0% of the question bank attempted

Subatomic Particles & Isotopes

Atoms are built from protons, neutrons, and electrons, and isotopes of an element differ only in neutron count.
  • Protons (+1, in nucleus) define the element via atomic number Z; neutrons (0, in nucleus) add mass; electrons (-1) occupy orbitals around the nucleus
  • Mass number A = protons + neutrons; isotopes have the same Z but different A
  • Atomic mass on the periodic table is a weighted average of all naturally occurring isotopes
  • Ions form when atoms gain or lose electrons: cations (+) lose electrons, anions (-) gain electrons
  • Nuclear symbol notation: superscript = mass number, subscript = atomic number, e.g. carbon-14 is written with A=14, Z=6

The Mole and Avogadro's Number

The mole is chemistry's counting unit, linking the atomic scale to measurable macroscopic quantities.
  • 1 mole = 6.022 x $10^{23}$ particles (Avogadro's number, $N_A$)
  • Molar mass (g/mol) numerically equals the atomic/molecular mass in amu from the periodic table
  • moles = mass (g) / molar mass (g/mol); mass = moles x molar mass
  • number of particles = moles x 6.022 x $10^{23}$
  • Molar mass of a compound is the sum of the molar masses of all atoms in its formula

Mass Spectrometry & Average Atomic Mass

Mass spectrometry measures isotope masses and relative abundances, which are used to calculate an element's average atomic mass.
  • A mass spectrometer ionizes, accelerates, and deflects particles by mass-to-charge ratio to separate isotopes
  • Average atomic mass = sum of (isotope mass x fractional abundance) for all isotopes
  • Example: chlorine is ~75.77% Cl-35 (34.97 amu) and ~24.23% Cl-37 (36.97 amu), giving an average of about 35.45 amu
  • Peaks further right on a mass spectrum correspond to heavier isotopes; peak height/intensity corresponds to relative abundance

Empirical & Molecular Formulas

The empirical formula is the simplest whole-number ratio of atoms in a compound; the molecular formula is a whole-number multiple of it.
  • To find an empirical formula from mass or % composition: convert to moles, divide by the smallest mole value, then convert to whole numbers
  • Molecular formula = empirical formula x n, where n = molar mass (molecular) / empirical formula mass
  • Percent composition of an element = (mass of element in 1 mole compound / molar mass of compound) x 100%
  • Combustion analysis of a hydrocarbon uses moles of CO2 produced to find moles of C, and moles of H2O to find moles of H

Coulomb's Law and Atomic-Scale Interactions

Coulomb's law governs the electrostatic attraction between the nucleus and electrons, underlying atomic size and ionization trends.
  • Coulomb's law: $F$ is proportional to $(q_1 q_2)/r^2$ — force increases with charge magnitude and decreases with the square of distance
  • Higher effective nuclear charge pulls electrons closer, shrinking atomic radius
  • Greater distance between nucleus and valence electrons (more shielding/energy levels) weakens attraction, easing ionization
  • This same law explains why removing successive electrons from an atom requires increasingly more energy
Atomic mass on the periodic table is a weighted average of isotopes, not the mass of any single atom
Molar mass and molecular mass have the same numeric value but different units (g/mol vs amu) — students often confuse them
An empirical formula is the simplest ratio; it is not necessarily the actual molecular formula unless n = 1
Isotopes of the same element have identical chemical behavior (same electron count) but different mass — mass differences don't change reactivity

Balancing Chemical Equations

A balanced equation conserves atoms of each element and reflects the law of conservation of mass.
  • Balance by adjusting coefficients only, never subscripts (changing a subscript changes the substance's identity)
  • Balance elements that appear in only one reactant and one product first; balance free elements (like O2, H2) last
  • Check work by counting atoms of every element on both sides after balancing
  • Balanced coefficients give the mole ratios used in all stoichiometry calculations

Mole Ratios and Stoichiometric Calculations

Balanced equation coefficients give exact mole ratios that convert between amounts of any two substances in a reaction.
  • General path: mass/volume of A -> moles of A -> moles of B (using mole ratio from balanced equation) -> mass/volume of B
  • Mole ratio = coefficient of desired substance / coefficient of given substance
  • For gases at STP, 1 mole of any ideal gas occupies 22.4 L
  • For solutions, moles = Molarity (mol/L) x Volume (L)

Limiting Reactants and Percent Yield

The limiting reactant is used up first and determines the maximum theoretical amount of product; percent yield compares actual to theoretical.
  • To find the limiting reactant, calculate moles of product possible from each reactant — the one giving less product is limiting
  • Excess reactant is left over after the reaction goes to completion
  • Theoretical yield is the maximum product calculated from the limiting reactant
  • Percent yield = (actual yield / theoretical yield) x 100%
  • Percent yield is always less than or equal to 100% due to side reactions, impurities, or practical losses

Solution Stoichiometry and Dilution

Molarity expresses solution concentration, and dilution calculations track moles of solute as volume changes.
  • Molarity (M) = moles of solute / liters of solution
  • Dilution equation: M1V1 = M2V2 (moles of solute stay constant when solvent is added)
  • To make a solution of known molarity, calculate moles needed, then mass needed via molar mass
  • Titration uses the equation moles acid = moles base at the equivalence point (for a 1:1 acid-base reaction) to find an unknown concentration

Types of Chemical Reactions

Reactions are often classified by pattern, which helps predict products before balancing.
  • Synthesis: A + B -> AB; Decomposition: AB -> A + B
  • Single replacement: A + BC -> AC + B (predict using an activity series for metals)
  • Double replacement (often precipitation or acid-base): AB + CD -> AD + CB
  • Combustion of a hydrocarbon: CxHy + O2 -> CO2 + H2O
  • Net ionic equations omit spectator ions, showing only species that actually change in a reaction
Mole ratios come from balanced coefficients, not from the masses or grams given in the problem — convert to moles first, not last
The reactant with the smaller mass or fewer grams is not automatically the limiting reactant — you must compare moles of product each could form
Percent yield over 100% signals an experimental error (like impure product), not a real result — it should be flagged, not accepted
Balancing equations changes coefficients, never subscripts — changing a subscript makes a different compound entirely

Kinetic Molecular Theory

KMT models gases as particles in constant, random motion whose average kinetic energy depends only on temperature.
  • Gas particles are in constant, random, straight-line motion until they collide
  • Collisions between gas particles and container walls are perfectly elastic (no energy lost)
  • The volume of gas particles themselves is negligible compared to the container volume
  • Average kinetic energy is directly proportional to Kelvin temperature: $KE_{avg} = (3/2)RT$
  • There are no attractive or repulsive forces between ideal gas particles

The Ideal Gas Law

PV = nRT relates pressure, volume, moles, and temperature for an ideal gas in a single equation.
  • PV = nRT, where R = 0.0821 L·atm/(mol·K) (or 8.314 J/(mol·K) with SI units)
  • Temperature must always be converted to Kelvin: K = °C + 273
  • Can be rearranged to find molar mass: M = mRT/PV, or density: d = PM/RT
  • STP (standard conditions) is 0°C (273 K) and 1 atm, where 1 mole of ideal gas occupies 22.4 L

Combined and Individual Gas Laws

Boyle's, Charles's, Gay-Lussac's, and the combined gas law describe relationships between two gas variables when others are held constant.
  • Boyle's Law (constant T, n): P1V1 = P2V2 — pressure and volume are inversely proportional
  • Charles's Law (constant P, n): V1/T1 = V2/T2 — volume and temperature are directly proportional
  • Gay-Lussac's Law (constant V, n): P1/T1 = P2/T2 — pressure and temperature are directly proportional
  • Combined gas law (constant n): P1V1/T1 = P2V2/T2
  • Avogadro's Law (constant P, T): V1/n1 = V2/n2 — volume and moles are directly proportional

