Must-know sheet

Chemistry must-know sheet

The real AP Chemistry exam gives you a periodic table and a sheet of equations and constants for the whole exam, and you can use a scientific or graphing calculator on both sections. This sheet covers what that sheet doesn't: when to use each relationship, units, sign conventions, the solubility rule, acid and base strength, common ions and the rules you need to know by heart.

Which relationship to use

Units 1, 2, 3, 4, 5, 6, 7, 8, 9

Grams, moles or particles: n = m ÷ M, then × 6.022 × 10²³: Use this whenever a question gives a mass or asks for a number of atoms, molecules or ions. Every stoichiometry problem runs in moles, so convert to moles first.
A gas: PV = nRT: Use it when you know three of pressure, volume, moles and temperature for a gas. Temperature must be in kelvins, and the value of R must match your pressure and volume units.
A solution: moles = M × V (in liters): Use it for any dissolved reactant, including titrations. Change mL to L before you multiply.
Adding only water: M₁V₁ = M₂V₂: Dilution keeps the moles of solute the same, so concentration × volume is unchanged. Don't use it when a reaction happens; do stoichiometry with moles instead.
Heat with a temperature change: q = mcΔT: Use it when a substance warms or cools without changing phase, and for calorimetry. Use q = n × ΔH (fusion or vaporization) instead while a phase change is happening, because the temperature stays flat.
ΔH of a reaction: pick the method that fits the data: Given steps that add up to the reaction, use Hess's law. Given a table of ΔH°f values, use products minus reactants; given bond enthalpies, use bonds broken minus bonds formed, which is only an estimate.
Favorability: ΔG° from whichever data you have: From ΔH° and ΔS°, use ΔG° = ΔH° − TΔS°; from K, use ΔG° = −RT ln K; from a cell potential, use ΔG° = −nFE°. All three must agree: ΔG° < 0, K > 1 and E° > 0 go together.
pH: name the species in the solution first: Strong acid or base: pH comes straight from the concentration; weak acid or base alone: ICE table with Ka or Kb; weak acid with its conjugate base: Henderson–Hasselbalch. If an acid and a base were mixed, react them completely first, then decide.
Rates: initial-rates table or concentration–time data?: A table of trials with different starting concentrations gives the orders in the rate law. Concentration measured over time in one run gives the order from which plot is a straight line ([A], ln[A] or 1/[A] against t).
Concentration from light: A = εbc: Use it when a question gives absorbance. Make a calibration line of absorbance against known concentrations at one wavelength, then read the unknown off the line.

Units, constants and conversions

Units 1, 2, 3, 4, 5, 6, 7, 8, 9

Kelvin: K = °C + 273: Use kelvins in PV = nRT, ΔG° = ΔH° − TΔS°, ΔG° = −RT ln K and any kinetic-energy reasoning. A temperature change ΔT is the same number in °C and K.
Volume: 1 L = 1000 mL = 1000 cm³: Molarity and the gas constant use liters, so divide mL by 1000. 1 mL and 1 cm³ are the same volume.
Pressure: 1 atm = 760 torr = 760 mm Hg ≈ 101.3 kPa: Convert pressure to match the R value you use. With R = 0.08206 L·atm/(mol·K), pressure must be in atm and volume in L.
Two values of R: Use 0.08206 L·atm/(mol·K) for gas problems with pressure in atm and 8.314 J/(mol·K) for energy equations such as ΔG° = −RT ln K. Picking the wrong one is a very common mistake.
J versus kJ: ΔH° and ΔG° are usually in kJ/mol, but S° and ΔS° are in J/(mol·K). Divide ΔS° by 1000 before using ΔG° = ΔH° − TΔS°, and divide ΔG° from −RT ln K or −nFE° by 1000 to get kJ.
“kJ/mol” means per mole of reaction: A ΔH° of −890 kJ/mol goes with the amounts in the balanced equation as written. To find the heat for a real sample, find the moles that react and scale using the coefficients.
Water: c ≈ 4.18 J/(g·°C) and density ≈ 1.00 g/mL: Dilute water solutions are usually treated as having water's specific heat and density, so 50.0 mL of solution is about 50.0 g. Use the total mass of solution in q = mcΔT.
Light: 1 nm = 10⁻⁹ m, c = 3.00 × 10⁸ m/s, h = 6.626 × 10⁻³⁴ J·s: Convert nanometers to meters before using c = λν. E = hν gives joules per photon; multiply by 6.022 × 10²³ for joules per mole of photons.
Units of the rate constant k depend on overall order: Zero order: M/s; first order: s⁻¹; second order: M⁻¹·s⁻¹. The units of k are a quick check of the overall order.
Beer–Lambert units: Absorbance A has no units, path length b is in cm (usually a 1.00 cm cuvette), concentration c is in M, so ε is in M⁻¹·cm⁻¹.
Electricity: 1 A = 1 C/s, F = 96,485 C per mole of electrons, 1 V = 1 J/C: Charge q = I × t with time in seconds. With E in volts and F in C/mol, ΔG° = −nFE° comes out in joules.
K, Q, Ksp, Ka and Kb are written without units: Write equilibrium constants as plain numbers. pH and pOH have no units either.
Significant figures in logs: The number of decimal places in a pH equals the number of significant figures in the concentration: [H₃O⁺] = 2.5 × 10⁻⁴ M gives pH = 3.60.

