you can revise quickly without hunting through notes. Keep it open while you study, and use it alongside our free practice tests to check that you can apply each formula, not just recognise it.
Key Constants
- Gas constant: R = 8.314 J mol−1 K−1 and R = 0.08206 L atm mol−1 K−1
- Avogadro constant: NA = 6.022 × 1023 mol−1
- Faraday constant: F = 96,485 C mol−1
- Ion product of water at 25 °C: Kw = 1.0 × 10−14
- Speed of light: c = 3.00 × 108 m s−1
- Planck constant: h = 6.626 × 10−34 J s
Atomic Structure & Periodicity
| Formula / Equation | What it is / When to use it |
|---|
| E = hν | Energy of one photon; h is Planck’s constant and ν (nu) is the frequency of the radiation. |
| c = λν | Links wavelength (λ) and frequency (ν) of a wave; c is the speed of light. |
| Zeff = Z − S | Effective nuclear charge: the pull an outer electron actually feels after inner electrons (S) shield it from the full nuclear charge (Z); explains periodic trends such as atomic radius and ionisation energy. |
Moles & Stoichiometry
| Formula / Equation | What it is / When to use it |
|---|
| n = m / M | Amount in moles from mass (m, in grams) divided by molar mass (M, in g mol−1). |
| Number of particles = n × NA | Converts moles into atoms, molecules or ions using Avogadro’s constant. |
| Percentage composition = (mass of element / total mass) × 100 | Mass percentage of one element in a compound; also used in reverse to find an empirical formula. |
Solutions
| Formula / Equation | What it is / When to use it |
|---|
| M = n / V | Molarity (mol L−1) from moles of solute divided by the volume of solution in litres. |
| M1V1 = M2V2 | Dilution equation: moles of solute stay the same when solvent is added, so concentration and volume trade off. |
| A = εbc | Beer–Lambert law: absorbance (A) from molar absorptivity (ε), path length (b) and concentration (c); used with spectrophotometry and calibration curves. |
Gases
| Formula / Equation | What it is / When to use it |
|---|
| PV = nRT | Ideal gas law linking pressure, volume, moles and temperature (always in kelvin); pick the value of R that matches your pressure unit. |
| Ptotal = P1 + P2 + … | Dalton’s law: in a gas mixture, the total pressure is the sum of the partial pressures. |
| Xi = ni / ntotal | Mole fraction of one gas in a mixture: its moles divided by the total moles present. |
| Pi = Xi × Ptotal | Partial pressure of one gas from its mole fraction and the total pressure. |
| KEavg = (3/2)RT | Average kinetic energy of one mole of gas particles; depends only on temperature, not on the gas. |
| rate1 / rate2 = √(M2 / M1) | Graham’s law: lighter gases effuse or diffuse faster, in inverse proportion to the square root of their molar masses. |
Thermochemistry & Thermodynamics
| Formula / Equation | What it is / When to use it |
|---|
| q = mcΔT | Heat absorbed or released when a mass (m) with specific heat capacity (c) changes temperature by ΔT, with no phase change. |
| ΔHrxn = Σ bond enthalpies broken − Σ bond enthalpies formed | Estimates a reaction enthalpy from bond enthalpy data: energy in to break bonds minus energy out when new bonds form. |
| ΔHoverall = ΔH1 + ΔH2 + … | Hess’s law: enthalpy change is a state function, so add (or subtract/reverse) step enthalpies to get the overall value. |
| ΔG = ΔH − TΔS | Gibbs free energy change from enthalpy and entropy changes (T in kelvin); a negative ΔG means the process is thermodynamically favoured. |
| ΔG° = −RT ln K | Connects the standard free energy change to the equilibrium constant; large K gives a negative ΔG°. |
| q = nΔH | Heat for a phase change at constant temperature, using moles (n) and the molar enthalpy of fusion or vaporisation. |
Kinetics
| Formula / Equation | What it is / When to use it |
|---|
| rate = k[A]m[B]n | Rate law: k is the rate constant and the exponents m and n (the orders) are found from experimental data. |
