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NY Regents · Chemistry

Chemistry Study Guide Expanded Edition

16 Units · 469 Quiz Questions · 155 Flashcards · Full Reference Tables · Diagrams · Tuned to Jan 2026 Regents

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Classification of matter
Matter is either a pure substance (fixed composition) or a mixture (variable composition). Elements are single atom types; compounds are chemically bonded elements in fixed ratios; mixtures are physically separable.
  • Element: one atom type; cannot be broken down chemically (Fe, O₂, Cu, Ne)
  • Compound: two or more elements chemically bonded in fixed ratio; separated only by chemical means (H₂O, NaCl, CO₂)
  • Homogeneous mixture (solution): uniform throughout, single phase (salt water, air, brass, vinegar)
  • Heterogeneous mixture: non-uniform, visible different parts (sand+water, salad, granite, blood)
  • Colloid: particles 1–1000 nm; Tyndall effect (milk, fog, gelatin) — between solution and suspension
  • Suspension: particles >1000 nm; settles on standing; filtered easily (muddy water, Italian dressing)
Separation techniques
All based on physical properties — no new substances form.
  • Filtration: separates insoluble solid from liquid (sand from water; coffee grounds from liquid)
  • Distillation: separates two miscible liquids with different boiling points (alcohol from water; crude oil refining)
  • Evaporation/crystallization: recovers dissolved solid from solution (salt from seawater)
  • Chromatography: separates dissolved substances by polarity/affinity differences (ink pigments, amino acids)
  • Magnetism: separates magnetic material from non-magnetic (iron filings from sand)
  • Centrifugation: separates by density using centrifugal force (cream from milk; blood components)
Allotropes
Allotropes are different structural forms of the SAME element. Same element, different molecular structure → different physical and chemical properties.
  • O₂ (oxygen) and O₃ (ozone): same element (oxygen), different molecular structures → different properties. O₃ is more reactive and has a distinct smell.
  • Diamond and graphite: both pure carbon, but different bonding structures → diamond is hardest known substance; graphite is soft and conducts electricity
  • White phosphorus (P₄) and red phosphorus: both pure P, different properties
  • Key point: allotropes of the same element have DIFFERENT molecular structures AND DIFFERENT properties
  • They have the same atomic number and are made of the same type of atom — only the bonding arrangement differs
Chemical vs physical change
Physical: form/phase changes, composition unchanged. Chemical: new substance with new properties forms.
  • Physical changes: melting, boiling, freezing, dissolving, cutting, crushing, bending, mixing
  • Chemical change indicators: color change, gas produced (bubbles), precipitate formed, irreversible temperature change, light/sound emitted, new odor
  • Dissolving is PHYSICAL — NaCl in water is still NaCl; evaporate the water and you get NaCl back
  • Burning is CHEMICAL — cellulose → CO₂ + H₂O; cannot recover the wood
  • Rusting is CHEMICAL — Fe + O₂ → Fe₂O₃; new substance with new properties
Physical vs chemical properties
  • Physical property: observable without changing composition — color, density, melting point, boiling point, conductivity, solubility, hardness, odor
  • Chemical property: describes how a substance reacts — flammability, reactivity with acids, ability to corrode, toxicity
  • Intensive property: independent of sample size — density, temperature, melting point, color, concentration
  • Extensive property: depends on amount — mass, volume, length, heat content
Dissolving is PHYSICAL — no new substance forms, fully reversible by evaporation.
Compounds separated only by CHEMICAL means; mixtures by PHYSICAL means.
Colloids show the Tyndall effect (light scattering); true solutions do not.
Intensive properties (density, BP) don't change when you cut a sample in half.
D = m / V
% error = |measured − accepted| / accepted × 100
Significant figures
Atlantic-Pacific Rule: decimal Present → count from Pacific side (left) starting at first nonzero; decimal Absent → count from Atlantic side (right) starting at first nonzero.
  • Non-zero digits: ALWAYS significant (245 → 3 sig figs)
  • Leading zeros: NEVER significant (0.0034 → 2 sig figs)
  • Captive zeros (between nonzeros): ALWAYS significant (2005 → 4 sig figs)
  • Trailing zeros WITH decimal point: significant (2.500 → 4 sig figs; 100. → 3 sig figs)
  • Trailing zeros WITHOUT decimal: ambiguous (1500 → 2 sig figs; write 1.500×10³ for 4 sig figs)
  • Exact numbers (counted/defined): infinite sig figs (12 eggs, 100 cm = 1 m)
Sig figs in calculations
  • Multiply/divide: answer has fewest sig figs of any factor (2.5 × 3.45 = 8.6, not 8.625)
  • Add/subtract: answer has fewest DECIMAL PLACES (12.5 + 3.45 = 16.0, not 15.95)
  • Mixed: follow order of operations, apply sig fig rule at each step
Accuracy vs precision
  • Accuracy: closeness to the true/accepted value → measured by % error