Sign conventions

Units 4, 5, 6, 7, 8, 9

q and ΔH: positive means the system absorbs energy: Endothermic: ΔH > 0 and the surroundings cool. Exothermic: ΔH < 0 and the surroundings warm.
Calorimetry: q(reaction) = −q(solution): If the solution's temperature rises, the solution gained heat, so the reaction released it and ΔH is negative. Divide q(reaction) by the moles that reacted to get ΔH per mole.
Breaking bonds is always endothermic: Bond enthalpies are listed as positive numbers, the energy needed to break the bond. Forming the same bond releases that much energy.
Reversing a reaction: ΔH, ΔS, ΔG and E° all change sign, and the new K is 1/K.
Multiplying a reaction by n: ΔH, ΔS and ΔG are multiplied by n, and K is raised to the power n. E° does not change, because voltage doesn't depend on how much reacts.
ΔS > 0 means more spread out: Positive entropy change: more gas moles, solid to liquid to gas, mixing, expansion or heating.
ΔG < 0 means thermodynamically favored: ΔG° > 0 means the reverse reaction is favored under standard conditions. ΔG = 0 (not ΔG°) means the system is at equilibrium.
Rates are reported as positive numbers: A reactant's concentration falls, so Δ[reactant]/Δt is negative; put a minus sign in front to report its rate as positive.
Slopes of the straight-line rate plots: [A] against t and ln[A] against t both have slope −k; 1/[A] against t has slope +k.
Oxidation numbers: An oxidation number that goes up means that atom was oxidized (it lost electrons); one that goes down means it was reduced (it gained electrons).
Electrodes and electron flow: Oxidation happens at the anode and reduction at the cathode, in both galvanic and electrolytic cells. Electrons flow through the wire from anode to cathode.
E°cell = E°(cathode) − E°(anode): Use both values as written in a reduction table. A positive E°cell means the cell reaction is thermodynamically favored.

Moles, composition and stoichiometry

Units 1, 3, 4

Average atomic mass = Σ (isotope mass × fractional abundance): Use the peak positions and relative heights of a mass spectrum. The average sits closest to the most abundant isotope.
Percent by mass = (mass of element ÷ mass of compound) × 100: From a formula, use (number of atoms × atomic mass) ÷ molar mass × 100. A pure compound always has the same percent composition (the law of definite proportions).
Empirical formula in four steps: Treat percents as grams in a 100 g sample, convert each to moles, divide by the smallest number of moles, then multiply to get whole numbers (× 2 for a ratio near 1.5, × 3 for one near 1.33 or 1.67).
Molecular formula = empirical formula × (molar mass ÷ empirical formula mass): The ratio must be a whole number. CH₂O with a molar mass of 180 g/mol gives a multiplier of 6, so the molecular formula is C₆H₁₂O₆.
Purity of a mixture: Convert the measured mass of one element to moles, use the formula to get moles of the compound that contains it, convert to grams, then divide by the sample's mass. A mixture can have any composition; a pure substance can't.
Stoichiometry road map: Given amount → moles → mole ratio from the balanced coefficients → moles wanted → the units asked for. Grams, gas data (PV = nRT) and solution data (M × V) all plug into the same middle step.
Limiting reactant: Find the moles of product each reactant could make (or divide each reactant's moles by its coefficient); the smallest result marks the limiting reactant. The excess left over equals what you started with minus what reacted.
Equivalence point in a titration: Moles of titrant (M × V) × mole ratio = moles of analyte. M(acid) × V(acid) = M(base) × V(base) only works when the acid and base react 1 : 1.
Gas volumes follow the coefficients: At the same temperature and pressure, equal volumes of gases hold equal numbers of moles, so in N₂ + 3H₂ → 2NH₃, 1 L of N₂ reacts with 3 L of H₂.
Particle diagrams of reactions: Keep every atom, match the coefficient ratios, and show any excess reactant that is left over. Don't break polyatomic ions or molecules that don't react.