Partial Pressures and Gas Mixtures

Dalton's Law states that in a mixture of non-reacting gases, each gas contributes a partial pressure independent of the others.
  • Dalton's Law: $P_{total} = P1 + P2 + P3$ + ...
  • Partial pressure of a gas = mole fraction of that gas x total pressure: $Pi = Xi × P_{total}$
  • Mole fraction Xi = moles of gas i / total moles of gas
  • Common application: collecting gas over water requires subtracting water vapor pressure from total pressure to find the dry gas pressure

Effusion, Diffusion, and Real Gas Deviations

Graham's Law describes how gas molar mass affects speed, while real gases deviate from ideal behavior at high pressure and low temperature.
  • Graham's Law: rate1/rate2 = sqrt(M2/M1) — lighter gases effuse/diffuse faster than heavier gases
  • Effusion is escape through a tiny hole; diffusion is gas spreading through space or another gas
  • Real gases deviate from ideal behavior most at high pressure (particle volume becomes significant) and low temperature (attractive forces become significant)
  • The van der Waals equation adds correction terms for intermolecular attraction (a) and particle volume (b) to the ideal gas law
Temperature must be in Kelvin for all gas law calculations, not Celsius — forgetting this is the single most common gas law error
Real gases deviate most from ideal behavior at high pressure and low temperature, not at STP where ideal behavior is a good approximation
Lighter gases effuse faster, not slower — students often reverse Graham's Law's inverse square-root relationship
Ideal Gas Law assumes negligible particle volume and no intermolecular forces; these assumptions break down for real gases under extreme conditions

Heat, Temperature, and Specific Heat

Heat is energy transferred due to a temperature difference, and specific heat capacity determines how much a substance's temperature changes for a given heat input.
  • q = mcΔT, where q = heat (J), m = mass (g), c = specific heat (J/g·°C), $ΔT = T_{final} - T_{initial}$
  • Specific heat of water is 4.18 J/(g·°C), unusually high, which is why water resists temperature change
  • Temperature is a measure of average kinetic energy; heat is energy transferred between objects at different temperatures
  • Heat flows spontaneously from a higher-temperature object to a lower-temperature object until thermal equilibrium is reached

Calorimetry

Calorimetry measures heat flow in physical or chemical processes, typically assuming heat lost by one substance equals heat gained by another.
  • In a coffee-cup calorimeter (constant pressure), $q_{reaction} = -q_{solution}$, and $q_{solution}$ = mcΔT of the water/solution
  • Heat capacity of the calorimeter itself is often included in more precise calculations: $q_{cal} = C_{cal} × ΔT$
  • Bomb calorimeters measure heat at constant volume, giving ΔE (internal energy change) rather than ΔH directly
  • Molar enthalpy of reaction = $q_{reaction}$ / moles of limiting reactant

Enthalpy and Hess's Law

Enthalpy (H) is a state function, so Hess's Law allows ΔH for a reaction to be calculated by adding known steps regardless of path.
  • Hess's Law: if a reaction is the sum of steps, $ΔH_{total}$ = sum of ΔH for each step
  • Reversing a reaction changes the sign of ΔH; multiplying a reaction by a factor multiplies ΔH by that factor
  • $ΔH_{rxn} = Σ ΔH_f°(products) - Σ ΔH_f°(reactants)$, using standard enthalpies of formation
  • ΔHf° of an element in its standard state is defined as zero
  • Exothermic reactions release heat (ΔH < 0); endothermic reactions absorb heat (ΔH > 0)

Bond Energies and Enthalpy

Enthalpy change can be estimated from the energy required to break bonds in reactants versus the energy released forming bonds in products.
  • $ΔH_{rxn} ≈ Σ(bond\ energies\ broken) - Σ(bond\ energies\ formed)$
  • Breaking bonds always requires energy input (endothermic); forming bonds always releases energy (exothermic)
  • This method gives an estimate because average bond energies vary slightly depending on molecular environment
  • A reaction is exothermic overall if more energy is released forming new bonds than was required to break old ones

Thermodynamics: Enthalpy, Entropy, and Gibbs Free Energy

Gibbs free energy combines enthalpy and entropy to predict whether a process is spontaneous at a given temperature.
  • ΔG = ΔH - TΔS (T in Kelvin); a negative ΔG indicates a spontaneous process
  • Entropy (S) is a measure of disorder/dispersal of energy; ΔS > 0 favors spontaneity, especially at high T
  • Four sign combinations: ΔH<0,ΔS>0 always spontaneous; ΔH>0,ΔS<0 never spontaneous; the other two combinations are temperature-dependent
  • Phase changes (solid→liquid→gas) increase entropy because molecular disorder and freedom of motion increase
Exothermic means the system releases energy (ΔH negative), but the surroundings get warmer, not colder — students often confuse which side loses energy
In calorimetry, $q_{reaction} = -q_{solution}$ (opposite signs) because energy lost by one is gained by the other, not equal positive values
A reaction can be spontaneous even if endothermic, as long as ΔS is positive enough and T is high enough to make ΔG negative — spontaneity is not just about heat release
Bond breaking always costs energy and bond forming always releases energy; a common error is reversing which process is endothermic vs. exothermic

Electron Configuration

Electrons fill orbitals in a predictable order set by energy, and this arrangement explains chemical behavior.
  • Aufbau principle: electrons fill lowest-energy orbitals first, following the order 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p...
  • Pauli exclusion principle: each orbital holds at most 2 electrons, with opposite spins
  • Hund's rule: electrons fill degenerate (same-energy) orbitals singly before pairing up
  • Noble gas (condensed) notation abbreviates configurations, e.g. Cl is [Ne]$3s^2\ 3p^5$
  • Transition metals lose 4s electrons before 3d electrons when forming cations, e.g. Fe -> Fe2+ removes two 4s electrons
  • Valence electrons (outermost s and p, plus d for transition metals) determine bonding and chemical properties

Quantum Numbers & Orbital Shapes

Four quantum numbers uniquely describe each electron's energy, shape, orientation, and spin within an atom.
  • Principal quantum number n (1, 2, 3...) gives the energy level/shell size
  • Angular momentum number l (0 to n-1) gives the subshell shape: l=0 is s, l=1 is p, l=2 is d, l=3 is f
  • Magnetic quantum number $m_l$ gives orbital orientation (e.g. p has 3 orbitals: px, py, pz)
  • Spin quantum number $m_s$ is +1/2 or -1/2, describing the two possible electron spins in an orbital
  • s orbitals are spherical; p orbitals are dumbbell-shaped along an axis; d orbitals have more complex cloverleaf shapes

Periodic Trends: Atomic & Ionic Radius

Atomic size changes predictably across periods and down groups due to nuclear charge and shielding.
  • Atomic radius decreases left to right across a period: increasing nuclear charge pulls electrons in with little added shielding
  • Atomic radius increases down a group: each row adds a new occupied shell, increasing distance from the nucleus
  • Cations are smaller than their parent atom (fewer electrons, same or more nuclear pull); anions are larger than their parent atom
  • Isoelectronic species (same electron count) shrink as nuclear charge increases, e.g. O2- > F- > Ne > Na+ > Mg2+
  • Effective nuclear charge ($Z_{eff}$) is the net positive charge felt by valence electrons after accounting for shielding by inner electrons

Periodic Trends: Ionization Energy & Electronegativity

Ionization energy and electronegativity both generally increase toward fluorine, reflecting how tightly an atom holds electrons.
  • First ionization energy (IE1) is the energy to remove one electron from a gaseous atom; it increases across a period and decreases down a group
  • Successive ionization energies increase, with a large jump after removing all valence electrons (breaking into a stable core shell)
  • Exceptions: IE dips slightly from Group 2 to 13 (p orbital easier to remove than filled s) and from Group 15 to 16 (paired electron easier to remove than half-filled set)
  • Electronegativity measures an atom's pull on shared electrons in a bond; it increases across a period and decreases down a group
  • Fluorine is the most electronegative element; cesium/francium are among the least (most metallic/electropositive)
  • Electron affinity (energy change when an atom gains an electron) is generally most negative (most favorable) near the halogens