  • Precision: closeness of repeated measurements to each other → measured by range/deviation
  • High precision, low accuracy: consistent but wrong (systematic error)
  • High accuracy, low precision: correct on average but scattered (random error)
  • Calibration improves accuracy; technique improves precision
Mole concept
A mole is 6.02×10²³ particles (Avogadro's number). It is chemistry's 'counting unit' — like a dozen = 12, a mole = 6.02×10²³.
  • 1 mol = 6.02×10²³ particles (atoms, molecules, ions, formula units)
  • 1 mol of any substance = its molar mass in grams (e.g., 1 mol H₂O = 18.0 g)
  • Moles→particles: × 6.02×10²³ | Particles→moles: ÷ 6.02×10²³
  • Moles→grams: × GFM | Grams→moles: ÷ GFM
  • GFM (gram formula mass) = sum of all atomic masses in formula
  • Example: GFM of Ca(NO₃)₂ = 40.1 + 2(14.0 + 3×16.0) = 164.1 g/mol
Scientific notation & dimensional analysis
  • Scientific notation: M × 10ⁿ where 1 ≤ M < 10 (e.g., 0.00034 = 3.4×10⁻⁴)
  • Dimensional analysis: cancel units by writing conversion factors as fractions
  • Always write units with every number; check that unwanted units cancel
  • Example: 5.0 km × (1000 m/1 km) × (100 cm/1 m) = 5.0×10⁵ cm
0.0034 has only 2 sig figs — leading zeros never count.
% error is ALWAYS positive — use absolute value.
1500 = 2 sig figs; 1500. = 4 sig figs (the decimal point matters).
Accuracy ≠ precision — you can be precise AND wrong.
n = m / GFM
% error = |measured − accepted| / accepted × 100
1 mol = 6.02×10²³ particles
History of atomic models
Each model was replaced when experimental evidence it couldn't explain emerged.
  • Dalton (1803): solid, indivisible sphere — explained fixed mass ratios; no substructure
  • Thomson (1897): plum pudding — discovered electrons via cathode ray tube; positive sphere with embedded e⁻
  • Rutherford (1911): nuclear model — gold foil experiment; dense positive nucleus, mostly empty space; most α passed through, few deflected back
  • Bohr (1913): planetary/shell model — electrons in fixed circular orbits at set energy levels; explained hydrogen bright-line spectrum
  • Wave-mechanical (quantum) model (current): electrons in probability clouds (orbitals), not fixed paths; explains all elements' spectra
Subatomic particles
  • Proton: charge +1, mass ≈1 amu, located in nucleus; atomic number = number of protons = element identity
  • Neutron: charge 0, mass ≈1 amu, located in nucleus; number of neutrons = mass number − atomic number
  • Electron: charge −1, mass ≈0 amu (1/1836 of proton), in orbitals outside nucleus
  • Neutral atom: protons = electrons
  • Cation (+): atom LOST electrons (Na → Na⁺ lost 1 e⁻)
  • Anion (−): atom GAINED electrons (Cl → Cl⁻ gained 1 e⁻)
Electron configuration
Electrons fill lowest energy levels first (aufbau principle). Each orbital holds max 2 electrons with opposite spins (Pauli). One electron per orbital before pairing (Hund's rule).
  • s sublevel: max 2 e⁻ (1 orbital) | p: max 6 e⁻ (3 orbitals) | d: max 10 e⁻ (5 orbitals) | f: max 14 e⁻ (7 orbitals)
  • Fill order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p
  • Ground state: lowest energy config (unique to each element, matches position on periodic table)
  • Excited state: electron absorbed energy and moved to a higher sublevel — total e⁻ count still equals atomic number
  • Special exceptions on Regents: Cr (24) = [Ar] 3d⁵ 4s¹; Cu (29) = [Ar] 3d¹⁰ 4s¹ (half-filled/filled d is extra stable)
Isotopes & atomic mass
Isotopes: same element (same protons), different neutrons, different mass number.
  • Isotope notation: ᴬ_Z X or element-mass (e.g., ¹²₆C or Carbon-12)
  • Same: atomic number, number of protons, chemical behavior, element identity
  • Different: mass number, number of neutrons, nuclear stability, physical mass
  • Atomic mass (on periodic table) = weighted average of all isotopes' masses × their natural abundances
  • Example: Cl has two isotopes — Cl-35 (75.77%) and Cl-37 (24.23%) → avg = 35.5 amu
Bright-line spectra
Excited electrons fall to lower energy levels → release energy as photons of specific wavelengths → unique spectral 'fingerprint' for each element.
  • Each element has a unique bright-line spectrum (used to identify elements in stars, flames)
  • Continuous spectrum: all wavelengths (white light through prism)
  • Bright-line (emission) spectrum: only specific wavelengths emitted
  • Higher jump → shorter wavelength → higher frequency → more energy
  • EM spectrum order (low→high energy): radio, microwave, infrared, visible (ROYGBIV), UV, X-ray, gamma
  • c = λν: speed of light = wavelength × frequency
Excited state is VALID — total electrons still equal atomic number; just not the lowest arrangement.
4s fills BEFORE 3d (4s is lower energy during filling); but 3d is listed below 4s in configs.
Rutherford DISPROVED Thomson's model.
Atomic mass ≠ mass number — atomic mass is a weighted average (often a decimal).
Atomic mass = Σ(isotope mass × fractional abundance)
Neutrons = mass number − atomic number
c = λν
Diagram
foil + α particles → ← few deflect

Rutherford gold-foil experiment — most α particles pass through (empty space); a few deflect off the dense positive nucleus.

