Master the foundational concepts of chemistry: atomic structure, mole theory, gas laws, thermodynamics, equilibrium, and redox reactions. All formulas in one reference sheet for quick problem-solving.
n = given mass (g) / molar mass (g/mol)n is always in moles; divide grams by atomic/molecular weightn = N / NₐN = number of particles, Nₐ = Avogadro's number = 6.022 × 10²³M = dRT / Pd = density (g/L), R = 0.0821 L·atm/(mol·K), T in Kelvin, P in atm% element = (atomic mass × no. of atoms / molar mass) × 100Sum of all percentages = 100%n = molar mass / empirical formula massMolecular formula = (empirical formula)ₙmol A / mol B = coefficient A / coefficient BFrom balanced chemical equationCompare moles of reactant / stoichiometric coefficientSmallest ratio is limiting; controls theoretical yield% yield = (actual yield / theoretical yield) × 100Actual from experiment; theoretical from stoichiometryM = n / V(L) = moles of solute / litres of solutionTemperature-dependent; liters of final solution, not solventm = n / W(kg) = moles of solute / kg of solventTemperature-independent; uses mass of solvent onlyN = n × equivalents / V(L)Equivalents = n × valency for acids/bases/saltsχₐ = nₐ / (nₐ + nᵦ + ...)Sum of all mole fractions = 1; dimensionlessw/w % = (mass of solute / mass of solution) × 100Solution = solute + solventv/v % = (volume of solute / volume of solution) × 100For liquids; may not be additivem = M / (1 - M × M / 1000)M = molar mass of solute; holds for dilute solutionsM₁V₁ = M₂V₂Moles solute conserved; works for any molarity scalePV = nRTP (Pa or atm), V (m³ or L), n (mol), R = 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K), T (K)P₁V₁ = P₂V₂At constant T and n; inverse relationshipV₁/T₁ = V₂/T₂At constant P and n; direct relationshipP₁/T₁ = P₂/T₂At constant V and n; direct relationshipP₁V₁/T₁ = P₂V₂/T₂No mole change needed; compare two statesPₜₒₜₐₗ = P₁ + P₂ + P₃ + ...Each gas contributes its own pressure independentlyPgas = Kₕ × χsolute (in solution)Kₕ = Henry's law constant; Pgas = partial pressurer₁/r₂ = √(M₂/M₁)r = rate of diffusion; M = molar mass; lighter gas diffuses fasterd = PM / RTd (g/L); relates density to molar massc = λνc = 3 × 10⁸ m/s, λ = wavelength (m), ν = frequency (Hz)E = hν = hc/λh = 6.626 × 10⁻³⁴ J·s; higher frequency = higher energy1/λ = R∞(1/n₁² − 1/n₂²)R∞ = 1.097 × 10⁷ m⁻¹; n₁ < n₂ for emission; n₁ = 1 is Lyman, 2 is BalmerEₙ = −13.6/n² eVn = 1, 2, 3...; negative energy means bound stateλ = h / p = h / mvAll particles have wavelike behavior; h = Planck constantΔx × Δp ≥ h / 4πCannot know position and momentum simultaneously with certaintyIE = 13.6 × Z² / n² eVZ = atomic number, n = principal quantum numberψ² = probability density at a point in spaceψ = wave function; ψ² gives electron densityq = mcΔTm = mass (g), c = specific heat capacity (J/g·°C), ΔT = temperature change (K or °C)ΔH = q_p (at constant pressure)ΔH > 0 endothermic, ΔH < 0 exothermicΔH_reaction = Σ ΔH_products − Σ ΔH_reactantsEnthalpy is a state function; independent of reaction pathΔH°f = enthalpy change for 1 mol pure compound from elementsΔH°f(element) = 0; sum of ΔH°f gives ΔH°rxnΔS = q_rev / TS > 0 disorder increases; state functionΔG = ΔH − TΔSΔG < 0 spontaneous, ΔG > 0 non-spontaneous at that TΔG° = −RT ln KₑqR = 8.314 J/(mol·K); Kₑq = equilibrium constantq_solution + q_calorimeter + q_reaction = 0Heat lost = heat gained (closed system)Kc = [C]^c[D]^d / [A]^a[B]^bFor aA + bB ⇌ cC + dD; square brackets = molar concentration at equilibriumKp = P_C^c × P_D^d / P_A^a × P_B^bP = partial pressure (atm or Pa)Kp = Kc(RT)^ΔnΔn = (c + d) − (a + b) = change in moles of gasKw = [H⁺][OH⁻] = 10⁻¹⁴ at 25°CAlways 10⁻¹⁴ at 25°C regardless of acid/basepH = −log[H⁺]; pOH = −log[OH⁻]pH + pOH = 14 at 25°C; pH < 7 acidic, pH > 7 basicKa = [H⁺][A⁻] / [HA]Larger Ka = stronger acid; pKa = −log KaKb = [BH⁺][OH⁻] / [B]Ka × Kb = Kw for conjugate acid-base pairpH = pKa + log([A⁻]/[HA])For buffer solutions; [A⁻] = conjugate base, [HA] = weak acidBuffer resists pH change when small amounts of acid/base are addedBest when pH ≈ pKa; ratio [A⁻]/[HA] ≈ 1Adding common ion shifts equilibrium left, decreases solubilityE.g. adding NaCl to NaCl(aq) ⇌ Na⁺ + Cl⁻Element = 0; monatomic ion = charge; O usually −2; H usually +1; F always −1Sum of oxidation numbers = 0 (neutral) or charge (ion)Oxidation = loss of e⁻ (O.N. increases); Reduction = gain of e⁻ (O.N. decreases)OIL RIG; redox pair involved in every redox reactionBalance atoms except O & H → balance O with H₂O → balance H with H⁺ or OH⁻ → balance charge with e⁻Multiply half-reactions to equalize electrons lost/gainedEq.M = molar mass / valency change per atomFor redox, valency change = no. of e⁻ transferred per formula unitN = n / (Eq.M × V) × 1000; n_e⁻ = N × VElectrons gained = electrons lost in balanced equationAnode (−) | salt bridge | Cathode (+); read −→ + for conventional currentOxidation at anode (left), reduction at cathode (right)E°cell = E°cathode − E°anodeE° > 0 spontaneous, E° < 0 non-spontaneous; look up in tablesΔG° = −nFE°celln = moles of e⁻, F = Faraday constant = 96,500 C/molNₐ = 6.022 × 10²³ particles/molDefines the mole; used to count atoms, molecules, ionsVm = 22.4 L/mol (at 0°C, 1 atm)Useful for gas stoichiometry; nearly 24 L/mol at ~25°C, 1 atmR = 8.314 J/(mol·K) = 0.0821 L·atm/(mol·K) = 2 cal/(mol·K)Use first form for SI; second for gas law calculationsF = 96,500 C/mol e⁻Charge of 1 mole of electrons; coulomb = amp × second1 u = 1.66 × 10⁻²⁷ kgMass of one nucleon (proton or neutron); ¹²C standard = 12.000 u