AP Chemistry cheat sheet

Coulomb potential energy between charges q1 and q2 separated by distance r is proportional to q1q2/r; opposite charges attract and like charges repel.

Photon energy is E = hν = hc/λ; the photoelectric effect requires photon energy at least equal to the work function Φ.

de Broglie wavelength is λ = h/(mv); wave behavior is significant for particles with small mass and low speed.

Quantum numbers: n is a positive integer; l = 0 to n−1; ml = −l to +l; ms = ±1/2; the Pauli exclusion principle forbids identical sets of all four.

Electron configuration follows Aufbau lowest energy, Hund maximum parallel spins in degenerate orbitals, and Pauli exclusion.

Periodic trends: atomic radius generally decreases across a period and increases down a group; ionization energy generally shows the opposite trend.

Mass spectrometry gives m/z peaks whose positions indicate isotopic masses and whose heights indicate relative abundances.

Average atomic mass = Σ(fractional abundance of isotope × isotopic mass).

Beer-Lambert law A = εbc relates absorbance to concentration for a fixed path length and wavelength.

Formal charge = valence electrons − nonbonding electrons − ½(bonding electrons); Lewis structures usually minimize formal charge.

VSEPR theory: electron domains repel and spread out; lone pairs occupy more space than bonding pairs and reduce bond angles.

Hybridization from steric number: 2 gives sp, 3 gives sp2, and 4 gives sp3; sigma bonds use hybrid orbitals and pi bonds use unhybridized p orbitals.

Molecular orbital bond order = (bonding electrons − antibonding electrons)/2; higher bond order generally means a shorter, stronger bond.

Molecular polarity depends on both bond dipoles and geometry; symmetric cancellation of dipoles can make a molecule nonpolar.

Resonance delocalizes electrons; the actual structure is a hybrid of equivalent resonance forms and is lower in energy than any single form.

Intermolecular forces: London dispersion in all substances, dipole-dipole in polar molecules, hydrogen bonding when H is bonded to N, O, or F, and ion-dipole in ion-molecule mixtures.

Structural isomers differ in connectivity; geometric isomers differ in spatial arrangement; enantiomers are nonsuperimposable mirror images.

Ideal gas law PV = nRT; at 0°C and 1 atm, one mole of ideal gas occupies about 22.4 L.

Dalton law: total pressure equals the sum of partial pressures, and P_i = x_i P_total for gas i.

Molarity M = moles solute/L solution; dilution satisfies M1V1 = M2V2 because solute moles are conserved.

Raoult law: P_A = x_A P°_A for a volatile component; a nonvolatile solute lowers vapor pressure.

Colligative properties depend on particle count: boiling point elevation ΔTb = Kb m and freezing point depression ΔTf = Kf m, with electrolyte factor i.

Phase-change energy uses q = nΔHfus or q = nΔHvap; temperature-change energy uses q = mCΔT.

Separation methods exploit properties: filtration uses particle size, distillation uses boiling point, and chromatography uses differing intermolecular interactions.

Henry law C = kP states that gas solubility in a liquid is proportional to the gas partial pressure above the liquid.

Balanced equations conserve atoms and charge; net ionic equations include only species that react and omit spectator ions.

Stoichiometry uses mole ratios from coefficients; the limiting reactant is completely consumed first and sets the maximum theoretical product.

Percent yield = (actual yield/theoretical yield) × 100%.

Acid-base neutralization: H+ + OH− → H2O; strong acids and strong bases dissociate completely in water.

Redox: oxidation is loss of electrons and reduction is gain; balance half-reactions by mass and charge, adding H2O and H+ or OH− as needed.

Solubility rules: most nitrates, alkali metal salts, and ammonium salts are soluble; most carbonates and hydroxides are insoluble; most sulfates are soluble except Ba2+, Pb2+, Ca2+, and Sr2+.

Combustion of a hydrocarbon with excess oxygen produces CO2 and H2O; balance carbon, hydrogen, then oxygen.

For gas reactions, use PV = nRT to convert pressure, volume, and temperature data into moles before applying mole ratios.

For aA → bB, reaction rate = −(1/a)Δ[A]/Δt = (1/b)Δ[B]/Δt; average rate uses a time interval and instantaneous rate uses the tangent.

Rate law: rate = k[A]^m[B]^n; exponents are determined experimentally, and overall order is m + n.

Integrated rate laws: zero order [A] = [A]0 − kt; first order ln[A] = ln[A]0 − kt; second order 1/[A] = 1/[A]0 + kt.

First-order half-life t1/2 = ln2/k is independent of initial concentration; zero- and second-order half-lives depend on initial concentration.