Organization & groups
118 elements arranged by increasing atomic number. Properties repeat periodically (periodic law).
  • Period (row): elements in same period have same number of electron shells
  • Group/family (column): elements with same number of valence electrons, similar chemical properties
  • Group 1 (Alkali metals): 1 valence e⁻, very reactive, +1 ions, react violently with water
  • Group 2 (Alkaline earth): 2 valence e⁻, reactive, +2 ions
  • Groups 3–12 (Transition metals): variable oxidation states, colored compounds, use Table S for charges
  • Group 17 (Halogens): 7 valence e⁻, most reactive nonmetals, form −1 ions, diatomic molecules
  • Group 18 (Noble gases): full valence shell (8 e⁻, or 2 for He), nonreactive, monatomic
Metals, nonmetals, metalloids
The staircase line on the periodic table separates metals (left) from nonmetals (right).
  • Metals (~75% of elements): shiny luster, malleable, ductile, good conductors of heat & electricity, lose electrons to form cations
  • Nonmetals (upper right): dull/brittle, poor conductors (except graphite), gain/share electrons, form anions or covalent bonds
  • Metalloids (B, Si, Ge, As, Sb, Te — along the staircase): intermediate properties; semiconductors used in electronics
  • Hydrogen: unique — placed in Group 1 but is a nonmetal gas; can behave as +1 or −1
Periodic trends
All trends driven by nuclear charge (# protons) vs. shielding (inner electron shells). More protons = stronger pull on outer electrons. More shells = more shielding = weaker effective nuclear charge.
  • Atomic radius: DECREASES left→right (more protons, same shell), INCREASES top→bottom (more shells)
  • Ionization energy (energy to remove 1 e⁻): INCREASES left→right, DECREASES top→bottom
  • Electronegativity (pull on shared electrons): INCREASES left→right, DECREASES top→bottom; highest = F (4.0); lowest = Fr
  • Metallic character: DECREASES left→right, INCREASES top→bottom (opposite of EN)
  • Ionic radius: cations are SMALLER than parent atom (lost e⁻, same protons pull fewer e⁻ closer); anions are LARGER (gained e⁻, same protons spread over more e⁻)
Transition metal naming (Roman numerals)
Transition metals have variable oxidation states. Roman numerals in the name tell you which charge the metal has in that compound.
  • Format: metal name (Roman numeral) anion name — e.g., Iron(II) chloride = FeCl₂ (Fe²⁺); Iron(III) chloride = FeCl₃ (Fe³⁺)
  • The Roman numeral = the oxidation state/charge of the transition metal in that compound
  • To find the Roman numeral: use the anion charge to figure out what the metal charge must be so everything sums to zero
  • FeCl₂: Cl = −1 (×2 = −2) → Fe = +2 → iron(II). FeCl₃: Cl = −1 (×3 = −3) → Fe = +3 → iron(III)
  • PdO: O = −2 → Pd = +2 → palladium(II) oxide
  • CuO = copper(II) oxide; Cu₂O = copper(I) oxide — same elements, different ratios, different names
  • Common transition metals with multiple charges: Fe (2+,3+), Cu (1+,2+), Cr (2+,3+,6+), Mn (2+,4+,7+), Pb (2+,4+), Sn (2+,4+)
Valence electrons & ion charges
  • Main-group valence electrons = group number (Group 1 = 1, Group 2 = 2, Group 13 = 3 ... Group 18 = 8)
  • Metals lose valence electrons to reach noble gas config → cations
  • Nonmetals gain electrons to fill valence shell → anions
  • Isoelectronic: same electron configuration (Na⁺, Mg²⁺, Ne, O²⁻, F⁻ all have 10 electrons)
  • Transition metals: use Table S — most have multiple possible charges (Fe²⁺/Fe³⁺, Cu⁺/Cu²⁺)
Fluorine has the HIGHEST electronegativity (4.0).
Coulombic attraction (F = kq₁q₂/r²) is the underlying reason for ALL periodic trends.
Transition metals don't follow main-group valence-electron rules for charges.
Noble gases are in Group 18 — 8 valence electrons (not 0).
EN diff: <0.4 nonpolar covalent | 0.4–1.7 polar covalent | ≥1.7 ionic
Coulomb's Law: F = k(q₁q₂)/r²
Diagram
Periodic Table EN / IE increase → Radius increases ↓ F

Periodic trends: atomic radius grows ↓ and ←. Ionization energy and electronegativity grow ↑ and → (toward F in the top-right).

