AP Chem Provides a Formula Sheet
The AP Chemistry exam provides an equation and constants sheet with most formulas. This guide covers all of those plus key conceptual equations and the context for when to apply each one — so you understand them, not just memorize them.
Thermodynamics
| Equation | Variables | When to Use |
|---|
| q = mcΔT | q = heat; m = mass; c = specific heat; ΔT = temp change | Calorimetry problems; finding heat absorbed or released |
| ΔH°rxn = Σ ΔH°f(products) − Σ ΔH°f(reactants) | ΔH°f = standard enthalpy of formation | Calculating enthalpy of reaction from formation values |
| ΔS°rxn = Σ S°(products) − Σ S°(reactants) | S° = standard molar entropy | Calculating entropy change; more moles gas = more entropy |
| ΔG = ΔH − TΔS | T = temperature in Kelvin | Spontaneity: ΔG < 0 spontaneous, ΔG > 0 nonspontaneous |
| ΔG° = −RT ln K | R = 8.314 J/mol·K; K = equilibrium constant | Connecting thermodynamics to equilibrium |
| Hess's Law | ΔH is a state function — can add/reverse steps | When given a series of reactions to combine into a target reaction |
Equilibrium
| Concept | Equation / Rule | Notes |
|---|
| Equilibrium expression (Kc) | Kc = [products]^coeff / [reactants]^coeff | Pure solids and liquids are omitted from Kc |
| Kp (for gases) | Kp = Kc(RT)^Δn | Δn = moles gas products − moles gas reactants |
| Reaction quotient Q | Same form as Kc but uses initial concentrations | If Q < K, reaction proceeds forward; if Q > K, backward |
| Le Chatelier's Principle | Stress on system → equilibrium shifts to relieve stress | Add reactant → shift right; increase pressure → shift toward fewer moles gas |
| Solubility product Ksp | Ksp = [cation]^a [anion]^b | Larger Ksp = more soluble compound |
| ICE table method | Initial / Change / Equilibrium | Set up ICE table, write Kc expression, solve for x |
Acids and Bases
| Equation | What It Means | Usage |
|---|
| pH = −log[H⁺] | pH scale: 0–14, lower = more acidic | Calculate pH from [H⁺] |
| pOH = −log[OH⁻] | pOH scale, parallel to pH | Calculate pOH from [OH⁻] |
| pH + pOH = 14 | At 25°C, Kw = 1×10⁻¹⁴ | Convert between pH and pOH |
| Ka × Kb = Kw | Conjugate acid-base pairs | Find Kb of conjugate base if Ka is given |
Henderson-Hasselbalch
pH = pKa + log([A⁻]/[HA]) | pH of a buffer solution | Buffer problems; at half-equivalence point, pH = pKa |
| Titration equivalence point | Moles acid = moles base at equivalence | moles = M × V; solve for unknown concentration |
Kinetics
| Order | Rate Law | Integrated Rate Law | Half-Life |
|---|
| Zero Order | rate = k | [A] = [A]₀ − kt | t½ = [A]₀/2k |
| First Order | rate = k[A] | ln[A] = ln[A]₀ − kt | t½ = 0.693/k |
| Second Order | rate = k[A]² | 1/[A] = 1/[A]₀ + kt | t½ = 1/(k[A]₀) |
Arrhenius Equation: k = Ae^(−Ea/RT) — increasing temperature increases k (rate constant) because more molecules have enough energy to overcome activation energy Ea. Catalysts lower Ea without being consumed.
Electrochemistry
| Equation | Meaning | Notes |
|---|
| E°cell = E°cathode − E°anode | Standard cell potential | E°cell > 0 means spontaneous; look up reduction potentials in standard table |
| ΔG° = −nFE° | Free energy from cell potential | n = moles electrons; F = Faraday's constant = 96,485 C/mol |
| Nernst Equation | E = E° − (RT/nF)ln Q | Non-standard conditions; simplifies to E = E° − (0.0592/n)log Q at 25°C |
| Cell notation | Anode | anode solution || cathode solution | Cathode | Oxidation at anode (left); reduction at cathode (right) |
Gas Laws
| Law | Equation | When to Use |
|---|
| Ideal Gas Law | PV = nRT | R = 0.08206 L·atm/mol·K; most gas calculation problems |
| Combined Gas Law | P₁V₁/T₁ = P₂V₂/T₂ | Same gas, changing conditions |
| Dalton's Law | Ptotal = P₁ + P₂ + P₃ + ... | Partial pressures in a gas mixture |
| Graham's Law | rate₁/rate₂ = √(M₂/M₁) | Comparing effusion or diffusion rates of two gases |
| Molar volume at STP | 1 mole of ideal gas = 22.4 L at 0°C, 1 atm | Stoichiometry with gases at STP |
Bonding and Molecular Geometry (VSEPR)
| Electron Groups | Lone Pairs | Shape | Bond Angle |
|---|
| 2 | 0 | Linear | 180° |
| 3 | 0 | Trigonal planar | 120° |
| 3 | 1 | Bent | ~117° |
| 4 | 0 | Tetrahedral | 109.5° |
| 4 | 1 | Trigonal pyramidal | ~107° |
| 4 | 2 | Bent | ~104.5° |
| 5 | 0 | Trigonal bipyramidal | 90°/120° |
| 6 | 0 | Octahedral | 90° |
✅ Key Takeaways
- ΔG = ΔH − TΔS is the most important equation in thermodynamics — it connects enthalpy, entropy, and spontaneity.
- ICE tables are the mechanical tool for almost every equilibrium calculation — set them up before touching numbers.
- For acid-base calculations, the Henderson-Hasselbalch equation handles buffers; at the half-equivalence point, pH = pKa.
- Integrated rate laws distinguish reaction orders — a linear plot of ln[A] vs. time means first order; 1/[A] vs. time means second order.
- E°cell > 0 is spontaneous in electrochemistry, which corresponds to ΔG° < 0 and K > 1 — all three quantities are connected.