Atoms, electrons, trends and light

Units 1, 3

Coulomb's law explains everything here: The attraction between charges grows with the size of the charges and weakens with distance (force ∝ q₁q₂/r²). Explain trends by naming both: the number of protons (or effective nuclear charge) and the distance or shielding of the electron.
Filling order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p: Fill the lowest-energy subshell first: s holds 2, p holds 6, d holds 10. Noble-gas shorthand is fine, for example Fe = [Ar] 4s² 3d⁶. Exceptions like Cr and Cu aren't tested.
Cations lose electrons from the highest shell first: Transition metals lose their 4s electrons before 3d, so Fe²⁺ = [Ar] 3d⁶. Anions add electrons to the next open subshell, so Cl⁻ = [Ar].
Reading a photoelectron spectrum (PES): Each peak is one subshell. A peak's binding energy is higher for inner electrons and for atoms with more protons, and its height is proportional to the number of electrons in that subshell. Check which way the energy axis runs, because graphs differ.
Atomic radius: Gets smaller across a period (more protons pull the same shell closer) and larger down a group (more shells). A cation is smaller than its atom and an anion is larger.
Isoelectronic ions: more protons means smaller: Ions with the same number of electrons shrink as nuclear charge rises: O²⁻ > F⁻ > Na⁺ > Mg²⁺.
Ionization energy: Rises across a period and falls down a group, the opposite of radius. Electrons closer to a more highly charged nucleus are harder to remove.
Successive ionization energies: look for the big jump: A huge jump appears once all valence electrons are gone and the next electron comes from an inner shell. Mg has a big jump between its 2nd and 3rd ionization energies, so it has 2 valence electrons.
Electronegativity and electron affinity: Electronegativity rises across a period and falls down a group; fluorine is the highest. More energy is generally released when an electron is added to atoms toward the right of a period, such as the halogens.
Valence electrons and typical ion charges: Main-group elements in the same group have the same number of valence electrons, so they form similar compounds and ions with the same charge (see Common ions).
c = λν and E = hν: Wavelength and frequency are inversely related. Shorter wavelength means higher frequency and more energy per photon, and the energy of an absorbed or emitted photon equals the energy difference between the two levels.
What each kind of light does: Microwaves make molecules rotate, infrared makes bonds vibrate, and visible and ultraviolet light move electrons to higher energy levels. Energy increases from radio to microwave to infrared to visible to ultraviolet to X-ray.

Bonding, Lewis diagrams and molecular shape

Unit 2

Bond type from the elements: Metal + nonmetal: ionic. Nonmetal + nonmetal: covalent, polar if the electronegativities differ and nonpolar if they're equal or nearly so. Metal + metal: metallic, with delocalized electrons.
Potential energy against distance between nuclei: The bottom of the well is the bond length, and its depth is the bond energy. Pushing the nuclei closer than that makes the energy shoot up from repulsion; double and triple bonds give shorter, deeper wells.
Ionic attraction: bigger charges and smaller ions win: Compare the ions' charges first, then their sizes. MgO has a much stronger attraction and a higher melting point than NaCl, and NaF is stronger than NaCl.
Alloys: Substitutional: atoms of similar size swap places, as zinc does for copper in brass. Interstitial: much smaller atoms fill the gaps, as carbon does in iron to make steel, which makes the metal harder and less malleable.
Drawing a Lewis diagram: Count all valence electrons (add one per negative charge, subtract one per positive charge), put the least electronegative atom in the center (never H), connect with single bonds, complete the outer atoms' octets, put leftovers on the central atom, then form double or triple bonds if the central atom is short.
Octet exceptions: H has only 2 electrons. B (as in BF₃) can have 6 and Be can have 4. Atoms in period 3 and below can have more than 8, as in PCl₅, SF₆ and XeF₄. A particle with an odd number of electrons, such as NO, can't give every atom an octet.
Formal charge = valence electrons − lone-pair electrons − number of bonds: The formal charges must add up to the particle's overall charge. The best diagram has formal charges closest to zero, with any negative one on the more electronegative atom.
Resonance: When equivalent diagrams differ only in where a double bond goes, the real particle is a blend: all those bonds are the same length, between single and double. Each N–O bond in NO₃⁻ has a bond order of 1⅓, and each O–O bond in O₃ is 1½.
2 and 3 electron domains: Count each lone pair and each bond (single, double or triple) as one domain around the central atom. 2 domains: linear, 180°. 3 domains: trigonal planar, 120°, or bent (just under 120°) with one lone pair.
4 electron domains: Tetrahedral, 109.5° (CH₄); trigonal pyramidal with one lone pair, about 107° (NH₃); bent with two lone pairs, about 104.5° (H₂O). Lone pairs push bonds closer together.
5 and 6 electron domains: 5: trigonal bipyramidal (90° and 120°), seesaw, T-shaped or linear as lone pairs replace bonds. 6: octahedral (90°), square pyramidal with one lone pair, square planar with two.
Hybridization: 2 domains sp, 3 sp², 4 sp³: Count electron domains around the atom, including lone pairs. Hybridization with d orbitals (5 and 6 domains) isn't tested.
Sigma and pi bonds: A single bond is 1 σ. A double bond is 1 σ + 1 π. A triple bond is 1 σ + 2 π.
Is the molecule polar?: It's polar if it has polar bonds arranged unevenly, such as with lone pairs on the central atom or different outer atoms (H₂O, NH₃, CH₂Cl₂). Symmetric shapes with identical outer atoms are nonpolar even with polar bonds (CO₂, BF₃, CH₄, XeF₄).

