- Aufbau principle
- Electrons fill the lowest-energy orbitals first when building an atom's ground-state configuration — so 4s fills before 3d.
- Pauli exclusion principle
- No two electrons in an atom can have the same four quantum numbers; an orbital holds at most 2 electrons, with opposite spins.
- Hund's rule
- Electrons singly occupy each orbital in a subshell, with parallel spins, before any orbital is doubly occupied.
- The four quantum numbers
- n (energy level), ℓ (orbital shape: s/p/d/f), mℓ (orientation), and mₛ (spin, ±½).
- Isotopes
- Atoms of the same element (same protons) with different numbers of neutrons, and so different mass numbers.
- Atomic number vs. mass number
- Atomic number = number of protons (defines the element); mass number = protons + neutrons.
- Trend: atomic radius
- Decreases across a period (left → right) and increases down a group.
- Trend: ionization energy
- Increases across a period and decreases down a group (it takes more energy to remove an electron from a smaller, tightly held atom).
- Trend: electronegativity
- Increases across a period and decreases down a group; fluorine is the most electronegative element.
- Energy of a photon
- E = hν = hc/λ — higher frequency (shorter wavelength) means higher energy.
- Maximum electrons per subshell
- s holds 2, p holds 6, d holds 10, f holds 14 (each orbital holds 2).
- Electron configuration of a cation
- Remove electrons from the highest n first — for transition metals the 4s electrons leave before the 3d (e.g., Fe²⁺ is [Ar]3d⁶).
- Effective nuclear charge
- The net positive charge an electron feels after shielding by inner electrons; it rises across a period, pulling electrons in.
- Noble gas (Group 18)
- Elements with a full valence shell, very stable and unreactive — all are monatomic gases at room temperature.
- Average atomic mass
- The abundance-weighted average mass of an element's naturally occurring isotopes.
- Ionic bond
- Electrostatic attraction between oppositely charged ions formed when a metal transfers electrons to a nonmetal (e.g., NaCl).
- Covalent bond
- A bond formed by two atoms sharing one or more pairs of electrons (typically between nonmetals).
- Polar vs. nonpolar covalent bond
- Unequal electron sharing (electronegativity difference ~0.4–1.7) is polar covalent; near-equal sharing is nonpolar.
- VSEPR theory
- Electron groups around a central atom arrange to minimize repulsion, which sets the molecule's geometry.
- Steric number
- Bonded atoms + lone pairs on the central atom; it sets the electron-domain geometry and the hybridization.
- Geometry: steric number 2 / 3 / 4
- 2 → linear (180°), 3 → trigonal planar (120°), 4 → tetrahedral (109.5°).
- Hybridization by steric number
- 2 → sp, 3 → sp², 4 → sp³, 5 → sp³d, 6 → sp³d².
- Why is water bent?
- Oxygen has steric number 4 (2 bonds + 2 lone pairs); the lone pairs push the bonds to a bent ~104.5° shape.
- Electron geometry vs. molecular geometry
- Electron geometry counts all bonding pairs and lone pairs; molecular geometry describes only the arrangement of bonded atoms.
- Formal charge
- FC = (valence electrons) − (nonbonding electrons) − ½(bonding electrons); the best Lewis structure minimizes formal charges.
- Resonance structures
- Structures that differ only in electron placement, not nuclear positions; the real molecule is a hybrid of all of them.
- Sigma vs. pi bond
- A sigma bond is head-on orbital overlap along the bond axis; a pi bond is side-to-side overlap above and below the axis.
- Single, double, triple bonds
- A single bond is 1 sigma; a double is 1 sigma + 1 pi; a triple is 1 sigma + 2 pi (shorter and stronger).
- Is a molecule polar?
- It is polar only if its individual bond dipoles do NOT cancel — CO₂ is nonpolar (symmetric), H₂O is polar (bent).
- Lewis structure steps
- Total valence electrons → least-electronegative atom (not H) in center → single bonds → distribute lone pairs to satisfy octets → add multiple bonds if needed.
- Octet rule (and exceptions)
- Atoms tend to gain a full 8-electron valence shell; exceptions include H (2), incomplete octets (B), and expanded octets (P, S).
- Bond dipole direction
- Points from the less electronegative atom toward the more electronegative atom.
- Intermolecular forces (strongest to weakest)
- Ion–dipole > hydrogen bonding > dipole–dipole > London dispersion.
- Hydrogen bonding
- A strong dipole–dipole attraction when H is bonded to N, O, or F; it gives water its high boiling point and surface tension.
- London dispersion forces
- Weak, temporary-dipole attractions present in ALL molecules; they grow with molar mass and polarizability.
- Effect of stronger IMFs
- Higher boiling point and melting point, higher viscosity and surface tension, and lower vapor pressure.
- Ideal gas law
- PV = nRT — relates pressure, volume, moles, and absolute temperature; R = 0.0821 L·atm/mol·K.
- Boyle's law
- At constant temperature, pressure and volume are inversely related: P ∝ 1/V, so P₁V₁ = P₂V₂.
- Charles's law
- At constant pressure, volume is directly proportional to absolute temperature: V ∝ T.
- Combined gas law
- P₁V₁/T₁ = P₂V₂/T₂ — temperature must be in kelvin.
- Dalton's law of partial pressures
- The total pressure of a gas mixture equals the sum of the partial pressures of its components.
- Graham's law of effusion
- Lighter gases effuse faster: r₁/r₂ = √(M₂/M₁).
- Kinetic molecular theory
- Gas particles are tiny, in constant random motion, with negligible volume and no IMFs; average kinetic energy ∝ absolute temperature.
- Colligative property
- A solution property that depends on the NUMBER of dissolved particles, not their identity.
- Boiling-point elevation
- A non-volatile solute raises the boiling point: ΔTb = i·Kb·m (m = molality, i = van't Hoff factor).
- Freezing-point depression
- A solute lowers the freezing point: ΔTf = i·Kf·m — why salt melts ice on roads.
- Raoult's law
- The vapor pressure of a solvent over an ideal solution is lowered: P = X(solvent)·P° (X = mole fraction).
- Van't Hoff factor (i)
- The number of particles a solute produces in solution: NaCl gives i ≈ 2, glucose i = 1.
- Like dissolves like
- Polar/ionic solutes dissolve in polar solvents; nonpolar solutes dissolve in nonpolar solvents.
- Critical point
- The temperature and pressure above which a distinct liquid phase can no longer exist (a supercritical fluid).
- Stoichiometry
- Using the mole ratios in a balanced equation to relate amounts of reactants and products.
- The mole
- The amount of substance containing Avogadro's number (6.022 × 10²³) of particles; it bridges mass and number of particles.
- Moles from mass
- n = mass ÷ molar mass.
- Limiting reactant
- The reactant consumed first; it caps the amount of product (theoretical yield).
- Percent yield
- (actual yield ÷ theoretical yield) × 100%.
- Molarity
- Concentration = moles of solute ÷ liters of solution (mol/L, M).
- Dilution equation
- M₁V₁ = M₂V₂ — moles of solute are conserved when you add solvent.
- Oxidation vs. reduction (OIL RIG)
- Oxidation Is Loss of electrons; Reduction Is Gain of electrons. They always occur together.
- Oxidizing vs. reducing agent
- The oxidizing agent is reduced (gains electrons); the reducing agent is oxidized (loses electrons).
- Combustion reaction
- A hydrocarbon + O₂ → CO₂ + H₂O, releasing heat (exothermic).
- Precipitation reaction
- Two soluble salts react to form an insoluble solid (precipitate) — predicted with solubility rules.
- Acid–base (neutralization) reaction
- An acid + a base → a salt + water (H⁺ + OH⁻ → H₂O).
- Avogadro's number
- 6.022 × 10²³ — the number of particles in one mole.
- Enthalpy (ΔH)
- Heat exchanged at constant pressure; ΔH < 0 is exothermic (releases heat), ΔH > 0 is endothermic (absorbs heat).
- Calorimetry equation
- q = mcΔT — heat = mass × specific heat × temperature change.
- Hess's law
- The overall ΔH of a reaction equals the sum of the ΔH of its steps, because enthalpy is a state function.
- ΔH from heats of formation
- ΔH°rxn = ΣΔHf°(products) − ΣΔHf°(reactants).
- Standard enthalpy of formation of an element
- Zero — for an element in its standard state (e.g., O₂(g), N₂(g)).
- Entropy (ΔS)
- A measure of disorder / dispersal of energy and matter; gases have higher entropy than liquids or solids.
- Second law of thermodynamics
- The total entropy of the universe (system + surroundings) increases for any spontaneous process.
- Gibbs free energy
- ΔG = ΔH − TΔS; a process is spontaneous when ΔG < 0, at equilibrium when ΔG = 0.
- When is a reaction spontaneous at all temperatures?
- When ΔH < 0 (exothermic) and ΔS > 0 (more disorder) — both favor a negative ΔG.
- When is a reaction never spontaneous?
- When ΔH > 0 (endothermic) and ΔS < 0 (less disorder) — ΔG is positive at every temperature.
- Sign of ΔS for fewer moles of gas
- Negative — converting more moles of gas to fewer (e.g., N₂ + 3H₂ → 2NH₃) decreases disorder.
- First law of thermodynamics
- Energy is conserved: ΔU = q + w (internal energy change = heat added + work done on the system).
- ΔG° and the equilibrium constant
- ΔG° = −RT ln K — a negative ΔG° means K > 1 (products favored).
- Rate law
- rate = k[A]ᵐ[B]ⁿ; the orders m and n are found experimentally, NOT from the balanced coefficients.
- Reaction order
- The exponent on a reactant in the rate law; the overall order is the sum of the exponents.
- Activation energy (Eₐ)
- The minimum collision energy needed for a reaction to occur — the barrier on the energy profile.
- How does a catalyst work?
- It provides an alternate pathway with lower Eₐ, speeding both directions; it is not consumed and does not change ΔH or K.
- First-order half-life
- t½ = 0.693/k — constant, independent of the starting concentration.
- Arrhenius equation
- k = A·exp(−Eₐ/RT); raising temperature or lowering the activation energy Eₐ increases the rate constant k.
- Collision theory
- A collision leads to reaction only if the molecules have enough energy (≥ Eₐ) AND the correct orientation.
- Rate-determining step
- The slowest elementary step in a mechanism; it controls the overall reaction rate.
- Effect of temperature on rate
- Higher temperature increases the fraction of molecules with energy ≥ Eₐ, so the rate rises sharply.
- Effect of concentration / surface area
- Higher reactant concentration or surface area increases collision frequency, raising the rate.
- Integrated first-order rate law
- ln[A] = ln[A]₀ − kt — a plot of ln[A] vs. time is linear for a first-order reaction.
- Chemical equilibrium
- The state where forward and reverse reaction rates are equal, so concentrations stay constant (dynamic, not static).
- Equilibrium constant (K)
- Products over reactants, each raised to its coefficient: K > 1 favors products, K < 1 favors reactants.
- Reaction quotient (Q)
- The same ratio as K but at any moment: Q < K shifts forward, Q > K shifts reverse, Q = K is equilibrium.
- Le Chatelier's principle
- A disturbed equilibrium shifts to partly counteract the change and restore balance.
- Effect of pressure on a gas equilibrium
- Increasing pressure (decreasing volume) shifts toward the side with fewer moles of gas.
- Effect of temperature on K
- Treat heat as a reactant/product: raising T raises K for endothermic reactions and lowers K for exothermic ones.
- Does a catalyst change K?
- No — a catalyst speeds the approach to equilibrium but does not change the equilibrium position or K.
- pH
- pH = −log[H⁺]; below 7 acidic, 7 neutral, above 7 basic. At 25 °C, pH + pOH = 14.
- Strong vs. weak acid
- A strong acid ionizes completely (HCl); a weak acid only partially ionizes, described by its Ka.
- Kw and its value
- The ion-product of water, Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C; Ka·Kb = Kw for a conjugate pair.
- Buffer
- A solution of a weak acid + its conjugate base that resists pH change when small amounts of acid/base are added.
- Henderson–Hasselbalch equation
- pH = pKa + log([A⁻]/[HA]); a buffer works best when pH ≈ pKa.
- Equivalence point of a titration
- Where moles of added titrant exactly neutralize the analyte; an indicator marks it by changing color.
- Solubility product (Ksp)
- The equilibrium constant for dissolving a slightly soluble salt; a smaller Ksp means a less soluble compound.
- Common-ion effect
- Adding an ion already present in the equilibrium shifts it toward the solid, decreasing solubility.
- Conjugate acid–base pair
- Two species differing by one H⁺ (e.g., NH₄⁺/NH₃); the stronger the acid, the weaker its conjugate base.
- Galvanic (voltaic) cell
- An electrochemical cell that uses a spontaneous redox reaction to generate electricity (ΔG < 0, E°cell > 0).
- Anode vs. cathode (AN OX, RED CAT)
- Oxidation occurs at the ANode; reduction occurs at the CAThode.
- Standard cell potential
- E°cell = E°cathode − E°anode; a positive E°cell means a spontaneous reaction.
- Nernst equation
- E = E° − (0.0592/n)·log Q at 25 °C — gives the cell potential under non-standard conditions.
- ΔG° and cell potential
- ΔG° = −nFE°cell (F = 96,485 C/mol); a positive E° gives a negative ΔG° (spontaneous).
- Standard hydrogen electrode (SHE)
- The reference half-cell, assigned E° = 0 V; all other standard reduction potentials are measured against it.
- Significant figures: × and ÷
- The answer keeps the fewest significant figures of any factor used.
- Significant figures: + and −
- The answer keeps the fewest decimal places of any value used.
- Accuracy vs. precision
- Accuracy is closeness to the true value; precision is reproducibility — they are independent.
- Systematic vs. random error
- A systematic error (uncalibrated balance) biases every reading the same way; random error scatters readings unpredictably.
- Titration
- A technique to find an unknown concentration by adding a measured titrant until the equivalence point (indicator color change).
- Distillation
- Separates liquids by boiling point — the lower-boiling component vaporizes and is collected first.
- Gravimetric analysis
- Quantifies an analyte by the mass of a precipitate that is filtered, dried, and weighed.
- Three levels of representation (Visualization)
- Particulate (atoms/molecules), macroscopic (what you observe), and symbolic (formulas, equations, graphs).
- Blank titration
- A titration run with all reagents except the analyte, used to correct for impurities in the reagents.
- Why calibrate a pH meter with two buffers?
- To check linearity — calibrating at two known pH values verifies the meter's response across a range.
- Reflux
- Heating with a vertical condenser so vapor condenses and returns, allowing a long reaction without losing volatile reactants.
- Exact vs. measured numbers
- Exact (counted or defined) numbers have unlimited significant figures; measured numbers carry uncertainty in the last digit.