| ln[A] = −kt + ln[A]0 | Integrated rate law for a first-order reaction; a plot of ln[A] against t is a straight line. |
| t1/2 = 0.693 / k | Half-life of a first-order reaction; it stays constant and does not depend on the starting concentration. |
| 1/[A] = kt + 1/[A]0 | Integrated rate law for a second-order reaction; a plot of 1/[A] against t is a straight line. |
| t1/2 = 1 / (k[A]0) | Half-life of a second-order reaction; it gets longer as the reactant is used up. |
| [A] = −kt + [A]0 | Integrated rate law for a zero-order reaction; concentration falls at a constant rate. |
| k = A e(−Ea/RT) | Arrhenius equation: the rate constant rises with temperature and falls as activation energy (Ea) increases; A is the frequency factor. |
| ln(k2/k1) = (Ea/R)(1/T1 − 1/T2) | Two-temperature Arrhenius form: find Ea from rate constants measured at two different temperatures. |
Equilibrium
| Formula / Equation | What it is / When to use it |
|---|
| Kc = [products]coefficients / [reactants]coefficients | Equilibrium constant in concentration terms; for example, for aA + bB ⇌ cC + dD, Kc = ([C]c[D]d) / ([A]a[B]b), with pure solids and liquids left out. |
| Kp = Kc(RT)Δn | Converts between Kc and Kp for gases; Δn is the change in moles of gas (products minus reactants). |
| Compare Q with K | Reaction quotient Q has the same form as K but uses current concentrations: if Q < K the reaction moves forward, if Q > K it moves in reverse, and if Q = K the system is at equilibrium. |
| Percent ionisation = ([H+] formed / initial [HA]) × 100 | Share of a weak acid that has ionised at equilibrium; it increases as the solution is diluted. |
Acids, Bases & Solubility
| Formula / Equation | What it is / When to use it |
|---|
| pH = −log[H+] | Definition of pH from the hydrogen ion (hydronium) concentration. |
| pOH = −log[OH−] | Definition of pOH from the hydroxide ion concentration. |
| pH + pOH = 14 | Shortcut linking pH and pOH in aqueous solutions at 25 °C. |
| Kw = Ka × Kb | For a conjugate acid–base pair, the product of Ka and Kb equals Kw; the stronger the acid, the weaker its conjugate base. |
| pKa = −log Ka | Log form of the acid dissociation constant; a smaller pKa means a stronger acid. |
| pH = pKa + log([A−] / [HA]) | Henderson–Hasselbalch equation for buffer pH from the conjugate base and acid concentrations. |
| Ksp = [ions]coefficients | Solubility product for a saturated solution; for example, for MxXy(s) ⇌ xM + yX, Ksp is the product of the ion concentrations each raised to its coefficient, with the solid left out. |
| s from Ksp | Molar solubility (s) is found by writing each ion concentration in terms of s in the Ksp expression — for a 1:1 salt such as AgCl, Ksp = s2, so s = √Ksp. |
Electrochemistry
| Formula / Equation | What it is / When to use it |
|---|
| E°cell = E°cathode − E°anode | Standard cell potential from the standard reduction potentials (reduction at the cathode minus oxidation at the anode). |
| ΔG° = −nFE° | Links standard free energy change to cell potential; n is the moles of electrons transferred and F is the Faraday constant. |
| E = E° − (RT / nF) ln Q | Nernst equation: the cell potential under non-standard conditions, from the reaction quotient Q. |
| E = E° − (0.0592 / n) log Q | The 25 °C version of the Nernst equation, using log base 10; handy for concentration cells and pH-related cells. |
| q = I × t | Total charge passed (coulombs) from current (I, in amps) multiplied by time (t, in seconds). |
| moles of e− = q / F | Converts charge into moles of electrons, the bridge to masses deposited or dissolved in electrolysis. |
All formulas on this page are standard chemistry facts. This page is an original revision aid created by QuaidianPoint and is not affiliated with, or endorsed by, the College Board.
