AP Chemistry Equations Sheet- Complete Exam Reference

E: energy of photon

h: Planck’s constant

ν: frequency of radiation

Use when relating electromagnetic radiation frequency to energy. Higher frequency = higher energy photons.

Essential for photoelectric effect and spectroscopy problems

c: speed of light

λ: wavelength

ν: frequency

Speed of light is constant, so frequency and wavelength are inversely related.

Combine with E = hν to get E = hc/λ for wavelength-based calculations

E_Coulomb: electrostatic potential energy

k: Coulomb’s constant

q₁, q₂: charges on particles

r: distance between charges

Describes attraction/repulsion between charged particles. Inversely proportional to distance squared.

Used for ion-ion interactions and atomic structure

P: pressure

V: volume

n: number of moles

R: gas constant

T: absolute temperature

Central equation for gas behavior under ideal conditions. Use when T > 273K and P < 10 atm for most gases.

Combines Boyle’s, Charles’s, and Avogadro’s laws

P_A: partial pressure of gas A

P_total: total pressure of gas mixture

X_A: mole fraction of gas A

Each gas in a mixture contributes pressure proportional to its mole fraction.

Essential for gas mixture calculations and Dalton’s Law

P_total: total pressure of mixture

P_A, P_B, P_C: partial pressures of individual gases

Total pressure equals sum of individual gas pressures.

Gases behave independently in mixtures

n: number of moles

m: mass of substance

M: molar mass

Converts between mass and moles using molar mass.

Bridge between macroscopic measurements and particle counting

D: density

m: mass

V: volume

For gases: combine with PV = nRT to get D = PM/RT.

Gas density depends on pressure, temperature, and molar mass

KE: kinetic energy

m: mass of particle

v: velocity of particle

Average KE is proportional to absolute temperature.

Foundation of kinetic molecular theory (KMT)

M: molarity (mol/L)

n_solute: moles of solute

L_solution: liters of solution

Most common concentration unit in chemistry. Temperature dependent (volume changes with T).

Use for solution stoichiometry and dilution calculations

A: absorbance (no units)

ε: molar absorptivity

b: path length

c: concentration

Relates light absorption to concentration. Linear relationship allows spectroscopic analysis.

Used in colorimetry and UV-Vis spectroscopy

[A]_t: concentration of A at time t

[A]₀: initial concentration of A

k: rate constant

t: time

Linear decrease in concentration over time.

Rate is independent of reactant concentration

ln[A]_t: natural log of concentration at time t

ln[A]₀: natural log of initial concentration

k: rate constant

t: time

Exponential decay of concentration.

Most common kinetic order for elementary reactions

1/[A]_t: reciprocal of concentration at time t

1/[A]₀: reciprocal of initial concentration

k: rate constant

t: time

Linear relationship between 1/[A] and time.

Common for bimolecular elementary reactions

t_1/2: half-life

k: rate constant

Time for concentration to decrease by half. Independent of initial concentration for first-order reactions.

Useful for radioactive decay and drug metabolism

K_c: equilibrium constant (concentration)

[C], [D]: product concentrations

[A], [B]: reactant concentrations

c, d, a, b: stoichiometric coefficients

Products in numerator, reactants in denominator. Each raised to its stoichiometric coefficient.

K > 1 favors products, K < 1 favors reactants

K_p: equilibrium constant (pressure)

P_A, P_B, P_C, P_D: partial pressures of gases

Use when dealing with gaseous equilibria. Related to K_c by: K_p = K_c(RT)^Δn

Δn = moles of gaseous products – moles of gaseous reactants

pH: measure of acidity

pOH: measure of basicity

[H₃O⁺]: hydronium ion concentration

[OH⁻]: hydroxide ion concentration

pH < 7 is acidic, pH > 7 is basic, pH = 7 is neutral (at 25°C).

pH + pOH = 14 at 25°C

K_a: acid strength measure

[HA]: weak acid concentration

[A⁻]: conjugate base concentration

[H₃O⁺]: hydronium ion concentration

Larger K_a = stronger acid.

For HA + H₂O ⇌ H₃O⁺ + A⁻

K_b: base strength measure

[B]: weak base concentration

[HB⁺]: conjugate acid concentration

[OH⁻]: hydroxide ion concentration

Larger K_b = stronger base.

For B + H₂O ⇌ HB⁺ + OH⁻

pK_a: negative log of acid constant

pK_b: negative log of base constant

Smaller pK_a = stronger acid. Smaller pK_b = stronger base.

More convenient than working with very small K values

K_w: ion product of water

For any conjugate acid-base pair. At 25°C: K_w = 1.0 × 10⁻¹⁴, so pK_w = 14.

Allows calculation of K_b from K_a and vice versa

[A⁻]: conjugate base concentration

[HA]: weak acid concentration

pK_a: negative log of acid constant

Used for buffer calculations. When [A⁻] = [HA], then pH = pK_a.

Most effective buffers have pH within ±1 of pK_a

q: heat transferred

m: mass of substance

c: specific heat capacity

ΔT: temperature change

Calculate heat absorbed or released during temperature changes.

Assumes no phase changes occur

ΔH°: standard enthalpy change

ΔH°_f: standard enthalpy of formation

Calculate enthalpy change using formation enthalpies.

ΔH° < 0 = exothermic, ΔH° > 0 = endothermic. Standard conditions: 25°C, 1 atm pressure

ΔS°: standard entropy change

S°: standard molar entropy

Measures disorder change in reaction.

ΔS° > 0 = increased disorder, ΔS° < 0 = decreased disorder. Entropy generally increases: solid < liquid < gas

ΔG°: standard Gibbs free energy change

ΔG°_f: standard Gibbs free energy of formation

Predicts reaction spontaneity under standard conditions.

ΔG° < 0 = spontaneous, ΔG° > 0 = non-spontaneous. Alternative to calculating from ΔH° and ΔS°

ΔG°: Gibbs free energy change

ΔH°: enthalpy change

T: absolute temperature

ΔS°: entropy change

Relates thermodynamic quantities to predict spontaneity.

Temperature determines relative importance of enthalpy vs entropy

ΔG°: standard Gibbs free energy change

R: gas constant

T: absolute temperature

K: equilibrium constant

Links thermodynamics to equilibrium position.

Large K (equilibrium favors products) → negative ΔG°. Can calculate K from ΔG° or vice versa

ΔG: Gibbs free energy change

n: moles of electrons transferred

F: Faraday’s constant

E°: standard cell potential

Links electrochemistry to thermodynamics.

Positive E° means spontaneous electrochemical reaction. Bridge between electrical and chemical energy

I: electric current

q: electric charge

t: time

Fundamental relationship for electrolysis calculations.

1 ampere = 1 coulomb/second

E_cell: cell potential under non-standard conditions

E°_cell: standard cell potential

R: gas constant

T: absolute temperature

n: moles of electrons

F: Faraday’s constant

Q: reaction quotient

Calculate cell potential at any concentration.

At equilibrium: E_cell = 0, so Q = K. Shows how concentration affects cell voltage