Bond types
Determined by electronegativity difference (ΔEN) between bonded atoms.
  • Ionic (ΔEN ≥ 1.7): metal + nonmetal; electron TRANSFER; forms ions; electrostatic attraction (NaCl, MgO, CaF₂)
  • Polar covalent (ΔEN 0.4–1.7): nonmetal + nonmetal of different EN; UNEQUAL sharing; δ⁺ and δ⁻ partial charges (HF, H₂O, NH₃, HCl)
  • Nonpolar covalent (ΔEN <0.4): same element or very similar EN; EQUAL sharing (Cl₂, O₂, N₂, CH₄, C-C bonds)
  • Metallic: sea of delocalized valence electrons around fixed positive metal ion cores; explains conductivity, malleability, luster
Lewis dot structures
Count total valence electrons → draw skeleton (central atom = least electronegative, usually) → add lone pairs to satisfy octets.
  • Octet rule: most atoms want 8 valence electrons in bonds + lone pairs (exceptions: H = 2, B = 6, expanded octets for period 3+)
  • Single bond = 2 shared electrons; double bond = 4; triple bond = 6
  • Lone pairs count toward octet but are not bonding
  • Resonance: when multiple valid Lewis structures exist (O₃, NO₃⁻, SO₄²⁻) — actual structure is average
  • Formal charge: valence e⁻ − (lone pair e⁻ + ½ bonding e⁻) — minimize on each atom
VSEPR & molecular geometry
Electron pairs repel → arrange to minimize repulsion. Lone pairs repel MORE than bonding pairs.
  • 2 electron groups: linear (180°) — CO₂, BeCl₂
  • 3 groups, 0 lone pairs: trigonal planar (120°) — BF₃, SO₃
  • 4 groups, 0 lone pairs: tetrahedral (109.5°) — CH₄, CCl₄
  • 4 groups, 1 lone pair: trigonal pyramidal (107°) — NH₃
  • 4 groups, 2 lone pairs: bent/V-shaped (104.5°) — H₂O
  • Lone pairs compress bond angles
Molecular polarity
A polar molecule requires BOTH polar bonds AND asymmetric geometry. Symmetric molecules with polar bonds can cancel out.
  • CO₂: linear → dipoles cancel → nonpolar molecule (despite polar C=O bonds)
  • H₂O: bent → dipoles don't cancel → polar molecule
  • CH₄: tetrahedral, symmetric → nonpolar
  • NH₃: pyramidal, asymmetric → polar
  • CCl₄: tetrahedral, symmetric → nonpolar despite polar C-Cl bonds
  • CHCl₃: tetrahedral but asymmetric → polar
Compounds with BOTH ionic and covalent bonds
When an ionic compound contains a polyatomic ion, it has BOTH types of bonds: ionic bonds between the metal cation and the polyatomic ion, AND covalent bonds within the polyatomic ion itself.
  • Rule: if the formula contains a polyatomic ion, it has both bond types
  • KClO₂ (potassium chlorite): K⁺ and ClO₂⁻ are held by IONIC bonds; inside ClO₂⁻ the Cl−O bonds are COVALENT
  • NaOH: Na⁺ and OH⁻ ionic; O−H inside hydroxide is covalent
  • Ca(NO₃)₂: Ca²⁺ and NO₃⁻ ionic; N−O bonds inside nitrate are covalent
  • NH₄Cl: NH₄⁺ and Cl⁻ ionic; N−H inside ammonium are covalent
  • Pure ionic only: CaCl₂, NaCl, MgO, Li₂S (no polyatomic ions)
  • Pure covalent only: H₂O, CO₂, CH₄, HCl (no ions at all)
Network solids & properties
  • Network covalent solid: atoms covalently bonded throughout in a giant network — diamond (C), quartz (SiO₂), graphite
  • Very high melting points; hard; poor conductors (except graphite which conducts along layers)
  • Ionic solids: high MP, hard, brittle, conduct when molten or dissolved, NOT as solid
  • Molecular solids: low MP, soft, poor conductors (IMFs hold together, not ionic/covalent bonds)
  • Metallic solids: variable MP, malleable, ductile, excellent conductors
Ionic solids DON'T conduct — ions locked in lattice. Must melt or dissolve for conductivity.
Symmetry is KEY: CO₂ has polar bonds but is nonpolar because it's linear and symmetric.
H and He need only 2 electrons (duet rule), not 8.
Lone pairs are NOT shown in the molecular geometry name — only bonding pairs determine the shape name.
ΔEN: <0.4 nonpolar cov | 0.4–1.7 polar cov | ≥1.7 ionic
Criss-cross rule: swap charge magnitudes as subscripts, reduce to simplest ratio
Diagram
CO₂ — nonpolar linear → dipoles cancel H₂O — polar bent → dipoles don't cancel

Molecular polarity: CO₂ is linear (symmetric → nonpolar); H₂O is bent (asymmetric → polar).