Intermolecular forces, gases and solutions

Unit 3

London dispersion forces act between all particles: They get stronger with more electrons and a larger, more polarizable electron cloud, and with more surface contact (a long chain beats a compact, branched isomer).
Dipole–dipole forces: Act between polar molecules, in addition to dispersion forces.
Hydrogen bonding: Needs H bonded directly to N, O or F in one molecule, attracted to a lone pair on N, O or F in another. CH₃OCH₃ has no H–O bond, so it can't hydrogen bond with itself; CH₃CH₂OH can.
Ion–dipole forces: Attractions between ions and polar molecules such as water; they hold dissolved ions in solution.
Comparing IMF strength: For molecules of similar size, hydrogen bonding > dipole–dipole > dispersion only. But a large nonpolar molecule can beat a small polar one: octane (C₈H₁₈) boils at a higher temperature than water.
Stronger IMFs mean…: Higher melting and boiling points, a larger enthalpy of vaporization, and a lower vapor pressure. A liquid boils when its vapor pressure equals the outside pressure.
Boiling breaks IMFs, not covalent bonds: When water boils, whole H₂O molecules move apart; no H₂ or O₂ forms. Say “attractions between molecules”, not “bonds”, in these answers.
Ionic and covalent network solids: Ionic solids: high melting points, brittle, conduct only when melted or dissolved. Covalent network solids (diamond, SiO₂): very hard with very high melting points; graphite is the exception that conducts.
Molecular and metallic solids: Molecular solids: low melting points, soft, don't conduct. Metals: conduct as solids, and are malleable and ductile because the electron sea lets atoms slide.
PV = nRT and the combined form: When the moles stay fixed, P₁V₁/T₁ = P₂V₂/T₂ (T in K). Pressure doubles if the kelvin temperature doubles at constant volume.
Partial pressures: P(total) = P(A) + P(B) + …, and P(A) = X(A) × P(total), where X(A) is the mole fraction of A.
Molar mass or density of a gas: M = mRT ÷ (PV) = dRT ÷ P: This is PV = nRT with n replaced by mass ÷ molar mass. At the same temperature and pressure, a gas with a larger molar mass has a greater density.
Kinetic molecular theory: Average kinetic energy is proportional to kelvin temperature. At the same temperature all gases have the same average kinetic energy, so lighter molecules move faster on average.
Maxwell–Boltzmann speed graphs: At higher temperature, or for a lighter gas, the curve is flatter and wider and its peak moves to higher speeds. The area under the curve (the number of particles) stays the same.
Real gases: They deviate most at high pressure, where particle volume matters, and at low temperature, where attractions matter. Attractions make pressure lower than ideal; particle volume makes volume larger than ideal. Small, nonpolar gases such as He behave most ideally.
Molarity counts ions too: M = moles of solute ÷ liters of solution. 0.10 M CaCl₂ is 0.10 M Ca²⁺ and 0.20 M Cl⁻.
“Like dissolves like”: Ionic and polar solutes dissolve in polar solvents such as water; nonpolar solutes dissolve in nonpolar solvents. Solutes dissolve best when the new solute–solvent attractions are similar in strength to the ones broken.
Drawing a dissolved ionic compound: Show separate ions in the right ratio, with water's partly negative O pointing toward cations and its partly positive H atoms pointing toward anions. Molecular solutes such as sugar stay as whole molecules.
Chromatography and distillation: In chromatography, a component more attracted to the stationary phase moves more slowly and travels a shorter distance. In distillation, the component with weaker IMFs has the higher vapor pressure and boils off first.
Beer–Lambert law: A = εbc: At a fixed wavelength and path length, absorbance is directly proportional to concentration. Measure at the wavelength of maximum absorbance; fingerprints or scratches on the cuvette raise the absorbance, so the calculated concentration comes out too high.