Arrhenius equation k = Ae^(−Ea/RT); a plot of ln k versus 1/T has slope −Ea/R.

Collision theory: a reaction occurs when collisions have sufficient energy and proper orientation; a catalyst lowers activation energy.

A mechanism is a sequence of elementary steps whose sum is the overall reaction; the rate-determining step controls the observed rate.

Intermediates are produced then consumed; catalysts are consumed then regenerated and do not appear in the overall balanced equation.

First law: ΔU = q + w; for pressure-volume work, w = −PΔV when work is done on the system.

Enthalpy change ΔH = q_p at constant pressure; exothermic reactions have ΔH < 0 and endothermic reactions have ΔH > 0.

Calorimetry: q = mCΔT for a substance and q = CcalΔT for a calibrated calorimeter.

Hess law: ΔH for an overall reaction equals the sum of step enthalpies; reversing a step changes the sign, and multiplying a step multiplies ΔH.

Standard reaction enthalpy: ΔH°rxn = Σ nΔH°f(products) − Σ mΔH°f(reactants); ΔH°f is zero for an element in its standard state.

Bond enthalpy estimate: ΔH ≈ Σ(bonds broken) − Σ(bonds formed).

Phase-change heat uses q = nΔHfus or q = nΔHvap; total heat for a heating curve is the sum of temperature-change and phase-change segments.

Entropy generally increases from solid to liquid to gas and with increasing temperature, volume, or number of particles.

At equilibrium, forward and reverse rates are equal and concentrations are constant but not necessarily equal; equilibrium is dynamic.

Equilibrium expressions omit pure solids and pure liquids; for gases, Kp = Kc(RT)^Δn, where Δn is moles gaseous products minus reactants.

Compare Q with K: Q < K favors the forward reaction, Q > K favors the reverse reaction, and Q = K means equilibrium.

Le Châtelier principle: adding or removing a species, changing pressure or volume, or changing temperature shifts the equilibrium to counteract the stress.

Changing temperature changes the value of K; adding a catalyst speeds approach to equilibrium but does not change K or the equilibrium position.

ICE tables track initial, change, and equilibrium concentrations; small K often permits approximations when x is negligible compared with initial concentration.

For a sparingly soluble salt, Ksp is the product of ion concentrations in a saturated solution, each raised to its stoichiometric coefficient.

Coupled equilibrium rules: reversing a reaction gives 1/K, multiplying coefficients by n gives K^n, and adding reactions multiplies their K values.

Acid-base definitions: Arrhenius produces H+ or OH− in water; Brønsted-Lowry is proton donor or acceptor; Lewis is electron-pair acceptor or donor.

pH = −log[H3O+], pOH = −log[OH−], and at 25°C pH + pOH = 14 with Kw = 1.0 × 10^−14.

Strong acids and bases ionize completely; weak acids and bases require Ka or Kb and an ICE table.

Percent ionization = ([H3O+]eq/[HA]initial) × 100% for a weak acid.

For a conjugate acid-base pair, Ka × Kb = Kw; a stronger acid has a weaker conjugate base.

Buffer pH from Henderson-Hasselbalch: pH = pKa + log([A−]/[HA]); a buffer is effective near pKa, roughly within ±1 pH unit.

Titration equivalence uses stoichiometric moles of acid and base; strong acid-strong base equivalence is pH 7, and weak acid half-equivalence has pH ≈ pKa.

Salt hydrolysis: the conjugate of a weak acid or weak base reacts with water; ions from strong acids or strong bases are spectator ions.

Indicators change color over approximately pKa ± 1; choose an indicator whose pKa is near the equivalence-point pH.

Gibbs free energy ΔG = ΔH − TΔS; a process is spontaneous at constant T and P when ΔG < 0, nonspontaneous when ΔG > 0, and at equilibrium when ΔG = 0.

ΔG° = −RT ln K and ΔG° = −nFE°cell relate standard free energy to equilibrium and cell potential.

Standard cell potential E°cell = E°cathode − E°anode; more positive reduction potentials indicate stronger oxidizing agents.

Galvanic cell: oxidation occurs at the anode and reduction at the cathode; electrons flow from anode to cathode through the external circuit.

Nernst equation: E = E° − (RT/nF)lnQ; at 25°C, E = E° − (0.0592/n)logQ.

Electrolytic cells use external electrical energy to drive nonspontaneous reactions; moles of electrons transferred equal It/F.

Second law: ΔS_univ > 0 for a spontaneous process; ΔS_univ = 0 at equilibrium.

E° values are intensive: reversing a half-reaction changes the sign but not the magnitude, and coefficients do not multiply E°.