Molar mass (GFM)
Sum of atomic masses of all atoms in the formula. Look up atomic masses on the periodic table.
  • Example: H₂O = 2(1.0) + 16.0 = 18.0 g/mol
  • Example: Ca(NO₃)₂ = 40.1 + 2(14.0 + 3×16.0) = 164.1 g/mol
  • Parentheses mean multiply: Ca(OH)₂ has 2 O and 2 H from the (OH) group
  • GFM bridges grams ↔ moles
Percent composition
  • % element = (total mass of that element in 1 mol / GFM) × 100
  • Example: % H in H₂O = (2×1.0)/18.0 × 100 = 11.1%
  • Sum of all % compositions = 100% (good check)
Empirical & molecular formulas
Empirical = simplest whole-number ratio. Molecular = actual number of atoms.
  • Empirical steps: (1) % → g (assume 100 g); (2) g ÷ molar mass → moles; (3) ÷ by smallest; (4) × to get whole numbers
  • Molecular formula: n = molecular mass ÷ empirical formula mass; multiply subscripts by n
  • Example: empirical CH₂ (mass=14), molecular mass=56 → n=4 → C₄H₈
  • Empirical and molecular can be identical (H₂O, CO₂, CH₄)
Stoichiometry — the 4-step roadmap
Every stoichiometry problem follows the same path: grams → moles → moles → grams. Moles are always the bridge.
  • Step 1 (Given → mol): divide grams of given substance by its GFM
  • Step 2 (Mole ratio): multiply by the coefficient ratio from the balanced equation (wanted ÷ given)
  • Step 3 (mol → wanted): multiply by GFM of wanted substance (for mass) OR by 6.02×10²³ (for particles) OR by 22.4 L (for gas at STP)
  • Mass→mass example: 2H₂ + O₂ → 2H₂O. How many g H₂O from 4.0 g H₂? → 4.0/2.0 = 2.0 mol H₂ × (2 mol H₂O/2 mol H₂) × 18.0 g/mol = 36 g H₂O
  • Mass→volume (STP): g ÷ GFM × 22.4 L/mol = liters of gas at STP
  • Mass→particles: g ÷ GFM × 6.02×10²³ = number of particles
Limiting & excess reagent
When two reactants are given, find which runs out first — that is the limiting reagent and sets the ceiling on products.
  • Method: convert BOTH reactants to moles of product; whichever gives LESS product is the limiting reagent
  • Example: 4 mol H₂ and 3 mol O₂ react (2H₂+O₂→2H₂O). H₂ gives 4 mol H₂O; O₂ gives 6 mol H₂O → H₂ is limiting (gives less)
  • Excess reagent: the reactant that is NOT used up; some is left over after the reaction
  • Amount of excess = initial moles − moles consumed by limiting reagent × stoichiometric ratio
  • Theoretical yield = max product from the limiting reagent
  • % yield = (actual yield / theoretical yield) × 100 — cannot exceed 100%
  • Causes of <100% yield: incomplete reaction, side reactions, product lost during transfer/purification
Mole–mole, mole–volume, and volume–volume
At STP, gas volumes are directly proportional to moles. This allows volume ratios.
  • Mole–mole: use coefficient ratio directly (2 mol H₂ : 1 mol O₂ : 2 mol H₂O)
  • Mole–volume at STP: 1 mol any ideal gas = 22.4 L; use as a conversion factor
  • Volume–volume at STP (Gay-Lussac): gas volumes combine in same ratio as coefficients — 2 L H₂ + 1 L O₂ → 2 L H₂O
  • Example: 3 L N₂ + 9 L H₂ → 6 L NH₃ (ratio maintained: 1:3:2)
Hydrates
Ionic compounds with water molecules embedded in the crystal lattice.
  • Formula written as: ionic compound · nH₂O (e.g., CuSO₄·5H₂O = copper(II) sulfate pentahydrate)
  • % water = (mass of H₂O per formula unit / total molar mass) × 100
  • Heating a hydrate drives off water of crystallization → anhydrous compound remains
  • Mass lost when heated = mass of water in the hydrate
  • To find n: (mass lost / 18.0) ÷ (remaining mass / GFM of anhydrous salt)
Multiply through parentheses in formulas: Mg(OH)₂ has 2 O and 2 H.
Limiting reagent determines theoretical yield — excess is what's left over.
% yield cannot exceed 100% — if it does, there's a measurement or calculation error.
Always convert % to grams first when finding empirical formulas.
For limiting reagent: compare moles of PRODUCT each reactant could make, not just moles of reactant.
n = m/GFM
% composition = (mass of part / total mass) × 100
n_molecular = MW / EFM
% yield = (actual/theoretical) × 100
1 mol gas at STP = 22.4 L
g given ÷ GFM_given × (mol wanted/mol given) × GFM_wanted = g wanted
Reaction types
  • Synthesis (combination): A + B → AB (2H₂ + O₂ → 2H₂O)
  • Decomposition: AB → A + B (2H₂O → 2H₂ + O₂; CaCO₃ → CaO + CO₂)
  • Single replacement: A + BC → AC + B (Zn + CuSO₄ → ZnSO₄ + Cu) — use Table J
  • Double replacement (metathesis): AB + CD → AD + CB — ions switch partners (NaCl + AgNO₃ → AgCl↓ + NaNO₃)
  • Combustion: CₓHᵧ + O₂ → CO₂ + H₂O (complete combustion); CO or C produced if incomplete
  • Neutralization: acid + base → salt + water (special case of double replacement)
Balancing equations
Conservation of mass — atoms cannot be created or destroyed.
  • Only change COEFFICIENTS — NEVER subscripts (changing subscripts changes the substance)
  • Strategy: balance metals first → nonmetals → H → O
  • Diatomic elements (H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂) — don't forget the subscript 2
  • Check: same number of each atom on both sides AND total charge balanced for ionic equations
Activity series & solubility rules
  • Table J (Activity series): single replacement is spontaneous only if the replacing element is HIGHER on the list
  • Halogens: F > Cl > Br > I (each displaces those below it)
  • If replacing element is LOWER → NR (no reaction)
  • Table F (Solubility): predicts precipitates in double replacement
  • Precipitate forms when product is listed as insoluble — write ↓ after its formula
  • Most nitrates (NO₃⁻), alkali metals, and NH₄⁺ compounds are soluble
Net ionic equations
  • Full ionic equation: write all soluble ionic compounds as separated ions
  • Spectator ions: appear on both sides unchanged — cancel them out
  • Net ionic equation: shows only species that actually change / react
  • Example: Pb²⁺(aq) + 2I⁻(aq) → PbI₂(s) (spectators Na⁺ and NO₃⁻ cancelled)
NEVER change subscripts — only coefficients.
Check Table J BEFORE predicting single replacement products. If lower on list → NR.
Table F for precipitate prediction — if the product ion combination is listed insoluble, ↓ forms.
Combustion of hydrocarbons ALWAYS produces CO₂ and H₂O (complete combustion).
g given ÷ GFM × mole ratio × GFM wanted = g product
% yield = actual/theoretical × 100
States of matter & particle motion
  • Solid: particles in fixed positions, vibrate in place; definite shape & volume; incompressible
  • Liquid: particles close but mobile; definite volume, no definite shape; slightly compressible
  • Gas: particles far apart, random rapid motion; no definite shape or volume; highly compressible
  • Plasma: high-energy ionized gas (4th state) — present in stars, lightning, fluorescent lights
  • Temperature = average kinetic energy of particles; KE = ½mv²
Potential energy during phase changes & evaporation
A Regents favorite: what happens to KE and PE during phase changes and evaporation.
  • During a phase change (melting, boiling): KE (temperature) stays CONSTANT; PE INCREASES as particles overcome intermolecular forces
  • During evaporation: PE of water molecules INCREASES as they escape the liquid — they overcome attractive forces between molecules
  • The molecules that evaporate are the HIGH-energy ones — this lowers the average KE of the remaining liquid → evaporative cooling
  • Heat flows from HOT to COLD — always from higher temperature to lower temperature
  • Evaporation is endothermic: the liquid absorbs energy (cools down) as molecules escape
  • Condensation is exothermic: gas → liquid releases energy (warms surroundings)
Experimental design in lab questions
Regents lab questions always ask about controls, variables, and what conclusions can be drawn.
  • Control group: the group where the independent variable is NOT applied — establishes a baseline for comparison
  • Independent variable: what the experimenter deliberately changes
  • Dependent variable: what is measured/observed as a result
  • A dry towel (no water) in an evaporation experiment = control — shows temperature change is due to evaporation, not other factors
  • 'State why the student left one towel dry' → it serves as a control to compare against
Heating/cooling curve — 5 segments
  • Segment 1 (sloped): solid heating — KE increases, temperature rises, q = mCΔT (C_ice = 2.09 J/g·K)
  • Segment 2 (flat at MP): melting — PE increases (bonds between particles weaken), T constant, q = mH_f
  • Segment 3 (sloped): liquid heating — KE increases, T rises, q = mCΔT (C_water = 4.18 J/g·K)
  • Segment 4 (flat at BP): boiling — PE increases (particles escape), T constant, q = mH_v
  • Segment 5 (sloped): gas heating — KE increases, T rises, q = mCΔT (C_steam = 2.01 J/g·K)
  • Cooling curve is the exact reverse — energy released, segments run backward
Intermolecular forces (IMFs)
Forces BETWEEN molecules. Stronger IMF → higher BP, higher MP, lower vapor pressure, lower evaporation rate, higher surface tension, higher viscosity.
  • Hydrogen bonds (STRONGEST): only when H is directly bonded to N, O, or F (H-N, H-O, H-F)
  • Examples: H₂O, NH₃, HF, alcohols, DNA base pairing
  • Dipole-dipole: between polar molecules that lack H bonded to N/O/F
  • London dispersion forces (LDF/van der Waals): present in ALL molecules; ONLY force in nonpolar; increases with molar mass and surface area (more electrons → stronger temporary dipoles)
  • Strength: H-bond > dipole-dipole > LDF
Vapor pressure & boiling
  • Vapor pressure: pressure exerted by vapor above a liquid in a closed system
  • Higher temperature → higher vapor pressure (more molecules have enough energy to escape)
  • Weaker IMFs → higher vapor pressure (easier to escape)
  • Boiling point: temperature where vapor pressure = atmospheric pressure (Table H gives curves)
  • Normal BP: temp where VP = 101.3 kPa (1 atm)
  • At higher altitude (lower P_atm): water boils at LOWER temperature
During a phase change, T does NOT change — heat changes PE only, not KE.
LDF exists in ALL molecules — not just nonpolar ones.
Flat segment on heating curve → use q = mH (NOT q = mCΔT, because ΔT = 0).
Higher vapor pressure means WEAKER IMFs and LOWER boiling point.
K = °C + 273
q = mCΔT (sloped — T changing)
q = mH_f (melting/freezing) | q = mH_v (boiling/condensing)
Table B: C_water=4.18 J/g·K, H_f=334 J/g, H_v=2260 J/g
Diagram
Heat added → Temp (°C) solid ↑ melting liquid ↑ boiling gas ↑

Heating curve: sloped = KE↑ (q=mCΔT); flat plateaus = phase change, PE↑, T constant (q=mH).

Kinetic Molecular Theory (KMT)
Ideal gas assumptions — real gases approximate these under high T and low P.
  • Gas particles in constant, random, straight-line motion
  • Particle volume is negligible compared to container
  • No attractive or repulsive forces between gas particles
  • All collisions are perfectly elastic (no net energy lost)
  • Average kinetic energy is directly proportional to Kelvin temperature (KE ∝ T)
Gas laws — ALWAYS convert to Kelvin!
  • Boyle's Law: P₁V₁ = P₂V₂ (constant T and n) — inverse relationship (↑P → ↓V)
  • Charles's Law: V₁/T₁ = V₂/T₂ (constant P and n) — direct relationship (↑T → ↑V)
  • Gay-Lussac's Law: P₁/T₁ = P₂/T₂ (constant V and n) — direct relationship (↑T → ↑P)
  • Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂ (covers all three above; covers any two changing)
  • Avogadro's Law: equal volumes of gas at same T and P contain equal numbers of molecules
STP, molar volume, and ideal vs real
  • STP (Standard Temperature and Pressure): 273 K (0°C) and 101.3 kPa (Table A)
  • 1 mole of ANY ideal gas at STP = 22.4 L
  • Most ideal conditions: HIGH temperature, LOW pressure (particles far apart, minimal attractions)
  • Most ideal gases: small, nonpolar molecules (H₂, He, Ne) with very weak IMFs
  • Real gases deviate most at: LOW temperature, HIGH pressure — particles close, attractions matter
Dalton's Law & Graham's Law
  • Dalton's Law of Partial Pressures: P_total = P₁ + P₂ + P₃ + ...
  • Each gas in a mixture exerts pressure independently
  • Graham's Law (diffusion/effusion): lighter molecules move faster at same temperature
  • Effusion rate ∝ 1/√(molar mass) — H₂ diffuses much faster than O₂
ALWAYS convert °C to Kelvin BEFORE using any gas law formula (K = °C + 273).
Absolute zero (0 K = −273°C) is the lowest possible temperature — KE = 0.
Gas volume calculations: if T or P is not given/changing, use STP values.
P₁V₁/T₁ = P₂V₂/T₂
K = °C + 273
1 mol gas = 22.4 L at STP
P_total = P₁ + P₂ + ...
Solution vocabulary
  • Solute: what is dissolved (smaller quantity)
  • Solvent: what does the dissolving (larger quantity) — water is the universal solvent
  • Aqueous solution: solute dissolved in water
  • Like dissolves like: polar/ionic solutes dissolve in polar solvents; nonpolar in nonpolar
  • Solvation (hydration): water molecules surround and separate solute ions/molecules
  • Electrolyte: substance that produces ions in solution → conducts electricity (NaCl, HCl, NaOH)
  • Nonelectrolyte: does not ionize → does not conduct (sugar, ethanol, urea)
Factors affecting solubility
  • Temperature ↑ for SOLIDS: solubility usually increases (more thermal energy to break solute-solute bonds)
  • Temperature ↑ for GASES: solubility DECREASES (gas molecules have more energy to escape)
  • Pressure ↑ for GASES only: solubility increases (Henry's Law: S = kP) — explains carbonated drinks
  • Pressure has negligible effect on solid/liquid solubility
  • Stirring: increases rate of dissolving ONLY — not the maximum amount
  • Particle size (crushing): increases rate ONLY — more surface area exposed
Solubility curves (Table G)
  • On the line: saturated — maximum solute dissolved at that temperature
  • Below the line: unsaturated — more solute can still dissolve
  • Above the line: supersaturated — UNSTABLE; extra solute will crystallize out
  • Most solid solubility curves slope upward (higher T → more dissolves)
  • Gas solubility curves slope downward (higher T → less dissolves)
  • Reading Table G: find the temperature on the x-axis → read up to the curve → read left to get g solute per 100 g H₂O
  • How much crystallizes: dissolve at high T (saturated) → cool to lower T → excess = (solubility at T_high) − (solubility at T_low)
Crystallization
Crystallization is the process by which dissolved solute comes out of solution and forms solid crystals. It is a physical change and a key separation technique.
  • Occurs when a solution becomes supersaturated — more solute is dissolved than the solvent can hold at that temperature
  • Trigger methods: (1) Cool a hot saturated solution — solubility drops, excess solute crystallizes out; (2) Evaporate solvent — solution becomes concentrated until supersaturated; (3) Add a seed crystal — gives particles a surface to nucleate on
  • Seed crystal: a small crystal of the same substance added to a supersaturated solution to initiate crystallization
  • Fractional crystallization: using temperature changes to selectively crystallize one substance out of a mixture of dissolved solids (exploits different solubility curves)
  • Example (Table G): KNO₃ dissolves 110 g/100 g H₂O at 60°C. Cooled to 20°C, only 32 g dissolves → 78 g crystallizes out
  • Example: NaCl solubility barely changes with temperature → not easily purified by crystallization; KNO₃ solubility changes greatly → ideal for recrystallization
  • Crystallization vs. precipitation: crystallization is slow, produces well-formed crystals; precipitation is fast, produces amorphous solid
  • Crystal lattice: ions arrange in a repeating 3D pattern as they come out of solution — minimizing potential energy
Concentration
  • Molarity (M): M = moles of solute / liters of solution (mol/L)
  • ppm: (mass solute / mass solution) × 10⁶ (used for very dilute solutions, e.g., water quality)
  • Dilution: M₁V₁ = M₂V₂ (moles of solute stay constant when diluting)
Colligative properties
Properties that depend on the NUMBER of dissolved particles, not their identity.
  • Boiling point elevation: adding solute raises the boiling point (ΔBP = K_b × m × i)
  • Freezing point depression: adding solute lowers the freezing point — roads, antifreeze
  • Vapor pressure lowering: solute lowers VP of solvent
  • Osmotic pressure: water moves from low to high solute concentration through semipermeable membrane
  • Ionic solutes have greater effect: 1 mol NaCl → 2 mol ions; 1 mol CaCl₂ → 3 mol ions
Saturated ≠ concentrated; saturated just means at maximum capacity (on the curve line).
Stirring and crushing only affect RATE, not final equilibrium amount dissolved.
Gases become less soluble as temperature rises (opposite of most solids).
Molarity uses LITERS of solution, not solvent — convert mL to L.
Crystallization is a PHYSICAL change — the same substance is recovered, just in solid form.
Amount that crystallizes = solubility at T_high − solubility at T_low (per 100 g H₂O).
M = mol solute / L solution
ppm = (mass solute / mass solution) × 10⁶
M₁V₁ = M₂V₂ (dilution)
g crystallized = solubility(T₁) − solubility(T₂), per 100 g H₂O
Diagram
Temperature → g / 100g H₂O supersaturated ↑ ← saturated (on line) unsaturated ↓

Solubility curve zones. On the line = saturated; below = unsaturated; above = supersaturated (unstable).

Endothermic vs exothermic
ENDOthermic = Energy goes IN. EXOthermic = Energy EXits.
  • Endothermic: absorbs energy from surroundings; ΔH = positive (+); heat is a REACTANT; surroundings feel cold; products at HIGHER PE than reactants
  • Exothermic: releases energy to surroundings; ΔH = negative (−); heat is a PRODUCT; surroundings feel warm; products at LOWER PE
  • Real-world endothermic: cold packs, photosynthesis, evaporation, melting ice, dissolving NH₄NO₃
  • Real-world exothermic: combustion, hand warmers, neutralization, respiration, dissolving NaOH, nuclear fission
Potential energy diagrams
Reactants on left, products on right. Peak = activated complex (transition state). The curve shows PE as reaction proceeds.
  • Activation energy (Ea forward): peak height ABOVE reactants = minimum energy to start reaction
  • Activation energy (Ea reverse): peak height ABOVE products = energy to reverse the reaction
  • ΔH = H_products − H_reactants (can be + or −)
  • Exothermic diagram: products LOWER than reactants; ΔH negative
  • Endothermic diagram: products HIGHER than reactants; ΔH positive
  • Catalyst: lowers Ea for BOTH directions, does NOT change ΔH or reactant/product energy levels
  • Activated complex (transition state): at the peak; highly unstable, cannot be isolated
Bond energy & ΔH
Breaking bonds requires energy (endothermic). Forming bonds releases energy (exothermic).
  • ΔH = energy of bonds BROKEN − energy of bonds FORMED
  • If broken > formed → ΔH positive → endothermic
  • If formed > broken → ΔH negative → exothermic
  • Bond energy values come from Table I on the Regents exam
Table I — Heats of reaction & dissolving
Table I gives ΔH values for specific reactions at 298 K and 101.3 kPa. Know how to read it for dissolving reactions.
  • Negative ΔH in Table I = exothermic process (releases heat — surroundings warm up)
  • Positive ΔH in Table I = endothermic process (absorbs heat — surroundings cool down)
  • Dissolving NaOH(s): ΔH is negative → exothermic — the solution gets WARM
  • Dissolving NH₄NO₃(s): ΔH is positive → endothermic — the solution gets COLD (used in cold packs)
  • Dissolving KNO₃(s): ΔH is positive → endothermic
  • Dissolving NH₄Cl(s): ΔH is positive → endothermic
  • Key: if the question asks which dissolving process is exothermic → find the one with NEGATIVE ΔH in Table I
Entropy (S)
Entropy = measure of disorder/randomness of a system.
  • Entropy increases: solid→liquid→gas, dissolving, more moles of gas produced, higher temperature
  • Entropy decreases: gas→liquid→solid, crystallization, fewer moles of gas, lower temperature
  • Spontaneous reactions tend toward lower energy AND higher entropy
  • ΔG = ΔH − TΔS (Gibbs free energy) — spontaneous when ΔG < 0
Activation energy is measured from REACTANTS up to peak — NOT from a zero baseline.
Catalyst lowers Ea but does NOT change ΔH or the energy of reactants/products.
Exothermic = −ΔH (releases energy). Don't flip the sign.
ΔH = bonds broken MINUS bonds formed (not the other way around).
ΔH = H_products − H_reactants
ΔH = bonds broken − bonds formed
Ea(forward) = peak − reactants | Ea(reverse) = peak − products
Diagram
Reaction progress → PE Ea → RP — catalyzed (lower Ea)

PE diagram: Ea = peak−reactants; ΔH = products−reactants. Dashed = catalyzed pathway (lower Ea, same ΔH).

Collision theory
For a reaction to occur, three conditions MUST ALL be met:
  • 1. