AP Chemistry Equations Sheet

The AP Chemistry Equations and Constants sheet and Periodic Table are provided on both sections of the exam, in Bluebook and in print. This annotated reference reorganizes the equations by theme so you can see what each one is for and when to reach for it. These are the standard, well-known AP Chemistry equations; always confirm the exact contents against the official College Board equations sheet before exam day, since College Board can revise it. The official PDF is on AP Central.

Constants and conversions

Provided on the AP Chemistry equations sheet · confirm against the official sheet

$R$Ideal gas constant 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K)

$F$Faraday's constant (charge per mole of electrons) 96,485 C/mol e⁻

$N_A$Avogadro's number 6.022 × 10²³ mol⁻¹

$h$Planck's constant 6.626 × 10⁻³⁴ J·s

$c$Speed of light 3.00 × 10⁸ m/s

$K_w$Ion-product constant of water (25 °C) 1.0 × 10⁻¹⁴

1 atmStandard pressure 760 mmHg = 101.3 kPa

$0\,°\text{C}$Celsius-to-Kelvin offset K = °C + 273.15

Theme 1

Atomic structure

Light, energy, and the relationships that connect a photon's frequency, wavelength, and energy.

$$ E = h\nu $$

Energy of a photon

The energy of one photon equals Planck's constant times its frequency. Higher frequency light carries more energy per photon.

Unit 1 · Atomic Structure

$$ c = \lambda \nu $$

Wave relationship

The speed of light equals wavelength times frequency, so wavelength and frequency are inversely related for light.

Unit 1 · Atomic Structure

Theme 2

Gases and solutions

The ideal gas law, partial pressures, the mole, molarity, and Beer's law for solution absorbance.

$$ PV = nRT $$

Ideal gas law

Relates pressure, volume, moles, and temperature of an ideal gas. Temperature must be in kelvin.

Unit 3 · Substances and Mixtures

$$ P_A = P_{\text{total}} \cdot X_A $$

Partial pressure and mole fraction

The partial pressure of a gas equals the total pressure times its mole fraction $X_A$. Total pressure is the sum of the partial pressures (Dalton's law).

Unit 3 · Substances and Mixtures

$$ n = \dfrac{m}{M} $$

Moles from mass

Number of moles equals sample mass divided by molar mass. The bridge between grams and moles in every stoichiometry problem.

Unit 4 · Chemical Reactions

$$ M = \dfrac{n_{\text{solute}}}{V_{\text{solution}}} $$

Molarity

Concentration in moles of solute per liter of solution. Used throughout equilibrium, titration, and dilution problems.

Unit 3 · Substances and Mixtures

$$ A = \varepsilon b c $$

Beer's law

Absorbance equals molar absorptivity times path length times concentration. A straight-line calibration used to find an unknown concentration.

Unit 3 · Substances and Mixtures

Theme 3

Thermodynamics

Heat transfer, and the enthalpy, entropy, and free energy changes that determine whether a process is favorable.

$$ q = mc\,\Delta T $$

Heat transfer (calorimetry)

Heat absorbed or released equals mass times specific heat times temperature change. The core equation of every calorimetry problem.

Unit 6 · Thermodynamics

$$ \Delta H^\circ = \sum \Delta H_f^\circ(\text{prod}) - \sum \Delta H_f^\circ(\text{react}) $$

Standard enthalpy of reaction

Reaction enthalpy from standard enthalpies of formation: products minus reactants. Negative means exothermic.

Unit 6 · Thermodynamics

$$ \Delta S^\circ = \sum S^\circ(\text{prod}) - \sum S^\circ(\text{react}) $$

Standard entropy of reaction

Reaction entropy from standard molar entropies: products minus reactants. Positive means more disorder is produced.

Unit 9 · Applications of Thermo

$$ \Delta G^\circ = \Delta H^\circ - T\,\Delta S^\circ $$

Gibbs free energy

Free energy change from enthalpy, temperature, and entropy. A negative $\Delta G^\circ$ means the reaction is thermodynamically favorable.

Unit 9 · Applications of Thermo

Theme 4

Electrochemistry

The links between free energy, the equilibrium constant, cell potential, and the charge that flows in an electrochemical cell.

$$ \Delta G^\circ = -RT \ln K $$

Free energy and the equilibrium constant

A more negative standard free energy corresponds to a larger $K$. Connects thermodynamics to the position of equilibrium.

