AP Chemistry Cheat Sheet

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Constants and Common Values

• Avogadro’s Number: $N_A = 6.022 \times 10^{23}\ \text{mol}^{-1}$
• Ideal Gas Constant: $R = 0.08206\ \text{L·atm/(mol·K)} = 8.314\ \text{J/(mol·K)}$
• Faraday’s Constant: $F = 96485\ \text{C/mol e}^-$
• Specific heat of water: $c_{\text{water}} \approx 4.18\ \text{J/(g·}^\circ\text{C)}$
• Pressure conversions: $1\ \text{atm} = 760\ \text{mmHg} = 760\ \text{torr} = 101.325\ \text{kPa}$
• STP for AP Chem: $273.15\ \text{K}$ and $1\ \text{atm}$
• Molar volume of an ideal gas at STP: about $22.4\ \text{L/mol}$
• $K_w = 1.0 \times 10^{-14}$ at $25^\circ\text{C}$

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Unit 1: Atomic Structure and Properties

Essential ideas

• Mass number = protons + neutrons
• Atomic number = protons
• Average atomic mass is a weighted average of isotopes
• Moles connect microscopic particles to measurable mass
• Molarity:

$$M = \frac{\text{mol solute}}{\text{L solution}}$$

Electron configuration

• Aufbau order matters
• Pauli exclusion: max 2 electrons per orbital with opposite spin
• Hund’s rule: fill equal-energy orbitals singly first

Common order:

$$1s,\ 2s,\ 2p,\ 3s,\ 3p,\ 4s,\ 3d,\ 4p,\ 5s,\ 4d,\ 5p,\ 6s,\ 4f,\ 5d,\ 6p$$

Periodic trends

• Atomic radius: increases down, decreases across
• Ionization energy: decreases down, increases across
• Electron affinity: usually becomes more favorable across a period
• Electronegativity: decreases down, increases across
• More positive effective nuclear charge usually means electrons are held more tightly

Photoelectron spectroscopy

• Lower binding energy means easier to remove electron (so elements with higher nuclear charge have charts that are shifted left)
• Higher peaks can mean more electrons in a subshell
• Peak position tells energy level; peak height/area tracks electron count

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Unit 2: Compound Structure and Properties

Bond types

• Ionic: metal + nonmetal, electron transfer
• Covalent: nonmetal + nonmetal, electron sharing
• Metallic: metal cations in a sea of delocalized electrons

Lewis structures checklist

1. Count valence electrons
2. Pick central atom
3. Connect atoms with single bonds
4. Complete octets on outer atoms
5. Place remaining electrons on central atom
6. Make multiple bonds if needed
7. Check formal charges

Formal charge

$$\text{FC} = \text{valence} - \text{nonbonding} - \frac{1}{2}(\text{bonding})$$

VSEPR / geometry

• 2 electron groups: linear
• 3: trigonal planar
• 4: tetrahedral
• 5: trigonal bipyramidal
• 6: octahedral

Molecular shape depends on lone pairs.

Electron domains	Electron geometry	Common molecular shape	Example
2	linear	linear	$\mathrm{CO_2}$
3	trigonal planar	trigonal planar / bent	$\mathrm{BF_3}$ / $\mathrm{SO_2}$
4	tetrahedral	tetrahedral / trigonal pyramidal / bent	$\mathrm{CH_4}$ / $\mathrm{NH_3}$ / $\mathrm{H_2O}$
5	trigonal bipyramidal	seesaw / T-shaped / linear	$\mathrm{SF_4}$
6	octahedral	square pyramidal / square planar	$\mathrm{BrF_5}$ / $\mathrm{XeF_4}$

Hybridization

• 2 groups: $sp$
• 3 groups: $sp^2$
• 4 groups: $sp^3$
• 5 groups: $sp^3d$
• 6 groups: $sp^3d^2$

Bond order and bond properties

• Higher bond order -> shorter, stronger bond
• Longer bonds are usually weaker

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Unit 3: Substances and Mixtures

Intermolecular forces

Weakest to strongest, in common AP contexts:

1. London dispersion
2. Dipole-dipole
3. Hydrogen bonding
4. Ion-dipole

”Like dissolves like”

• Polar dissolves polar
• Nonpolar dissolves nonpolar
• Ionic compounds usually dissolve best in polar solvents

