AP Chemistry — Cheatsheet

Formulas & relationships

On the exam

• On the AP exam, moles are the hub of almost every quantitative problem. Train the reflex: grams → (÷ molar mass) → moles → (× ratio) → moles of target → (× molar mass or Avogadro) → answer.
• AP loves connecting configuration to the periodic table: the s-block is groups 1–2, the d-block is the transition metals, and the p-block is groups 13–18. An element’s valence configuration is readable straight off its position.
• Whenever a free-response asks you to *justify* a trend, name the mechanism — “higher Zₑff” or “additional shell / more shielding.” Stating the trend alone rarely earns the point; the reasoning does.
• On free-response Lewis questions, always tally your electrons against your step-1 total before moving on — an off-by-two count is the single most common way to lose the point. Then verify formal charges sum to the overall charge of the species.
• The AP exam constantly links a property to a structural cause. Never just name the bond type — state the mechanism: "conducts when molten because the ions become mobile" or "malleable because the nondirectional electron sea allows cores to slide."
• Keep two questions separate on the exam: "How many total domains?" fixes the electron-domain geometry and ideal angle; "How many of those are lone pairs?" fixes the named molecular shape and how far the real angle is squeezed below ideal.
• The exam's favorite two-step: first use domain count for both geometry AND hybridization (they come from the same number), then judge polarity by asking whether the shape lets the bond dipoles cancel. Symmetry with identical outer atoms → nonpolar; asymmetry or lone pairs → polar.
• On free-response, always name the IMF *and* the reason. "Water has hydrogen bonding, which is stronger than the dipole–dipole forces in H₂S, so water has the higher boiling point" earns the point; just saying "water boils higher" does not.
• Reading a phase diagram: moving right (heating) at constant pressure crosses from solid to liquid to gas; moving up (compressing) at constant temperature can push a gas into a liquid or solid. Locate the triple point and critical point first — they anchor the whole graph.
• When a problem gives grams but asks about a reaction or concentration, convert to moles first — moles are the currency of both molarity (mol ÷ L) and stoichiometry. Watch that volume is in liters and that "solution" volume, not solvent volume, goes in the denominator.
• AP free-response almost always asks for the *net ionic* equation, and it must be balanced for mass and charge — spectators earn no credit. Memorize the core solubility rules so you can decide instantly which species split and which stay solid.
• On limiting-reactant free-response, show the moles-of-product each reactant would make and explicitly state which is smaller. The reactant giving the *smaller* product amount is limiting, and that smaller number is your theoretical yield.
• To name agents, first find what is oxidized and what is reduced, then flip the labels: the reduced species is the oxidizing agent, the oxidized species is the reducing agent. Mixing these up is the single most common redox error on the AP exam.
• Every solution-stoichiometry problem runs the same loop: convert volume + molarity to moles, cross the balanced equation with the mole ratio, then convert back using the target’s volume or molar mass. Keep volumes in liters throughout and the arithmetic stays clean.
• When asked to *justify* a rate change, name the mechanism: more frequent collisions, a greater fraction of collisions exceeding Eₐ, or a lower Eₐ (catalyst only). Naming the factor without the mechanism rarely earns the point.
• The orders in a rate law come from **experimental data only** — never from the stoichiometric coefficients of the overall balanced equation. Reading exponents off the coefficients is the single most common kinetics mistake on the exam.
• A **constant** half-life is the signature of first order; a linear ln[A]-vs-t plot confirms it. If half-life instead grows as the reaction proceeds, suspect second order; if a plain [A]-vs-t plot is linear, it is zero order.
• To recover the RDS from data: if the experimental rate law is rate = k[A]²[B], the slow step must consume 2 A and 1 B (or an equivalent set once an intermediate is expressed via a fast equilibrium). Mechanism, RDS, and rate law must all agree.
• A quick reflex for the exam: "exo = exit," heat exits the system, ΔH < 0, surroundings warm. "Endo = into," heat goes into the system, ΔH > 0, surroundings cool. The temperature change you feel in the beaker is the *opposite* sign of the system's ΔH.
• Free-response calorimetry problems almost always want the heat *of the reaction*, not just of the water. Compute q(water) with m·c·ΔT, then flip the sign to get q(reaction), and finally divide by moles to report ΔH in kJ·mol⁻¹.
• Three routes, one answer: Hess's law with given steps, the ΔH°f formula with a table, and bond enthalpies for gas-phase estimates. If a problem hands you ΔH°f values, reach for Σproducts − Σreactants first — it is the fastest and the most exam-common.
• Memorize the four-case table: (−, +) spontaneous at all T; (+, −) never; (−, −) spontaneous at low T; (+, +) spontaneous at high T. When ΔH and ΔS pull the same direction, temperature is irrelevant; when they conflict, T > ΔH/ΔS marks the switch point.
• On the exam, state the reason with the comparison. "Q < K, so the reaction proceeds forward" earns the point; "it goes forward" alone often does not. Also remember: reversing a reaction inverts K (K becomes 1/K), and multiplying an equation through by n raises K to the nth power.
• To decide whether a precipitate forms, compute the ion product Q for the trial concentrations and compare to Ksp: Q > Ksp means the solution is supersaturated and a precipitate forms; Q < Ksp means it stays dissolved; Q = Ksp is exactly saturated. It is the same Q-versus-K logic from Lesson 1, applied to dissolving.
• Identify conjugate pairs by counting protons: the acid always has exactly one more H⁺ than its conjugate base. HCO₃⁻ can be the conjugate base of H₂CO₃ or the conjugate acid of CO₃²⁻ — amphoteric species show up often on the exam.
• Do not confuse concentration with strength. A concentrated weak acid can still have a modest pH, and a dilute strong acid can be nearly neutral. Ka/pKa describes *how completely* an acid ionizes; molarity describes *how much* acid is present.
• A buffer works best when pKa is within about 1 unit of the target pH, i.e. the [A⁻]/[HA] ratio stays between 1:10 and 10:1. To build a buffer for a given pH, choose a weak acid whose pKa is close to that pH.
• Polyprotic acids (H₂CO₃, H₃PO₄) donate protons one at a time, each with its own Ka, so their curves show *multiple* equivalence points — one steep jump per ionizable proton, with Ka1 > Ka2 > Ka3 since each successive H⁺ is harder to pull off a more negative ion.
• Do not confuse ΔG° with ΔG. ΔG° = −RT ln K compares the *standard state* to equilibrium; a large positive ΔG° just means a small K. The actual ΔG (which is 0 at equilibrium) depends on the real concentrations through ΔG = ΔG° + RT ln Q.
• The AP exam frequently tests the "do not multiply potentials" trap. When you scale a half-reaction to balance electrons, you multiply the atoms and the electrons — but never the E° value. Potential is energy *per charge*, an intensive property that is independent of how much reaction you run.
• The classic Faraday problem gives current and time and asks for mass. Chain the units without skipping steps: A × s = C, then C ÷ 96 485 = mol e⁻, then ÷ electrons-per-ion = mol product, then × molar mass = grams. Carrying units through each arrow prevents the most common errors.
• A concentration cell is the purest test of the Nernst idea: identical electrodes, same E° of 0, so E depends entirely on the concentration difference through −(0.0592/n) log Q. Electrons flow to equalize the two sides, and the voltage dies the instant the concentrations match.
• AP frequently shows two spectra and asks which belongs to the larger atom or which subshell was affected by ionization. Anchor every answer in the two rules: peak position = binding energy (tighter hold, higher Zₑff, shifts left), peak area = electron count. Removing an electron shrinks the corresponding peak’s height.
• When a free-response asks you to *justify* a ranking, cite both Coulomb levers explicitly: state whether Zₑff or r changed and in which direction, then conclude about the force. “Higher Zₑff, same shell → stronger attraction → higher IE / smaller radius” is the sentence that earns the point.
• On free response, never justify equal bond lengths by saying the molecule "switches" between structures — that earns no credit. State that the bonding is delocalized into one resonance hybrid with a single fractional bond order. And always confirm your chosen Lewis structure by showing formal charges that sum to the species' charge.
• Two exam reflexes: (1) σ bonds equal the number of bonded pairs, so σ + π together must equal the total bond count you drew — use that to self-check. (2) When asked to explain a solid's property, name the model explicitly — "delocalized electron sea/band" for metals, "continuous covalent network" for diamond, "mobile ions only when molten" for ionic — and connect it directly to the observed property.
• For real-gas questions, tie the deviation to a *cause*: high pressure → molecular volume no longer negligible (real V larger); low temperature → intermolecular attractions reduce wall impacts (real P smaller). Naming the mechanism, not just "it deviates," is what earns the point.
• For a Beer’s-law free-response, expect a calibration graph of absorbance vs concentration: its slope is εb, so a steeper line means a larger molar absorptivity. Read an unknown by finding its absorbance on the line and dropping to the concentration axis — and always confirm the path length is 1.00 cm before using ε directly.
• On the AP exam a redox equation earns full credit only when it is balanced for mass *and* charge. Always end by summing the charges on each side — if they are not equal, you mis-scaled the electrons or lost an H⁺/H₂O when combining the halves.
• Multi-step AP problems reward a clear moles ledger: write moles of every species, label each with its source, and apply the balanced mole ratio at each junction. Do all conversions to grams or molarity only after the moles are settled — that keeps limiting-reactant, gravimetric, and back-titration problems on the same reliable track.
• On free-response, justify the order by naming **which plot is linear**, then read k off the slope with the right sign (−k for zero/first order, +k for second order) and give **units by overall order** (M·s⁻¹, s⁻¹, M⁻¹·s⁻¹). A bare "second order" without pointing to the linear 1/[A] plot usually loses the justification point.
• To annotate a diagram fast: mark the **peak as the transition state**, arrow **up to it from reactants (Eₐ forward)** and **up to it from products (Eₐ reverse)**, and read **ΔH from reactant level to product level**. Check with ΔH = Eₐ(forward) − Eₐ(reverse). Count humps: two humps means a two-step mechanism with an intermediate in the valley.
• On the free-response section, calorimetry usually feeds Hess or ΔH°f: measure q(reaction) with the calorimeter, divide by moles to get a molar ΔH, then use it as one step or cross-check it against Σ ΔH°f(products) − Σ ΔH°f(reactants). Always report the final sign — exothermic is negative.
• A reliable free-response routine: compute ΔH°rxn and ΔS°rxn from tables, decide the sign case, and if ΔH and ΔS conflict solve T = ΔH/ΔS for the crossover (keep units consistent — ΔH in J with ΔS in J·K⁻¹). Then answer the temperature question by naming which side of the crossover is spontaneous.
• On the free-response, the point is often awarded for the justification, not just the number. After a small-x solve, explicitly write the ratio (e.g. "x/[initial] = 1% < 5%, so the approximation is valid"). If it fails, say so and switch to the quadratic — graders reward recognizing the boundary.
• Two exam reflexes for solubility problems: (1) after mixing solutions, recompute every concentration in the combined volume before finding Q — dilution is the most common oversight; (2) always carry the ion coefficient as an exponent, so a common ion or trial ion with coefficient 2 is squared. Both slips move the answer by orders of magnitude.
• On the exam, first sort each salt ion into "spectator" or "hydrolyzes." Group 1/Group 2 cations and the anions of strong acids (Cl⁻, Br⁻, I⁻, NO₃⁻, ClO₄⁻) are spectators. Any leftover ion traced to a weak acid or weak base is the one that sets the pH.
• Free-response titration questions reward naming the region before calculating. Say "this is the buffer region, so I use Henderson–Hasselbalch" or "this is past equivalence, so I use excess [OH⁻]." Choosing the right tool for the region earns the method points even before the arithmetic.
• Memorize the triangle: E° ↔ ΔG° ↔ K, joined by ΔG° = −nFE° and ΔG° = −RT ln K. Given any one vertex you can reach the other two. The single most common error is scaling E° by n or by a coefficient — E° is intensive and never changes; the n lives in the −nFE° expression, not inside the voltage.
• On the AP exam a concentration cell is instantly recognizable: same metal on both sides, same ion, E° = 0. Do not panic that the voltage looks like it should be zero — plug into E = −(0.0592/n) log Q and let the concentration ratio do the work. The concentrated half-cell is always the cathode.

How to get a 5

• Always show the full setup (formula → substituted numbers → answer) with correct units and sig figs — AP awards the substitution point even if the final arithmetic slips.
• For every "explain/justify," tie your reasoning to particle-level behavior (collisions, IMFs, Coulombic attraction, Zeff) — vague macroscopic statements don't earn the point.
• Master acid-base/equilibrium: buffers, ICE tables, titration curves, and Ksp appear on nearly every exam and are point-dense.
• On multiple choice, use dimensional analysis and proportional reasoning to eliminate answers fast rather than grinding exact calculations.
• Show every substitution with units, even when you have the arithmetic in your calculator. AP Chemistry rubrics award points for correct setup separately from the final number, so a substituted expression such as n = (0.962 atm)(0.155 L)/[(0.08206)(298 K)] earns credit even if you slip on the arithmetic. A bare number with no work earns nothing.
• Before any equilibrium or acid-base calculation, decide which of four situations you are in: pure weak acid or base (use Ka or Kb with an ICE table), buffer region (Henderson–Hasselbalch), equivalence point (only conjugate remains, so the salt hydrolyzes), or past equivalence (excess strong titrant dominates). Choosing the wrong regime is the single largest source of lost points in Unit 8.
• Keep signs and units straight in thermodynamics. Convert ΔS from J·K⁻¹ to kJ·K⁻¹ before combining with ΔH, remember that subtracting a negative TΔS adds to ΔH, and note that ΔG° = −nFE° gives joules while ΔH is usually tabulated in kilojoules. Also check that temperature is in kelvin in every gas, Nernst, and free-energy expression.
• Ground every explanation in particle-level reasoning. When a rubric asks "explain," it wants the behavior of atoms, ions, or molecules — Coulombic attraction, effective nuclear charge, relative strengths of intermolecular forces, collision frequency and orientation, or the number of gaseous particles. Restating the observation in different words, or citing a rule by name without the underlying interaction, does not earn the point.
• Practice lab-error questions deliberately, because at least one appears every year. Reason through the effect step by step: identify which measured quantity is wrong, decide whether it becomes larger or smaller, then trace it through the calculation to see whether the reported result is too high or too low. Answering "it would be inaccurate" without a direction earns zero.

Key terms