Unit 9 · Applications of Thermo

$$ \Delta G^\circ = -n F E^\circ $$

Free energy and cell potential

Relates standard free energy to standard cell potential, where $n$ is moles of electrons and $F$ is Faraday's constant. A positive $E^\circ$ means a spontaneous cell.

Unit 9 · Applications of Thermo

$$ \Delta G = \Delta G^\circ + RT \ln Q $$

Free energy under nonstandard conditions

Corrects standard free energy for the actual reaction quotient $Q$. The basis for the Nernst relationship between potential and concentration.

Unit 9 · Applications of Thermo

$$ I = \dfrac{q}{t} $$

Current, charge, and time

Current equals charge divided by time. Used with Faraday's constant to relate electrons transferred to mass deposited in electrolysis.

Unit 9 · Applications of Thermo

Theme 5

Equilibrium and acids/bases

Equilibrium constant expressions, the water constant, pH and pOH, and the buffer relationship.

$$ K_c = \dfrac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b} $$

Equilibrium constant expression

Products over reactants, each raised to its stoichiometric coefficient. $K_p$ uses partial pressures for gases. Pure solids and liquids are omitted.

Unit 7 · Equilibrium

$$ K_w = [\text{H}^+][\text{OH}^-] = 1.0\times10^{-14} $$

Ion-product of water

The product of hydrogen and hydroxide ion concentrations at 25 °C. Also equals $K_a \times K_b$ for a conjugate pair.

Unit 8 · Acids and Bases

$$ \text{pH} = -\log[\text{H}^+] \quad\quad \text{pH} + \text{pOH} = 14 $$

pH, pOH, and their sum

pH is the negative log of hydrogen ion concentration; pOH is defined the same way for hydroxide. They sum to 14 at 25 °C.

Unit 8 · Acids and Bases

$$ \text{pH} = \text{p}K_a + \log\dfrac{[\text{A}^-]}{[\text{HA}]} $$

Henderson-Hasselbalch (buffers)

The pH of a buffer from the acid's $\text{p}K_a$ and the ratio of conjugate base to weak acid. pH equals $\text{p}K_a$ when the two are equal.

Unit 8 · Acids and Bases

$$ \text{p}K_a = -\log K_a \quad\quad \text{p}K_b = -\log K_b $$

pKa and pKb

Log measures of acid and base strength. A smaller $\text{p}K_a$ means a stronger acid.

Unit 8 · Acids and Bases

Theme 6

Kinetics

Rate laws, the integrated forms for first and second order reactions, half-life, and the temperature dependence of the rate constant.

$$ \text{rate} = k[\text{A}]^m[\text{B}]^n $$

Rate law

Reaction rate as a function of concentration, where the orders $m$ and $n$ come from experiment, not from the coefficients.

Unit 5 · Kinetics

$$ \ln[\text{A}]_t = -kt + \ln[\text{A}]_0 $$

First-order integrated rate law

A plot of $\ln[\text{A}]$ versus time is linear with slope $-k$ for a first-order reaction.

Unit 5 · Kinetics

$$ \dfrac{1}{[\text{A}]_t} = kt + \dfrac{1}{[\text{A}]_0} $$

Second-order integrated rate law

A plot of $1/[\text{A}]$ versus time is linear with slope $k$ for a second-order reaction.

Unit 5 · Kinetics

$$ t_{1/2} = \dfrac{0.693}{k} $$

First-order half-life

For a first-order reaction the half-life is constant and independent of starting concentration.

Unit 5 · Kinetics

$$ \ln k = -\dfrac{E_a}{R}\cdot\dfrac{1}{T} + \ln A $$

Arrhenius equation

The rate constant rises with temperature and falls with activation energy. A plot of $\ln k$ versus $1/T$ is linear with slope $-E_a/R$.

Unit 5 · Kinetics

Don't just memorize. Diagnose.

Having the equations sheet in front of you is not the same as knowing when to use each equation. Most AP Chemistry points are lost to misconceptions: reversing a Le Chatelier shift, confusing rate with rate constant, getting the sign of ΔG backward, or treating a weak acid as fully dissociated. Mistake Master is built around fixing these specific failure modes.

Run a diagnostic