Gas laws

$$PV = nRT$$ $$P_{\text{total}} = \sum P_i$$ $$P_i = x_i P_{\text{total}}$$

Kinetic theory

• Higher temperature -> higher average kinetic energy
• For ideal gases:

$$KE_{\text{avg}} = \frac{3}{2}RT$$

Graham’s law

$$\frac{\text{rate}_1}{\text{rate}_2} = \sqrt{\frac{M_2}{M_1}}$$

Colligative properties

$$\Delta T_b = iK_bm$$ $$\Delta T_f = iK_fm$$ $$\Pi = iMRT$$

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Unit 4: Chemical Reactions

Reaction types

• Synthesis
• Decomposition
• Single replacement
• Double replacement
• Combustion
• Acid-base
• Redox

Net ionic equations

• Split strong electrolytes into ions
• Keep solids, liquids, gases, and weak electrolytes intact
• Cancel spectator ions

Solubility rules to memorize

• Always soluble: Group 1, $\text{NH}_4^+$, $\text{NO}_3^-$, acetate, chlorate, perchlorate
• Usually soluble: halides except with $\text{Ag}^+$, $\text{Pb}^{2+}$, $\text{Hg}_2^{2+}$
• Usually soluble: sulfates except with $\text{Ba}^{2+}$, $\text{Sr}^{2+}$, $\text{Pb}^{2+}$, often $\text{Ca}^{2+}$
• Usually insoluble: carbonates, phosphates, chromates, sulfides, hydroxides except with Group 1 and $\text{NH}_4^+$

Usually soluble	Important exceptions
Group 1 ions and $\mathrm{NH_4^+}$	none commonly tested
Nitrates, acetates, perchlorates	none commonly tested
Chlorides, bromides, iodides	insoluble with $\mathrm{Ag^+}$, $\mathrm{Pb^{2+}}$, $\mathrm{Hg_2^{2+}}$
Sulfates	insoluble/slightly soluble with $\mathrm{Ba^{2+}}$, $\mathrm{Sr^{2+}}$, $\mathrm{Pb^{2+}}$, $\mathrm{Ca^{2+}}$
Usually insoluble	Important exceptions
Carbonates, phosphates, sulfides	soluble with Group 1 ions or $\mathrm{NH_4^+}$
Hydroxides	soluble with Group 1; $\mathrm{Ca^{2+}}$, $\mathrm{Sr^{2+}}$, $\mathrm{Ba^{2+}}$ are more soluble

Oxidation number reminders

• Element alone: 0
• Monatomic ion: charge
• Oxygen: usually -2
• Hydrogen: usually +1 with nonmetals, -1 with metals
• Sum of oxidation numbers = overall charge

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Unit 5: Kinetics

Core ideas

• Rate depends on concentration, temperature, orientation, and activation energy
• Catalyst lowers activation energy but does not change $\Delta H$ or $K$

Rate law

$$\text{rate} = k[A]^m[B]^n$$

• Orders come from experiment, not from the balanced equation unless the step is elementary

Integrated rate laws

Zeroth:

$$[A] = [A]_0 - kt$$

First:

$$\ln[A] = \ln[A]_0 - kt$$

Second:

$$\frac{1}{[A]} = \frac{1}{[A]_0} + kt$$

Half-life

Zeroth:

$$t_{1/2} = \frac{[A]_0}{2k}$$

First:

$$t_{1/2} = \frac{0.693}{k}$$

Second:

$$t_{1/2} = \frac{1}{k[A]_0}$$

Arrhenius equation

$$k = Ae^{-E_a/(RT)}$$ $$\ln k = -\frac{E_a}{R}\frac{1}{T} + \ln A$$

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Unit 6: Thermochemistry

Heat and calorimetry

$$q = mc\Delta T$$

First law

$$\Delta U = q + w$$

Pressure-volume work

$$w = -P_{\text{ext}}\Delta V$$

Enthalpy

At constant pressure:

$$\Delta H = q_p$$

Hess’s law

• Reverse reaction -> change sign of $\Delta H$
• Multiply equation -> multiply $\Delta H$
• Add equations -> add $\Delta H$

Formation enthalpies

$$\Delta H^\circ_{\text{rxn}} = \sum \nu \Delta H_f^\circ(\text{products}) - \sum \nu \Delta H_f^\circ(\text{reactants})$$

Bond enthalpy estimate

$$\Delta H_{\text{rxn}} \approx \sum D(\text{broken}) - \sum D(\text{formed})$$

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Unit 7: Equilibrium

Core equilibrium idea

At equilibrium:

• forward rate = reverse rate
• concentrations are constant, not necessarily equal

Equilibrium expression

For

$$aA + bB \rightleftharpoons cC + dD$$ $$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$

Pure solids and liquids are omitted.

Reaction quotient

• $Q < K$ -> shifts right
• $Q > K$ -> shifts left
• $Q = K$ -> already at equilibrium

Gas-phase equilibrium

$$K_p = K_c(RT)^{\Delta n_{\text{gas}}}$$

ICE table logic

Initial, Change, Equilibrium

• use stoichiometric multiples of $x$
• approximation may work if $x$ is very small compared with initial concentration

Le Châtelier

• Add reactant -> shift right
• Add product -> shift left
• Increase pressure -> shift toward fewer moles gas
• Change temperature -> changes $K$
• Catalyst -> no change in $K$

Solubility product

$$K_{sp} = [\text{ions}]^{\text{coefficients}}$$

Thermodynamic connection

$$\Delta G^\circ = -RT\ln K$$

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Unit 8: Acid-Base Equilibrium

Definitions

• Arrhenius: acids increase $[H^+]$, bases increase $[OH^-]$
• Brønsted-Lowry: acid donates proton, base accepts proton
• Lewis: acid accepts electron pair, base donates electron pair

Strong acids to memorize

$$\text{HCl},\ \text{HBr},\ \text{HI},\ \text{HNO}_3,\ \text{HClO}_4,\ \text{HClO}_3,\ \text{H}_2\text{SO}_4 \text{ (first proton)}$$

Strong bases to memorize

Group 1 hydroxides and heavier Group 2 hydroxides:

$$\text{LiOH},\ \text{NaOH},\ \text{KOH},\ \text{Ca(OH)}_2,\ \text{Sr(OH)}_2,\ \text{Ba(OH)}_2$$

Weak acid/base equilibrium

$$K_a = \frac{[H_3O^+][A^-]}{[HA]}$$ $$K_b = \frac{[BH^+][OH^-]}{[B]}$$ $$K_aK_b = K_w$$

pH / pOH

$$\text{pH} = -\log[H_3O^+]$$ $$\text{pOH} = -\log[OH^-]$$ $$\text{pH} + \text{pOH} = 14$$

at $25^\circ\text{C}$.

Buffer equation

$$\text{pH} = \text{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$$

Titration checkpoints

• strong acid / strong base equivalence point near pH 7
• weak acid / strong base equivalence point above 7
• weak base / strong acid equivalence point below 7
• half-equivalence point for weak acid/base gives $\text{pH} = \text{p}K_a$ or $\text{pOH} = \text{p}K_b$

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Unit 9: Thermodynamics and Electrochemistry

Entropy and spontaneity

$$\Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}}$$

• spontaneous if $\Delta S_{\text{universe}} > 0$
• equilibrium if $\Delta S_{\text{universe}} = 0$

Gibbs free energy

$$\Delta G = \Delta H - T\Delta S$$

• spontaneous if $\Delta G < 0$
• equilibrium if $\Delta G = 0$

Standard free energy

$$\Delta G^\circ = -RT\ln K$$

Electrochemistry

$$\Delta G = -nFE_{\text{cell}}$$ $$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$$

Nernst equation

$$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF}\ln Q$$

At $25^\circ\text{C}$:

$$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0592}{n}\log Q$$

Faraday’s law

$$q = It = nF$$ $$m = \frac{MIt}{nF}$$

Galvanic vs electrolytic

• galvanic: spontaneous, anode negative, cathode positive
• electrolytic: nonspontaneous, anode positive, cathode negative
• oxidation always at anode
• reduction always at cathode

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Most Common AP Chemistry Mistakes

1. Forgetting units or using Celsius instead of Kelvin in gas/equilibrium/thermo work
2. Including solids or liquids in equilibrium expressions
3. Pulling rate-law exponents from the balanced equation without justification
4. Forgetting stoichiometric coefficients in equilibrium, entropy, or formation-energy sums
5. Mixing up anode/cathode with sign in galvanic vs electrolytic cells
6. Forgetting to do stoichiometry first in titration and buffer problems
7. Treating a catalyst as something that changes $K$ or $\Delta G^\circ$
8. Confusing molecular polarity with bond polarity

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Fast Problem-Solving Checklist

1. Write the balanced equation first.
2. Identify what unit/topic the problem belongs to.
3. Decide whether the problem is stoichiometric, equilibrium-based, energetic, or statistical/rate-based.
4. Track units before plugging in numbers.
5. Check whether the answer sign and magnitude make chemical sense.
6. For FRQs, explain with both particle-level logic and equation-level support when possible.