Reactions, net ionic equations and solubility

Unit 4

The solubility rule to memorize: Every compound containing Na⁺, K⁺, NH₄⁺ or NO₃⁻ dissolves in water. For any other salt, the question will tell you or show you whether it dissolves.
Writing a net ionic equation: Split only dissolved strong electrolytes into ions: soluble ionic compounds, strong acids and strong bases. Keep solids, liquids, gases, water and weak acids and bases (HF, CH₃COOH, NH₃) together, cancel the spectator ions, then check that atoms and charge balance.
Net ionic equations to know: Strong acid + strong base: H₃O⁺ + OH⁻ → 2H₂O; weak acid + strong base: HA + OH⁻ → A⁻ + H₂O; strong acid + weak base: H₃O⁺ + NH₃ → NH₄⁺ + H₂O; precipitation: Ag⁺ + Cl⁻ → AgCl(s).
Three main reaction types: Precipitation: ions form an insoluble solid. Acid–base: a proton (H⁺) moves. Redox: electrons move, so some oxidation numbers change.
Combustion: A redox reaction with O₂. A hydrocarbon burned completely gives CO₂ and H₂O.
Physical versus chemical change: A chemical change makes new substances by breaking and forming bonds; a physical change only changes attractions between particles. Clues to a chemical change: gas, precipitate, color change, or heat or light. Dissolving a salt can be argued either way.
Oxidation number rules: Free elements are 0, and a monatomic ion equals its charge. F is −1; O is usually −2 (−1 in peroxides); H is +1 with nonmetals and −1 in metal hydrides. The total equals the particle's charge.
Oxidation is loss, reduction is gain: Oxidation loses electrons and reduction gains them, and the two always happen together. The electrons lost must equal the electrons gained.
Balancing a redox reaction in acid: Split into half-reactions. In each, balance atoms other than O and H, then O with H₂O, then H with H⁺, then charge with electrons. Multiply so the electrons match, add the halves and cancel anything on both sides.
Brønsted–Lowry acids and bases: An acid donates H⁺ and a base accepts it. A conjugate pair differs by one H⁺ (HF and F⁻, NH₄⁺ and NH₃). Amphiprotic species such as H₂O and HCO₃⁻ can do either.
Titration vocabulary: The titrant (known concentration) goes in the buret and the analyte is in the flask. The equivalence point is when exactly enough titrant has been added; the endpoint is when the indicator changes color.

Common ions

Units 1, 2, 4, 8

Main-group ion charges by group: Group 1: 1+; group 2: 2+; Al: 3+; N and P: 3−; O and S: 2−; group 17 halogens: 1−. Noble gases don't form ions.
Metal ions you'll see often: Ag⁺, Zn²⁺, Cu⁺ and Cu²⁺, Fe²⁺ and Fe³⁺, Pb²⁺, Mn²⁺, Ni²⁺. A Roman numeral gives the charge: iron(III) chloride is FeCl₃.
Positive polyatomic ions: Ammonium NH₄⁺ and hydronium H₃O⁺.
1− polyatomic ions: Hydroxide OH⁻, nitrate NO₃⁻, nitrite NO₂⁻, acetate CH₃COO⁻ (also written C₂H₃O₂⁻), cyanide CN⁻, permanganate MnO₄⁻, hydrogen carbonate (bicarbonate) HCO₃⁻, hydrogen sulfate HSO₄⁻, dihydrogen phosphate H₂PO₄⁻, thiocyanate SCN⁻.
Chlorine oxyanions (all 1−): Hypochlorite ClO⁻, chlorite ClO₂⁻, chlorate ClO₃⁻, perchlorate ClO₄⁻. The same prefixes and endings work for bromine and iodine.
2− and 3− polyatomic ions: Sulfate SO₄²⁻, sulfite SO₃²⁻, carbonate CO₃²⁻, chromate CrO₄²⁻, dichromate Cr₂O₇²⁻, oxalate C₂O₄²⁻, hydrogen phosphate HPO₄²⁻, peroxide O₂²⁻, and phosphate PO₄³⁻.
-ate and -ite: An -ite ion has one fewer oxygen than the -ate ion with the same charge (sulfate SO₄²⁻, sulfite SO₃²⁻). Adding H⁺ to an anion makes its charge one less negative (CO₃²⁻ becomes HCO₃⁻).
Ions that change pH: Basic: anions of weak acids, such as F⁻, CH₃COO⁻, CN⁻, NO₂⁻, ClO⁻, CO₃²⁻ and PO₄³⁻. Acidic: NH₄⁺. No effect: Na⁺, K⁺, Ca²⁺ and the anions of strong acids (Cl⁻, Br⁻, I⁻, NO₃⁻, ClO₄⁻).

Kinetics

Unit 5

Rates of different species follow the coefficients: For aA → dD, rate = −(1/a)Δ[A]/Δt = (1/d)Δ[D]/Δt. In 2NO₂ → 2NO + O₂, NO₂ is used up twice as fast as O₂ forms.
Rate law: rate = k[A]ᵐ[B]ⁿ: The orders m and n come from experiments, not from the overall equation's coefficients. The overall order is m + n, and k changes only with temperature (or a catalyst).
Finding orders from initial rates: Pick two trials where only one concentration changes. If that concentration doubles, a rate that stays the same means order 0, a rate that doubles means order 1, and a rate that quadruples means order 2 (in general, rate ratio = concentration ratio raised to the order). Then plug one trial in to solve for k.
Which plot is straight tells the order: Zero order: [A] against t is linear. First order: ln[A] against t is linear. Second order: 1/[A] against t is linear.
First-order half-life: t½ = 0.693/k: Only first-order reactions have a constant half-life that doesn't depend on concentration. After n half-lives, (½)ⁿ of the reactant remains: 25% after 2, 12.5% after 3.
Collision model: A collision makes products only if the particles have at least the activation energy and hit with the right orientation.
Why heating speeds reactions: At a higher temperature a larger fraction of collisions have energy at or above Ea (the area to the right of Ea on the Maxwell–Boltzmann curve grows), and collisions also happen more often. So k increases; this is qualitative only on the exam.
Energy profile: Ea = transition-state energy − reactant energy, and ΔH = product energy − reactant energy. The reverse reaction's Ea = forward Ea − ΔH, so an exothermic reaction has a larger reverse Ea.
Elementary steps: A single step's rate law comes straight from its coefficients: for A + B → C, rate = k[A][B], and for 2A → C, rate = k[A]². Steps needing three particles to collide at once are rare.
Checking a proposed mechanism: The steps must add up to the overall equation, and the rate law they predict must match the experimental one. An intermediate is made in one step and used up later; a catalyst is used up in one step and made again later.
Slow first step: The rate law of the whole reaction is just the rate law of that slow step.
Fast equilibrium, then slow step: If the slow step's rate law contains an intermediate, use the fast step's equilibrium to replace it with reactants. For 2NO ⇌ N₂O₂ (fast) then N₂O₂ + O₂ → 2NO₂ (slow): [N₂O₂] = K[NO]², so rate = k[NO]²[O₂].
Multistep energy profiles: There is one hump per step, and intermediates sit in the dips between humps. The step with the largest activation energy (measured from the dip before it) is usually the slow step.
Catalysts: A catalyst provides a new pathway with a lower activation energy and is regenerated. It speeds up the forward and reverse reactions equally, so it changes neither ΔH nor K nor the equilibrium amounts. Types: enzymes, acid–base catalysis and surface catalysis.

Thermochemistry

Unit 6

Exothermic or endothermic?: Exothermic: energy flows out of the system, the surroundings warm, ΔH < 0, and products sit lower on an energy diagram. Endothermic: the reverse.
Thermal equilibrium: Heat flows from the warmer object to the cooler one until their temperatures (average kinetic energies) are equal. Heat lost by the hot object = heat gained by the cold one.
Calorimetry steps: Find q(solution) = mcΔT using the total solution mass, set q(reaction) = −q(solution), then divide by the moles of the limiting reactant to get ΔH in kJ/mol.
Calorimetry errors: Heat leaking to or from the surroundings makes the measured temperature change too small, so the calculated size of ΔH comes out too small.
Heating curves: Sloped parts: one phase warms (q = mcΔT). Flat parts: the phase changes at constant temperature (q = n × ΔH of fusion or vaporization). ΔH of vaporization is larger than ΔH of fusion.
Phase changes and their signs: Melting and boiling absorb energy (positive ΔH). Freezing and condensing release the same amount (negative ΔH).
Scaling ΔH: ΔH is proportional to the amount that reacts: double the moles, double the heat. Use the coefficient of the substance you were given to set up the ratio.
Bond enthalpies: ΔH ≈ Σ(bonds broken) − Σ(bonds formed): Count every bond in the Lewis diagrams of reactants and products. The answer is only an estimate because tabulated bond enthalpies are averages.
Enthalpies of formation: ΔH° = Σ n·ΔH°f(products) − Σ n·ΔH°f(reactants): Multiply each ΔH°f by its coefficient. An element in its standard state (O₂(g), C(graphite), Br₂(l), Fe(s)) has ΔH°f = 0, and H₂O(l) and H₂O(g) have different values.
Hess's law: Rearrange the given steps so they add up to the target reaction: reverse a step and flip the sign of its ΔH, multiply a step and multiply its ΔH. Substances on both sides cancel.
Energy of dissolving: Separating the solute particles and making room in the solvent take energy; forming solute–solvent attractions releases energy. The overall sign depends on which is larger.

Equilibrium and solubility (Ksp)

Unit 7

Dynamic equilibrium: The forward and reverse rates are equal, so concentrations stop changing, but they are usually not equal to each other and particles keep reacting.
Writing K or Q: Products over reactants, each raised to its coefficient. Leave out pure solids and pure liquids, including water as the solvent. Kc uses molarities and Kp uses partial pressures.
Q versus K: Q < K: the reaction goes forward, making more products. Q > K: it goes in reverse. Q = K: it's at equilibrium.
Size of K: K much greater than 1: mostly products at equilibrium. K much less than 1: mostly reactants.
Changing the equation changes K: Reverse it: 1/K. Multiply the coefficients by n: Kⁿ. Add reactions: multiply their K values.
ICE tables: Use concentrations (M) or pressures, not moles, unless the volume is 1 L. The Change row follows the coefficients (−x, −2x, +x …), and only the Equilibrium row goes into K.
Small-x shortcut: When K is small compared with the starting concentration, treat C − x as C. Check afterward that x is under about 5% of C.
Le Châtelier: adding or removing a substance: Adding a reactant or removing a product shifts the reaction toward products, and the reverse. Q changes but K does not. Adding more of a pure solid or liquid doesn't shift it.
Le Châtelier: volume and dilution: Shrinking a gas mixture's volume shifts it toward fewer moles of gas; if both sides have equal gas moles, there's no shift. Adding an inert gas at constant volume doesn't shift it. Diluting a solution shifts toward the side with more dissolved particles.
Le Châtelier: temperature is the only thing that changes K: Treat heat as a reactant for an endothermic reaction and as a product for an exothermic one. Heating an endothermic reaction shifts it forward and increases K; heating an exothermic one decreases K.
Ksp expressions: The solid is left out: for CaF₂(s) ⇌ Ca²⁺ + 2F⁻, Ksp = [Ca²⁺][F⁻]².
Molar solubility s from Ksp: 1 : 1 salts (AgCl): Ksp = s²; 1 : 2 or 2 : 1 salts (CaF₂, Ag₂CrO₄): Ksp = 4s³; 1 : 3 salts: Ksp = 27s⁴. Compare solubilities directly from Ksp only for salts with the same ion ratio.
Will a precipitate form?: Find the ion concentrations after mixing (remember the total volume grows), calculate Q, and compare: Q > Ksp means a precipitate forms; Q ≤ Ksp means none does.
Common-ion effect: A salt dissolves less in a solution that already contains one of its ions. Put that ion's starting concentration in the ICE table: AgCl is less soluble in NaCl solution than in pure water.
Equilibrium particle diagrams: Count particles and divide by the volume to get concentrations, then compare Q with K. If the counts don't change between two later snapshots, the system is at equilibrium.

Acid–base strength

Units 4, 8

The six strong acids: HCl, HBr, HI, HNO₃, HClO₄ and H₂SO₄ ionize completely in water (for H₂SO₄, only the first proton). Treat every other acid as weak unless you're told otherwise.
Strong bases: Group 1 hydroxides (LiOH, NaOH, KOH) and group 2 hydroxides such as Ca(OH)₂, Sr(OH)₂ and Ba(OH)₂. Count the OH⁻: Ba(OH)₂ gives 2 OH⁻ per formula unit.
Common weak acids: HF, HNO₂, HClO, HCN, CH₃COOH and other carboxylic acids (–COOH), H₂CO₃, H₃PO₄ and NH₄⁺.
Common weak bases: NH₃, amines such as CH₃NH₂, and the conjugate bases of weak acids, such as F⁻, CH₃COO⁻ and CO₃²⁻.
Strong versus concentrated: Strong and weak describe how completely an acid ionizes; concentrated and dilute describe how much is dissolved. A dilute strong acid can have a lower pH than a concentrated weak one.
Conjugate pairs: Ka × Kb = Kw: The stronger the acid, the weaker its conjugate base. At 25 °C, pKa + pKb = 14.00. Conjugate bases of strong acids (Cl⁻, NO₃⁻) don't act as bases in water.
Percent ionization = [H₃O⁺] at equilibrium ÷ starting [HA] × 100: It's 100% for a strong acid and small for a weak one. Diluting a weak acid raises its percent ionization even though its pH goes up.
pH of a salt solution: Anion from a weak acid makes the solution basic (NaF, CH₃COONa). Cation from a weak base makes it acidic (NH₄Cl). Both ions from a strong acid and a strong base: neutral (NaCl, KNO₃).
Structure and acid strength: An acid is stronger when its conjugate base is more stable. Electronegative atoms near the acidic H pull charge away (CCl₃COOH is stronger than CH₃COOH), more O atoms on an oxyacid help (HClO₄ > HClO₃ > HClO₂ > HClO), and resonance spreads out the negative charge (as in a carboxylate).
Polyprotic acids: They give up protons one at a time, and Ka₁ > Ka₂ > Ka₃. The first ionization usually sets the pH, and a titration curve can show one equivalence point for each proton.

pH, titrations and buffers

Unit 8

pH = −log[H₃O⁺], pOH = −log[OH⁻], Kw = [H₃O⁺][OH⁻]: At 25 °C, Kw = 1.0 × 10⁻¹⁴ and pH + pOH = 14.00. To go back, raise 10 to the power −pH to get [H₃O⁺]. Each drop of 1 pH unit is 10 times more H₃O⁺.
Neutral means [H₃O⁺] = [OH⁻], not always pH 7: Kw grows as water warms, so neutral water above 25 °C has a pH below 7 but is still neutral.
Strong acid or base pH in one step: 0.010 M HCl: [H₃O⁺] = 0.010 M, pH = 2.00. 0.010 M Ba(OH)₂: [OH⁻] = 0.020 M, pOH = 1.70, pH = 12.30.
Weak acid pH: Ka = x² ÷ (C − x): x is [H₃O⁺]. If x is small, x ≈ √(Ka × C): 0.10 M CH₃COOH with Ka = 1.8 × 10⁻⁵ gives x = 1.3 × 10⁻³ M, pH = 2.87 and 1.3% ionization. A weak base works the same way with Kb, giving [OH⁻] first.
Mixing an acid and a base: react first, then decide: Do the stoichiometry in moles. Leftover strong acid or base: its moles ÷ total volume sets the pH; weak acid and its conjugate base both left: a buffer; only a conjugate base left: basic, use Kb; only a conjugate acid left: acidic, use Ka.
Weak acid titrated with strong base: the landmarks: Starts above a strong acid's pH, rises slowly through the buffer region, reaches pH = pKa at the half-equivalence point, and has an equivalence-point pH above 7. A strong acid with a strong base has its equivalence point at pH 7; a weak base with a strong acid, below 7.
Equivalence volume depends only on moles: A weak and a strong acid with the same moles need the same volume of base to reach equivalence. Strength changes the shape of the curve, not where equivalence falls.
pH compared with pKa: pH < pKa: mostly HA. pH > pKa: mostly A⁻. pH = pKa: equal amounts.
Choosing an indicator: An indicator changes color near its own pKa, so choose one whose pKa is close to the equivalence-point pH. Phenolphthalein (changes around pH 8–10) suits a weak acid titrated with a strong base.
What a buffer is and how it works: Large, similar amounts of a weak acid and its conjugate base. Added acid is used up by the base (H₃O⁺ + A⁻ → HA + H₂O); added base is used up by the acid (OH⁻ + HA → A⁻ + H₂O).
Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]): You can use moles in place of concentrations, since both are in the same volume. Equal amounts give pH = pKa; a 10 : 1 ratio of A⁻ to HA gives pH = pKa + 1.
Making a buffer: Choose a weak acid whose pKa is close to the pH you want. You can also add strong base to a weak acid: adding half as many moles of OH⁻ as HA gives pH = pKa.
Buffer capacity: A more concentrated buffer has the same pH but absorbs more added acid or base. A buffer with more HA than A⁻ handles added base better than added acid.
pH and solubility: A salt with a basic anion (OH⁻, F⁻, CO₃²⁻, PO₄³⁻) dissolves more in acid, because the acid uses up the anion and pulls the dissolving equilibrium forward. Salts like AgCl, with an anion from a strong acid, aren't affected.

Entropy, free energy and electrochemistry

Unit 9

Predicting the sign of ΔS: ΔS > 0 when solids melt, liquids boil, gases expand, temperature rises, a solid dissolves, or a reaction makes more moles of gas than it uses.
ΔS° = Σ n·S°(products) − Σ n·S°(reactants): S° values are in J/(mol·K). Unlike ΔH°f, the S° of an element is not zero.
ΔG° = ΔH° − TΔS°: Use T in kelvins and convert ΔS° to kJ/(mol·K) first. ΔG° < 0 means thermodynamically favored.
The four sign combinations: ΔH < 0 and ΔS > 0: favored at all temperatures; ΔH > 0 and ΔS < 0: never favored; both negative: favored at low T; both positive: favored at high T. The switch happens near T = ΔH° ÷ ΔS° (same energy units).
ΔG° = −RT ln K: Use R = 8.314 J/(mol·K). ΔG° < 0 gives K > 1, ΔG° > 0 gives K < 1, and ΔG° near 0 gives K near 1, with large amounts of both reactants and products.
Free energy of dissolving: Dissolving takes energy to separate solute particles and make room in the solvent, releases energy as solute–solvent attractions form, and changes entropy at each step. These partly cancel, so ΔG° = ΔH° − TΔS° decides: NH₄NO₃ dissolves even though it's endothermic, because ΔS° is positive enough to make ΔG° negative.
Thermodynamic versus kinetic control: A favored reaction can still be too slow to notice if its activation energy is high. A reaction that seems not to happen is not necessarily at equilibrium.
Coupled reactions: Add an unfavored reaction to a favored one that shares an intermediate, and add their ΔG° values; if the total is negative, the overall process is favored. Cells use ATP this way, and outside sources like electricity or light can also drive unfavored changes.
Galvanic versus electrolytic cells: A galvanic cell runs a favored reaction to make electricity (E° > 0, ΔG° < 0). An electrolytic cell uses an outside power source to force an unfavored reaction.
Inside a galvanic cell: A metal anode (oxidation) usually loses mass, and metal often plates onto the cathode (reduction). Electrons go through the wire from anode to cathode, while salt-bridge cations move toward the cathode and anions toward the anode to keep charges balanced.
Building a cell from two half-reactions: For a galvanic cell, the half-reaction with the more positive reduction potential is the cathode; reverse the other one for the anode. Never multiply E° values by coefficients.
ΔG° = −nFE°: n is the moles of electrons transferred in the balanced overall equation. For n = 2 and E° = 1.10 V, ΔG° = −2 × 96,485 × 1.10 J ≈ −212 kJ/mol.
Nonstandard conditions (qualitative): If Q < 1 the cell voltage is higher than E°; if Q > 1 it's lower. As the cell runs, Q rises toward K and the voltage falls to zero at equilibrium: a dead battery.
Electrolysis: moles of electrons = I × t ÷ F: Then divide by the electrons each ion needs. 2.00 A for 965 s gives 0.0200 mol e⁻; plating Cu²⁺ needs 2 e⁻ each, so 0.0100 mol Cu (0.636 g) forms.