Photoelectron Spectroscopy (PES)

PES experimentally measures the binding energies of electrons in different orbitals, providing direct evidence for electron configuration and shielding.
  • PES bombards atoms with high-energy photons, ejecting electrons; measuring their kinetic energy gives the binding energy of the orbital they came from
  • Higher binding energy = electrons held more tightly = closer to the nucleus or less shielded (core electrons > valence electrons)
  • A PES spectrum shows peaks at different binding energies; peak height (relative intensity) is proportional to the number of electrons in that orbital/subshell
  • Peaks cluster into groups matching shells; within a shell, s orbitals have higher binding energy than p (closer to nucleus, less shielded)
  • PES data can be used to identify unknown elements or confirm electron configurations from first principles

Coulomb's Law & Atomic Behavior

Coulomb's law quantifies the electrostatic forces between charges and underlies most periodic trends and bonding.
  • Coulomb's law: $F = k(q_1 q_2)/r^2$ — force is proportional to the product of charges and inversely proportional to the square of distance
  • Larger effective nuclear charge (more protons felt) means stronger attraction, higher ionization energy, and smaller radius
  • Greater distance between nucleus and valence electrons (larger n, more shielding) means weaker attraction, lower ionization energy, larger radius
  • Shielding (inner electrons blocking nuclear charge) reduces the effective pull felt by valence electrons
  • These same electrostatic principles explain why ionic bond strength (lattice energy) increases with higher charge and smaller ionic radius
Transition metals lose 4s electrons first when ionizing, not 3d electrons — Fe2+ is [Ar]$3d^6$, not [Ar]$4s^2\ 3d^4$.
Ionization energy increases across a period and up a group, not down a group — don't mix up radius and IE directions.
PES peak height reflects the number of electrons in a subshell, not the energy — taller peaks mean more electrons, not more tightly bound.
Anions are larger, not smaller, than their neutral parent atom because added electron-electron repulsion outweighs the same nuclear charge.

Ionic, Covalent & Metallic Bonding

The three major bonding types arise from different ways atoms share or transfer electrons, driven by electronegativity differences.
  • Ionic bonds form via electron transfer between a metal and nonmetal, creating a lattice of oppositely charged ions held by electrostatic attraction
  • Covalent bonds form via electron sharing between nonmetals; can be nonpolar (equal sharing, same/similar electronegativity) or polar (unequal sharing)
  • Metallic bonding involves a 'sea of delocalized electrons' around a lattice of metal cations, explaining conductivity, malleability, and ductility
  • Bond polarity is judged by electronegativity difference: ~0 is nonpolar covalent, ~0.4-1.7 is polar covalent, >1.7 is generally ionic (rule of thumb)
  • Lattice energy (ionic bond strength) increases with higher ionic charge and smaller ionic radius, per Coulomb's law
  • Network covalent solids (e.g. diamond, SiO2) have covalent bonds throughout, giving very high melting points and hardness

Lewis Structures & Formal Charge

Lewis structures show how valence electrons are arranged as bonds and lone pairs, with formal charge helping choose the best structure.
  • Count total valence electrons, place atoms with least electronegative (usually) in center, connect with single bonds, then distribute remaining electrons as lone pairs to satisfy octets
  • Formal charge = (valence electrons) - (nonbonding electrons) - (1/2 bonding electrons); the best Lewis structure minimizes formal charges, with negative charges on more electronegative atoms
  • Resonance structures occur when multiple valid Lewis structures differ only in electron placement (e.g. ozone, nitrate); the real structure is an average (resonance hybrid)
  • Expanded octets are possible for period 3+ elements (e.g. S, P) using available d-orbitals or higher orbital availability, e.g. SF6, PCl5
  • Exceptions to the octet rule include odd-electron species (NO, NO2), electron-deficient atoms (BF3, B has 6 electrons), and expanded octets

VSEPR Theory & Molecular Geometry

VSEPR theory predicts 3D molecular shape from the number of electron domains (bonds + lone pairs) around a central atom, which repel each other to minimize energy.
  • 2 domains: linear (180 degrees), e.g. CO2; 3 domains: trigonal planar (120 degrees), e.g. BF3, or bent (~120) with 1 lone pair, e.g. SO2
  • 4 domains: tetrahedral (109.5 degrees), e.g. CH4; trigonal pyramidal with 1 lone pair, e.g. NH3; bent with 2 lone pairs, e.g. H2O
  • 5 domains: trigonal bipyramidal (90/120 degrees), e.g. PCl5; seesaw (1 lone pair), T-shaped (2 lone pairs), linear (3 lone pairs)
  • 6 domains: octahedral (90 degrees), e.g. SF6; square pyramidal (1 lone pair); square planar (2 lone pairs)
  • Lone pairs occupy more space than bonding pairs, compressing bond angles slightly below ideal (e.g. H2O is ~104.5 degrees, not 109.5)
  • Hybridization matches electron domain count: 2 domains = sp, 3 = sp2, 4 = sp3, 5 = sp3d, 6 = sp3d2

Molecular Polarity & Dipole Moments

A molecule's overall polarity depends on both individual bond polarities and molecular geometry, since bond dipoles can cancel by symmetry.
  • A polar bond contributes a bond dipole pointing toward the more electronegative atom
  • A molecule is nonpolar if bond dipoles cancel by symmetry, even with polar bonds (e.g. CO2, CCl4, BF3)
  • A molecule is polar if bond dipoles do not cancel, often due to lone pairs or asymmetry (e.g. H2O, NH3, CHCl3)
  • Symmetric molecules with identical terminal atoms and no lone pairs on the central atom (linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral) tend to be nonpolar
  • Molecular polarity determines solubility ('like dissolves like') and physical properties like boiling point

Intermolecular Forces (IMFs)

Intermolecular forces are attractions between separate molecules, weaker than covalent/ionic bonds, but they govern boiling points, solubility, and physical states.
  • London dispersion forces (LDFs) exist between all molecules/atoms, from temporary induced dipoles; strength increases with more electrons and larger surface area
  • Dipole-dipole forces occur between polar molecules, from permanent partial charges attracting oppositely charged ends of neighboring molecules
  • Hydrogen bonding is an especially strong dipole-dipole interaction when H is bonded directly to N, O, or F, which then attracts a lone pair on N/O/F of another molecule
  • Relative strength: ionic/covalent bonds > hydrogen bonding > dipole-dipole > London dispersion (for similar-sized molecules)
  • Stronger IMFs lead to higher boiling/melting points, higher viscosity, and lower vapor pressure
  • Water's unusually high boiling point, surface tension, and the fact that ice floats are all consequences of extensive hydrogen bonding

Solids & Phase Behavior

The type of particle and force holding a solid together determines its physical properties, and phase diagrams map how substances change state with temperature and pressure.
  • Ionic solids: hard, brittle, high melting point, conduct electricity only when molten/dissolved (e.g. NaCl)
  • Metallic solids: malleable, ductile, conduct electricity as solids (delocalized electrons), wide range of melting points
  • Molecular solids: held by IMFs (LDF, dipole-dipole, H-bonding); generally soft with low melting points, do not conduct electricity
  • Network covalent (atomic) solids: extremely hard, very high melting points, generally do not conduct (except graphite) (e.g. diamond, quartz)
  • Phase diagrams plot pressure vs. temperature, showing solid/liquid/gas regions separated by phase-boundary curves that meet at the triple point
A molecule with polar bonds is not automatically polar — check geometry, since symmetric shapes cancel dipoles (CO2 is nonpolar despite polar C=O bonds).
Hydrogen bonding requires H bonded directly to N, O, or F — an O-H bond elsewhere in a molecule counts, but C-H bonds never count as hydrogen bonding.
London dispersion forces exist in ALL molecules, not just nonpolar ones — they're often the dominant force in large nonpolar molecules, sometimes stronger than dipole-dipole in smaller polar ones.
Lone pairs count as electron domains for determining shape (VSEPR), but they are not counted when naming the molecular geometry itself (e.g. NH3 is 'trigonal pyramidal,' not 'tetrahedral,' despite 4 domains).

Reaction Rates & Rate Laws

Reaction rate measures how fast reactants are consumed or products form, and the rate law expresses this mathematically in terms of concentrations.
  • Rate = -(1/a)[d[A]/dt] = (1/b)[d[B]/dt]... using stoichiometric coefficients to relate rates of different species
  • Rate law: $rate = k[A]^m[B]^n$, where m and n are reaction orders determined experimentally (NOT from stoichiometric coefficients)
  • Overall reaction order = sum of individual orders (m + n); k is the rate constant, specific to a reaction at a given temperature
  • Method of initial rates: compare experiments where one concentration changes while others are held constant to solve for each order
  • Zero order: rate is independent of [A] (rate = k); first order: rate is proportional to [A]; second order: rate is proportional to $[A]^2$
  • Units of k depend on overall order: M/s for zero order, 1/s for first order, 1/(M*s) for second order

Integrated Rate Laws & Half-Life

Integrated rate laws relate concentration directly to time, letting you predict concentration at any point or determine reaction order from a graph.
  • Zero order: [A] = [A]0 - kt; a plot of [A] vs. t is linear
  • First order: ln[A] = ln[A]0 - kt (or ln([A]0/[A]) = kt); a plot of ln[A] vs. t is linear
  • Second order: 1/[A] = 1/[A]0 + kt; a plot of 1/[A] vs. t is linear
  • Half-life (t1/2) for first order is constant: t1/2 = 0.693/k, independent of concentration
  • Zero-order half-life decreases over time ([A]0/2k); second-order half-life increases over time (1/(k[A]0))
  • Graphing concentration data in these three ways (linear, ln, 1/[A]) and finding which gives a straight line reveals the reaction order

Collision Theory & Reaction Mechanisms

Reactions occur when molecules collide with sufficient energy and correct orientation, and most reactions proceed through a multi-step mechanism.
  • Collision theory: reaction rate depends on collision frequency, energy (must exceed activation energy Ea), and proper orientation
  • Activation energy (Ea) is the minimum energy needed for a collision to result in reaction; a catalyst lowers Ea by providing an alternate pathway
  • A reaction mechanism is a series of elementary steps that sum to the overall reaction; intermediates are produced then consumed (don't appear in overall equation)
  • The rate-determining step (slowest step) determines the overall rate law; for an elementary step, the rate law can be written directly from its stoichiometry
  • A valid mechanism must sum to the overall balanced equation and produce a rate law consistent with the experimentally observed one
  • Catalysts increase rate without being consumed; they appear in an early step and are regenerated in a later step

Chemical Equilibrium & Keq

Equilibrium is a dynamic state where forward and reverse reaction rates are equal, and Keq quantifies the ratio of products to reactants at that point.
  • At equilibrium, forward rate = reverse rate, so concentrations (not necessarily equal) remain constant over time
  • $Keq = [products]^{coefficients} / [reactants]^{coefficients}$, using equilibrium concentrations; pure solids and liquids are omitted
  • Kc uses concentrations; Kp uses partial pressures for gases, related by $Kp = Kc(RT)^{\Delta n}$
  • Large K (>>1) favors products at equilibrium; small K (<<1) favors reactants; K near 1 means comparable amounts of both
  • Reaction quotient Q has the same form as K but uses current (non-equilibrium) concentrations; if Q < K reaction shifts forward, if Q > K it shifts reverse, if Q = K it's at equilibrium
  • ICE tables (Initial, Change, Equilibrium) organize concentration changes to solve for equilibrium concentrations or K

Le Chatelier's Principle

Le Chatelier's principle predicts how an equilibrium system responds to a disturbance by shifting to partially counteract the change.
  • Adding a reactant (or removing a product) shifts equilibrium toward products (forward); the reverse shifts it toward reactants
  • Increasing volume/decreasing pressure shifts equilibrium toward the side with more moles of gas; decreasing volume/increasing pressure shifts toward fewer moles of gas
  • Adding an inert gas at constant volume does not shift equilibrium (partial pressures/concentrations of reactants and products are unchanged)
  • Increasing temperature shifts equilibrium in the endothermic direction; decreasing temperature shifts it in the exothermic direction (treat heat as a reactant or product)
  • Changing temperature is the only disturbance that actually changes the value of K; changing concentration, pressure, or volume shifts the position but K stays the same
  • Catalysts speed up the approach to equilibrium (both directions equally) but do not shift its position or change K

Free Energy & Equilibrium Connection

Gibbs free energy determines reaction spontaneity and connects thermodynamics to the equilibrium constant.
  • Delta G = Delta H - T*Delta S; a reaction is spontaneous (favorable) when Delta G < 0
  • Delta G < 0: exergonic/spontaneous as written; Delta G > 0: nonspontaneous as written (spontaneous in reverse); Delta G = 0: at equilibrium
  • Delta G° relates to K by Delta G° = -RT ln(K); large K corresponds to very negative Delta G°
  • Delta G = Delta G° + RT ln(Q) describes free energy under non-standard conditions, showing how a reaction proceeds toward equilibrium (Q approaches K)
  • Temperature can flip spontaneity when Delta H and Delta S have the same sign (e.g. endothermic but entropy-increasing reactions become spontaneous at high T)
Reaction order comes from experimental data (initial rates method), not from the stoichiometric coefficients in the balanced equation.
Adding an inert gas at constant volume does NOT shift equilibrium, because it doesn't change any reactant/product concentration or partial pressure.
A catalyst speeds up both the forward and reverse reactions equally — it changes the rate at which equilibrium is reached, not the equilibrium position or K.
Increasing temperature shifts equilibrium based on which direction is endothermic, not simply 'always toward products' — treat heat as a reactant (endothermic) or product (exothermic).

Acid-Base Definitions & pH/pOH

Acids and bases can be defined by proton or electron transfer, and pH/pOH provide a convenient scale for describing [H+] and [OH-].
  • Bronsted-Lowry: acids donate H+ (protons), bases accept H+; Lewis: acids accept electron pairs, bases donate electron pairs
  • pH = -log[H+]; pOH = -log[OH-]; pH + pOH = 14.00 at 25°C (from Kw = [H+][OH-] = 1.0 x $10^{-14}$)
  • Neutral: pH = 7; acidic: pH < 7; basic: pH > 7 (at 25°C)
  • Strong acids (HCl, HBr, HI, HNO3, H2SO4, HClO4) and strong bases (Group 1/2 hydroxides) dissociate 100% in water
  • For strong acids/bases, [H+] or [OH-] equals the given concentration directly (accounting for stoichiometry, e.g. Ca(OH)2 gives 2x [OH-])
  • Conjugate acid-base pairs differ by one H+ (e.g. NH4+/NH3, HCO3-/$CO_3^{2-}$); the stronger the acid, the weaker its conjugate base

Weak Acids/Bases: Ka, Kb & Equilibrium

Weak acids and bases only partially dissociate in water, and Ka/Kb quantify the extent of that ionization at equilibrium.
  • Ka = [H+][A-]/[HA] for HA <-> H+ + A-; larger Ka means a stronger (more dissociated) weak acid
  • Kb = [BH+][OH-]/[B] for B + H2O <-> BH+ + OH-; larger Kb means a stronger weak base
  • Ka x Kb = Kw = 1.0 x $10^{-14}$ for a conjugate acid-base pair (pKa + pKb = 14)
  • For a weak acid, use an ICE table with x = [H+] and the approximation x << [HA]0 (valid when Ka is small relative to concentration)
  • Percent ionization = ([H+]/[HA]0) x 100%; percent ionization increases as initial concentration decreases (more dilute = more dissociated)
  • pKa = -log(Ka); a lower pKa means a stronger acid

Buffers & the Henderson-Hasselbalch Equation

Buffers resist changes in pH by containing both a weak acid and its conjugate base (or weak base and conjugate acid) in significant amounts.
  • A buffer is made from a weak acid/conjugate base pair (or weak base/conjugate acid pair) present in comparable amounts
  • Henderson-Hasselbalch: pH = pKa + log([A-]/[HA]); useful for finding buffer pH or the ratio needed for a target pH
  • Buffer capacity is greatest when [A-] = [HA] (pH = pKa), and buffers work best within about 1 pH unit of pKa
  • Adding acid to a buffer: H+ reacts with the conjugate base (A-); adding base: OH- reacts with the weak acid (HA); the buffer components adjust to absorb the change
  • Buffers are used in blood (carbonic acid/bicarbonate), biological systems, and lab solutions to maintain stable pH

Titrations & Equivalence Points

Titrations use a solution of known concentration to determine the concentration or identity of an unknown acid or base, tracked via a pH curve.
  • Equivalence point: moles of acid = moles of base (accounting for stoichiometry); this is where the titration curve has its steepest rise (inflection point)
  • Strong acid + strong base titration: equivalence point pH = 7
  • Weak acid + strong base titration: equivalence point pH > 7 (conjugate base of the weak acid makes the solution basic)
  • Weak base + strong acid titration: equivalence point pH < 7 (conjugate acid makes the solution acidic)
  • Half-equivalence point (half of the acid neutralized): pH = pKa for a weak acid titration, since [HA] = [A-] there
  • Indicators change color near their own pKa; choose an indicator whose color-change range brackets the equivalence point pH
  • Titration curves for polyprotic acids show multiple equivalence points, one for each ionizable proton

Redox Reactions & Oxidation States

Oxidation-reduction (redox) reactions involve electron transfer, tracked using oxidation numbers and balanced with half-reactions.
  • Oxidation = loss of electrons (oxidation number increases); reduction = gain of electrons (oxidation number decreases) — 'OIL RIG'
  • The oxidizing agent is reduced (it causes oxidation of something else); the reducing agent is oxidized (it causes reduction of something else)
  • Assign oxidation numbers: free elements = 0; monatomic ions = ion charge; O is usually -2; H is usually +1; sum of oxidation numbers = overall charge
  • Balance redox equations using half-reactions: separate oxidation and reduction, balance atoms then charge (add electrons), then combine so electrons cancel
  • In acidic solution, balance O with H2O and H with H+; in basic solution, balance as if acidic, then add OH- to both sides to neutralize H+

Galvanic (Voltaic) Cells & Electrochemistry

Galvanic cells convert spontaneous redox reactions into electrical energy, with standard reduction potentials predicting voltage and spontaneity.
  • In a galvanic cell, oxidation occurs at the anode (negative electrode) and reduction occurs at the cathode (positive electrode) — 'AN OX, RED CAT'
  • Electrons flow through the external wire from anode to cathode; a salt bridge maintains charge neutrality by allowing ion flow between half-cells
  • E°cell = E°cathode(reduction) - E°anode(reduction), using standard reduction potentials from a table; a positive E°cell means a spontaneous reaction
  • Delta G° = -nFE°cell, linking cell potential to free energy (n = moles of electrons transferred, F = Faraday's constant, 96,485 C/mol)
  • The Nernst equation, E = E° - (RT/nF)ln(Q), gives cell potential under non-standard conditions; at 25°C this simplifies to E = E° - (0.0592/n)log(Q)
  • Electrolytic cells use an external power source to force a nonspontaneous redox reaction to occur (opposite of galvanic cells, but same electrode naming: oxidation at anode, reduction at cathode)
A weak acid-strong base titration has an equivalence point pH greater than 7, not 7 — don't assume every equivalence point is neutral.
Ka and Kb are related by Ka x Kb = Kw for a conjugate pair, not Ka = Kb — a stronger acid always has a weaker conjugate base.
In a galvanic cell, electrons flow from anode to cathode through the wire, while conventional current and cations in the salt bridge move to maintain charge balance — don't reverse anode/cathode with electrode charge sign.
Oxidation is loss of electrons (increase in oxidation number), not gain — mixing up OIL RIG is one of the most common redox errors.
Term
Press Enter or Space to flip the card. Left and right arrows move between cards. 1 marks it known, 2 marks it still learning.
Click or press Enter to flip · Rate yourself to track weak cards
Browse all 80 flashcards as a list

Unit 1: Atomic Structure & Moles

Mole
The SI unit for amount of substance, equal to 6.022 x $10^{23}$ particles (Avogadro's number).
Avogadro's Number
6.022 x $10^{23}$ particles per mole; the conversion factor between moles and number of atoms/molecules.
Isotopes
Atoms of the same element (same number of protons) that have different numbers of neutrons, giving different mass numbers.
Average Atomic Mass
The weighted average of the masses of an element's naturally occurring isotopes, calculated as Σ(isotope mass x fractional abundance).
Empirical Formula
The simplest whole-number ratio of atoms of each element in a compound, e.g. CH2O for glucose.
Molecular Formula
The actual number of atoms of each element in a molecule; a whole-number multiple of the empirical formula, e.g. C6H12O6.
Molar Mass
The mass in grams of one mole of a substance (g/mol), numerically equal to the atomic or molecular mass in amu.
Mass Spectrometry
An analytical technique that ionizes and deflects particles by mass-to-charge ratio to determine isotope masses and relative abundances.
Coulomb's Law
F ∝ $(q_1 q_2)/r^2$; describes the electrostatic force between charged particles, explaining nuclear-electron attraction.
Percent Composition
The percentage by mass that each element contributes to a compound's total molar mass.

Unit 2: Stoichiometry

Limiting Reactant
The reactant that is completely consumed first in a reaction, determining the maximum amount of product that can form.
Theoretical Yield
The maximum amount of product predicted by stoichiometric calculation based on the limiting reactant.
Percent Yield
(Actual yield / theoretical yield) x 100%; measures the efficiency of a real reaction compared to the ideal calculated amount.
Molarity (M)
Concentration expressed as moles of solute per liter of solution: M = mol solute / L solution.
Dilution Equation
M1V1 = M2V2; used to calculate concentration or volume changes when a solution is diluted, since moles of solute stay constant.
Net Ionic Equation
A chemical equation showing only the ions and molecules that actually participate in a reaction, omitting spectator ions.
Mole Ratio
The ratio of moles of one substance to another in a balanced chemical equation, taken directly from the coefficients.
Activity Series
A ranked list of metals by reactivity, used to predict whether a single replacement reaction will occur.
Titration
A technique using a solution of known concentration to determine the unknown concentration of another solution via a neutralization reaction.
Combustion Reaction
A reaction of a hydrocarbon with excess O2 that produces CO2 and H2O, releasing energy.

Unit 3: Gas Laws

Ideal Gas Law
PV = nRT, relating pressure, volume, moles, and temperature (in Kelvin) with R = 0.0821 L·atm/(mol·K).
Boyle's Law
At constant temperature and moles, pressure and volume are inversely proportional: P1V1 = P2V2.
Charles's Law
At constant pressure and moles, volume and temperature are directly proportional: V1/T1 = V2/T2.
Gay-Lussac's Law
At constant volume and moles, pressure and temperature are directly proportional: P1/T1 = P2/T2.
Dalton's Law of Partial Pressures
The total pressure of a gas mixture equals the sum of the partial pressures of each component gas.
Graham's Law of Effusion
rate1/rate2 = sqrt(M2/M1); lighter gas molecules effuse and diffuse faster than heavier ones.
Kinetic Molecular Theory
A model describing gases as particles in constant random motion with negligible volume, no intermolecular forces, and perfectly elastic collisions.
STP (Standard Temperature and Pressure)
0°C (273 K) and 1 atm; at STP, 1 mole of ideal gas occupies 22.4 L.
Mole Fraction
The ratio of moles of one component to total moles in a mixture; used to calculate partial pressure: $Pi = Xi × P_{total}$.
Real Gas Deviation
Departure from ideal gas behavior, most significant at high pressure (particle volume matters) and low temperature (intermolecular forces matter).

Unit 4: Thermochemistry

Specific Heat Capacity
The amount of heat required to raise 1 gram of a substance by 1°C; water's is 4.18 J/(g·°C).
Calorimetry
The experimental measurement of heat flow in a physical or chemical process, often using q=mcΔT.
Hess's Law
The enthalpy change of a reaction is the same whether it occurs in one step or several steps, since ΔH is a state function.
Standard Enthalpy of Formation (ΔHf°)
The enthalpy change when 1 mole of a compound forms from its elements in their standard states; zero for elements themselves.
Exothermic Reaction
A reaction that releases heat to the surroundings, with ΔH < 0.
Endothermic Reaction
A reaction that absorbs heat from the surroundings, with ΔH > 0.
Entropy (S)
A measure of the disorder or number of accessible microstates in a system; entropy generally increases from solid to liquid to gas.
Gibbs Free Energy (ΔG)
ΔG = ΔH - TΔS; determines spontaneity of a process — negative ΔG means the process is spontaneous.
Bond Energy
The energy required to break one mole of a specific bond in the gas phase; used to estimate $ΔH_{rxn}$ as bonds broken minus bonds formed.
State Function
A property, like enthalpy or entropy, that depends only on the current state of a system, not on the path taken to reach it.

Unit 5: Atomic Structure & Periodicity

Aufbau Principle
Electrons fill orbitals from lowest to highest energy, following the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p...
Hund's Rule
Electrons fill degenerate orbitals singly (with parallel spins) before pairing up in the same orbital.
Pauli Exclusion Principle
No two electrons in an atom can have the same four quantum numbers; each orbital holds at most 2 electrons with opposite spins.
Effective Nuclear Charge ($Z_{eff}$)
The net positive charge felt by a valence electron after accounting for shielding by inner (core) electrons.
Atomic Radius Trend
Decreases left to right across a period (rising nuclear charge); increases down a group (new occupied shells).
First Ionization Energy (IE1)
The energy required to remove the outermost electron from a neutral gaseous atom; increases across a period, decreases down a group.
Electronegativity
A measure of an atom's ability to attract shared electrons in a bond; highest for fluorine, increases across a period, decreases down a group.
Isoelectronic Series
A set of ions/atoms with the same number of electrons; radius decreases as nuclear charge (protons) increases within the series.
Photoelectron Spectroscopy (PES)
A technique that measures electron binding energies by ejecting electrons with photons; peak position shows binding energy, peak height shows relative electron count.
Coulomb's Law
$F = k(q_1 q_2)/r^2$; the electrostatic force between two charges is proportional to their product and inversely proportional to the square of the distance between them.

Unit 6: Bonding & IMFs

Ionic Bond
An electrostatic attraction between oppositely charged ions, typically formed by electron transfer from a metal to a nonmetal.
Covalent Bond
A bond formed by two nonmetal atoms sharing one or more pairs of electrons; can be polar or nonpolar depending on electronegativity difference.
Metallic Bonding
Metal cations held together in a lattice by a 'sea' of delocalized valence electrons, explaining conductivity and malleability.
VSEPR Theory
Valence Shell Electron Pair Repulsion theory: electron domains (bonds and lone pairs) around a central atom arrange themselves to minimize repulsion, determining molecular shape.
Lone Pair Effect
Nonbonding electron pairs occupy more space than bonding pairs, compressing bond angles below the ideal geometric value.
Molecular Polarity
A molecule is polar if its bond dipoles do not cancel by symmetry; nonpolar if they do (even with polar bonds present, e.g. CO2).
London Dispersion Forces
Weak, temporary attractive forces present in all molecules, caused by instantaneous fluctuations in electron distribution; strength increases with size/surface area.
Hydrogen Bonding
An especially strong dipole-dipole attraction that occurs when H bonded to N, O, or F is attracted to a lone pair on N, O, or F of a neighboring molecule.
Resonance Structures
Multiple valid Lewis structures for a molecule that differ only in electron (not atom) placement; the true structure is an average, or hybrid, of all of them.
Formal Charge
FC = valence electrons - nonbonding electrons - 1/2(bonding electrons); used to identify the most stable Lewis structure.

Unit 7: Kinetics & Equilibrium

Rate Law
An equation, $rate = k[A]^m[B]^n$, relating reaction rate to reactant concentrations, with orders m and n determined experimentally.
Rate Constant (k)
The proportionality constant in a rate law, specific to a given reaction at a given temperature; its units depend on overall reaction order.
Half-Life (t1/2)
The time required for a reactant's concentration to drop to half its initial value; constant for first-order reactions (t1/2 = 0.693/k).
Activation Energy (Ea)
The minimum energy that colliding particles must have for a reaction to occur; catalysts work by lowering it.
Reaction Mechanism
A sequence of elementary steps that together give the overall reaction; intermediates are formed and then consumed along the way.
Rate-Determining Step
The slowest elementary step in a mechanism, which controls the overall reaction rate and its rate law.
Equilibrium Constant (Keq)
The ratio of product to reactant concentrations (each raised to its stoichiometric coefficient) at equilibrium; large K favors products.
Reaction Quotient (Q)
Has the same expression as K but uses current (non-equilibrium) concentrations; comparing Q to K predicts which direction a reaction will shift.
Le Chatelier's Principle
A system at equilibrium responds to a disturbance (concentration, pressure/volume, or temperature change) by shifting to partially counteract it.
Gibbs Free Energy (Delta G)
Delta G = Delta H - TDelta S; determines spontaneity (Delta G < 0 is spontaneous) and relates to K via Delta G° = -RTln(K).

Unit 8: Acids-Bases & Electrochemistry

pH
pH = -log[H+]; a measure of hydrogen ion concentration where lower pH means more acidic (higher [H+]).
Kw (Ion-Product of Water)
Kw = [H+][OH-] = 1.0 x $10^{-14}$ at 25°C; the basis for pH + pOH = 14.00.
Ka (Acid Dissociation Constant)
Equilibrium constant for a weak acid's ionization, HA <-> H+ + A-; larger Ka means a stronger acid.
Buffer
A solution containing a weak acid and its conjugate base (or weak base and conjugate acid) in comparable amounts, resisting pH change on addition of acid or base.
Henderson-Hasselbalch Equation
pH = pKa + log([A-]/[HA]); used to calculate buffer pH or the acid/conjugate base ratio needed for a target pH.
Equivalence Point
The point in a titration where moles of acid equal moles of base (adjusted for stoichiometry); marked by the steepest part of the titration curve.
Oxidation
The loss of electrons by a species, corresponding to an increase in oxidation number (remembered as OIL: Oxidation Is Loss).
Reduction
The gain of electrons by a species, corresponding to a decrease in oxidation number (remembered as RIG: Reduction Is Gain).
Standard Cell Potential (E°cell)
E°cell = E°cathode - E°anode (using standard reduction potentials); a positive value indicates a spontaneous galvanic cell reaction.
Nernst Equation
E = E° - (0.0592/n)log(Q) at 25°C; gives the cell potential of a galvanic cell under non-standard concentration conditions.
Press 1–4 to answer · Enter for next

Unit 1: Atomic Structure & Moles

Subatomic Particles & Isotopes
Atoms are built from protons, neutrons, and electrons, and isotopes of an element differ only in neutron count.
The Mole and Avogadro's Number
The mole is chemistry's counting unit, linking the atomic scale to measurable macroscopic quantities.
Mass Spectrometry & Average Atomic Mass
Mass spectrometry measures isotope masses and relative abundances, which are used to calculate an element's average atomic mass.
Empirical & Molecular Formulas
The empirical formula is the simplest whole-number ratio of atoms in a compound; the molecular formula is a whole-number multiple of it.
Coulomb's Law and Atomic-Scale Interactions
Coulomb's law governs the electrostatic attraction between the nucleus and electrons, underlying atomic size and ionization trends.
Key fact
n = m/M (moles = mass / molar mass); particles = n x 6.022 x $10^{23}$
Key fact
Average atomic mass = Σ(isotope mass x fractional abundance)
Key fact
Molecular formula = empirical formula x n, where n = (molar mass)/(empirical formula mass)
Key fact
Mass number (A) = protons + neutrons; atomic number (Z) = protons = electrons in a neutral atom

Unit 2: Stoichiometry

Balancing Chemical Equations
A balanced equation conserves atoms of each element and reflects the law of conservation of mass.
Mole Ratios and Stoichiometric Calculations
Balanced equation coefficients give exact mole ratios that convert between amounts of any two substances in a reaction.
Limiting Reactants and Percent Yield
The limiting reactant is used up first and determines the maximum theoretical amount of product; percent yield compares actual to theoretical.
Solution Stoichiometry and Dilution
Molarity expresses solution concentration, and dilution calculations track moles of solute as volume changes.
Types of Chemical Reactions
Reactions are often classified by pattern, which helps predict products before balancing.
Key fact
Percent yield = (actual yield / theoretical yield) x 100%
Key fact
M1V1 = M2V2 for dilutions; moles = M x V for solutions
Key fact
The limiting reactant produces the least amount of product and is fully consumed
Key fact
At STP, 1 mole of ideal gas = 22.4 L

Unit 3: Gas Laws

Kinetic Molecular Theory
KMT models gases as particles in constant, random motion whose average kinetic energy depends only on temperature.
The Ideal Gas Law
PV = nRT relates pressure, volume, moles, and temperature for an ideal gas in a single equation.
Combined and Individual Gas Laws
Boyle's, Charles's, Gay-Lussac's, and the combined gas law describe relationships between two gas variables when others are held constant.
Partial Pressures and Gas Mixtures
Dalton's Law states that in a mixture of non-reacting gases, each gas contributes a partial pressure independent of the others.
Effusion, Diffusion, and Real Gas Deviations
Graham's Law describes how gas molar mass affects speed, while real gases deviate from ideal behavior at high pressure and low temperature.
Key fact
PV = nRT, with R = 0.0821 L·atm/(mol·K); always convert temperature to Kelvin
Key fact
P1V1/T1 = P2V2/T2 (combined gas law) when moles are constant
Key fact
Graham's Law: rate1/rate2 = sqrt(M2/M1)
Key fact
Dalton's Law: $P_{total}$ = sum of partial pressures; $Pi = Xi × P_{total}$

Unit 4: Thermochemistry

Heat, Temperature, and Specific Heat
Heat is energy transferred due to a temperature difference, and specific heat capacity determines how much a substance's temperature changes for a given heat input.
Calorimetry
Calorimetry measures heat flow in physical or chemical processes, typically assuming heat lost by one substance equals heat gained by another.
Enthalpy and Hess's Law
Enthalpy (H) is a state function, so Hess's Law allows ΔH for a reaction to be calculated by adding known steps regardless of path.
Bond Energies and Enthalpy
Enthalpy change can be estimated from the energy required to break bonds in reactants versus the energy released forming bonds in products.
Thermodynamics: Enthalpy, Entropy, and Gibbs Free Energy
Gibbs free energy combines enthalpy and entropy to predict whether a process is spontaneous at a given temperature.
Key fact
q = mcΔT for heat transfer in a substance without phase change
Key fact
$ΔH_{rxn} = Σ ΔH_f°(products) - Σ ΔH_f°(reactants)$
Key fact
ΔG = ΔH - TΔS; ΔG < 0 means spontaneous
Key fact
Hess's Law: ΔH values add when reaction steps are added; reversing a step flips the sign of ΔH

Unit 5: Atomic Structure & Periodicity

Electron Configuration
Electrons fill orbitals in a predictable order set by energy, and this arrangement explains chemical behavior.
Quantum Numbers & Orbital Shapes
Four quantum numbers uniquely describe each electron's energy, shape, orientation, and spin within an atom.
Periodic Trends: Atomic & Ionic Radius
Atomic size changes predictably across periods and down groups due to nuclear charge and shielding.
Periodic Trends: Ionization Energy & Electronegativity
Ionization energy and electronegativity both generally increase toward fluorine, reflecting how tightly an atom holds electrons.
Photoelectron Spectroscopy (PES)
PES experimentally measures the binding energies of electrons in different orbitals, providing direct evidence for electron configuration and shielding.
Coulomb's Law & Atomic Behavior
Coulomb's law quantifies the electrostatic forces between charges and underlies most periodic trends and bonding.
Key fact
Electron configurations fill in order of increasing energy (Aufbau) with Hund's rule maximizing unpaired spins in degenerate orbitals.
Key fact
Atomic radius decreases across a period and increases down a group; ionization energy and electronegativity show the opposite trend.
Key fact
PES peak position = binding energy (closer to nucleus = higher); peak height = number of electrons in that orbital.
Key fact
Effective nuclear charge and Coulomb's law ($F = kq_1q_2/r^2$) explain essentially every periodic trend.

Unit 6: Bonding & IMFs

Ionic, Covalent & Metallic Bonding
The three major bonding types arise from different ways atoms share or transfer electrons, driven by electronegativity differences.
Lewis Structures & Formal Charge
Lewis structures show how valence electrons are arranged as bonds and lone pairs, with formal charge helping choose the best structure.
VSEPR Theory & Molecular Geometry
VSEPR theory predicts 3D molecular shape from the number of electron domains (bonds + lone pairs) around a central atom, which repel each other to minimize energy.
Molecular Polarity & Dipole Moments
A molecule's overall polarity depends on both individual bond polarities and molecular geometry, since bond dipoles can cancel by symmetry.
Intermolecular Forces (IMFs)
Intermolecular forces are attractions between separate molecules, weaker than covalent/ionic bonds, but they govern boiling points, solubility, and physical states.
Solids & Phase Behavior
The type of particle and force holding a solid together determines its physical properties, and phase diagrams map how substances change state with temperature and pressure.
Key fact
Bond type follows electronegativity difference: metal + nonmetal = ionic; nonmetal + nonmetal = covalent (polar or nonpolar).
Key fact
VSEPR shape depends on total electron domains (bonding + lone pairs); lone pairs compress bond angles below the ideal.
Key fact
IMF strength ranking: ionic/covalent bonds > hydrogen bonding > dipole-dipole > London dispersion forces.
Key fact
A molecule can have polar bonds yet be nonpolar overall if the bond dipoles cancel by symmetry (e.g. CO2, CCl4).

Unit 7: Kinetics & Equilibrium

Reaction Rates & Rate Laws
Reaction rate measures how fast reactants are consumed or products form, and the rate law expresses this mathematically in terms of concentrations.
Integrated Rate Laws & Half-Life
Integrated rate laws relate concentration directly to time, letting you predict concentration at any point or determine reaction order from a graph.
Collision Theory & Reaction Mechanisms
Reactions occur when molecules collide with sufficient energy and correct orientation, and most reactions proceed through a multi-step mechanism.
Chemical Equilibrium & Keq
Equilibrium is a dynamic state where forward and reverse reaction rates are equal, and Keq quantifies the ratio of products to reactants at that point.
Le Chatelier's Principle
Le Chatelier's principle predicts how an equilibrium system responds to a disturbance by shifting to partially counteract the change.
Free Energy & Equilibrium Connection
Gibbs free energy determines reaction spontaneity and connects thermodynamics to the equilibrium constant.
Key fact
Rate laws ($rate = k[A]^m[B]^n$) are determined experimentally, never from the balanced equation's coefficients.
Key fact
First-order half-life is constant (t1/2 = 0.693/k); zero- and second-order half-lives change with concentration.
Key fact
Only a temperature change alters the value of K; concentration, pressure/volume, and catalysts shift the equilibrium position but not K itself.
Key fact
Delta G° = -RT ln(K): a very negative Delta G° corresponds to a very large K, and Delta G = 0 exactly at equilibrium.

Unit 8: Acids-Bases & Electrochemistry

Acid-Base Definitions & pH/pOH
Acids and bases can be defined by proton or electron transfer, and pH/pOH provide a convenient scale for describing [H+] and [OH-].
Weak Acids/Bases: Ka, Kb & Equilibrium
Weak acids and bases only partially dissociate in water, and Ka/Kb quantify the extent of that ionization at equilibrium.
Buffers & the Henderson-Hasselbalch Equation
Buffers resist changes in pH by containing both a weak acid and its conjugate base (or weak base and conjugate acid) in significant amounts.
Titrations & Equivalence Points
Titrations use a solution of known concentration to determine the concentration or identity of an unknown acid or base, tracked via a pH curve.
Redox Reactions & Oxidation States
Oxidation-reduction (redox) reactions involve electron transfer, tracked using oxidation numbers and balanced with half-reactions.
Galvanic (Voltaic) Cells & Electrochemistry
Galvanic cells convert spontaneous redox reactions into electrical energy, with standard reduction potentials predicting voltage and spontaneity.
Key fact
pH + pOH = 14.00 at 25°C; Ka x Kb = Kw = 1.0 x $10^{-14}$ for a conjugate acid-base pair.
Key fact
Henderson-Hasselbalch: pH = pKa + log([A-]/[HA]); buffers work best when pH is within about 1 unit of pKa.
Key fact
At the half-equivalence point of a weak acid titration, pH = pKa; strong acid-strong base equivalence point is pH 7.
Key fact
Galvanic cells: oxidation at the anode, reduction at the cathode, electrons flow anode to cathode, and a positive E°cell means a spontaneous reaction.
Common mistakes for each unit — read the mistake, then make sure you know why it's wrong.

Unit 1: Atomic Structure & Moles

Watch out
Atomic mass on the periodic table is a weighted average of isotopes, not the mass of any single atom
Watch out
Molar mass and molecular mass have the same numeric value but different units (g/mol vs amu) — students often confuse them
Watch out
An empirical formula is the simplest ratio; it is not necessarily the actual molecular formula unless n = 1
Watch out
Isotopes of the same element have identical chemical behavior (same electron count) but different mass — mass differences don't change reactivity

Unit 2: Stoichiometry

Watch out
Mole ratios come from balanced coefficients, not from the masses or grams given in the problem — convert to moles first, not last
Watch out
The reactant with the smaller mass or fewer grams is not automatically the limiting reactant — you must compare moles of product each could form
Watch out
Percent yield over 100% signals an experimental error (like impure product), not a real result — it should be flagged, not accepted
Watch out
Balancing equations changes coefficients, never subscripts — changing a subscript makes a different compound entirely

Unit 3: Gas Laws

Watch out
Temperature must be in Kelvin for all gas law calculations, not Celsius — forgetting this is the single most common gas law error
Watch out
Real gases deviate most from ideal behavior at high pressure and low temperature, not at STP where ideal behavior is a good approximation
Watch out
Lighter gases effuse faster, not slower — students often reverse Graham's Law's inverse square-root relationship
Watch out
Ideal Gas Law assumes negligible particle volume and no intermolecular forces; these assumptions break down for real gases under extreme conditions

Unit 4: Thermochemistry

Watch out
Exothermic means the system releases energy (ΔH negative), but the surroundings get warmer, not colder — students often confuse which side loses energy
Watch out
In calorimetry, $q_{reaction} = -q_{solution}$ (opposite signs) because energy lost by one is gained by the other, not equal positive values
Watch out
A reaction can be spontaneous even if endothermic, as long as ΔS is positive enough and T is high enough to make ΔG negative — spontaneity is not just about heat release
Watch out
Bond breaking always costs energy and bond forming always releases energy; a common error is reversing which process is endothermic vs. exothermic

Unit 5: Atomic Structure & Periodicity

Watch out
Transition metals lose 4s electrons first when ionizing, not 3d electrons — Fe2+ is [Ar]$3d^6$, not [Ar]$4s^2\ 3d^4$.
Watch out
Ionization energy increases across a period and up a group, not down a group — don't mix up radius and IE directions.
Watch out
PES peak height reflects the number of electrons in a subshell, not the energy — taller peaks mean more electrons, not more tightly bound.
Watch out
Anions are larger, not smaller, than their neutral parent atom because added electron-electron repulsion outweighs the same nuclear charge.

Unit 6: Bonding & IMFs

Watch out
A molecule with polar bonds is not automatically polar — check geometry, since symmetric shapes cancel dipoles (CO2 is nonpolar despite polar C=O bonds).
Watch out
Hydrogen bonding requires H bonded directly to N, O, or F — an O-H bond elsewhere in a molecule counts, but C-H bonds never count as hydrogen bonding.
Watch out
London dispersion forces exist in ALL molecules, not just nonpolar ones — they're often the dominant force in large nonpolar molecules, sometimes stronger than dipole-dipole in smaller polar ones.
Watch out
Lone pairs count as electron domains for determining shape (VSEPR), but they are not counted when naming the molecular geometry itself (e.g. NH3 is 'trigonal pyramidal,' not 'tetrahedral,' despite 4 domains).

Unit 7: Kinetics & Equilibrium

Watch out
Reaction order comes from experimental data (initial rates method), not from the stoichiometric coefficients in the balanced equation.
Watch out
Adding an inert gas at constant volume does NOT shift equilibrium, because it doesn't change any reactant/product concentration or partial pressure.
Watch out
A catalyst speeds up both the forward and reverse reactions equally — it changes the rate at which equilibrium is reached, not the equilibrium position or K.
Watch out
Increasing temperature shifts equilibrium based on which direction is endothermic, not simply 'always toward products' — treat heat as a reactant (endothermic) or product (exothermic).

Unit 8: Acids-Bases & Electrochemistry

Watch out
A weak acid-strong base titration has an equivalence point pH greater than 7, not 7 — don't assume every equivalence point is neutral.
Watch out
Ka and Kb are related by Ka x Kb = Kw for a conjugate pair, not Ka = Kb — a stronger acid always has a weaker conjugate base.
Watch out
In a galvanic cell, electrons flow from anode to cathode through the wire, while conventional current and cations in the salt bridge move to maintain charge balance — don't reverse anode/cathode with electrode charge sign.
Watch out
Oxidation is loss of electrons (increase in oxidation number), not gain — mixing up OIL RIG is one of the most common redox errors.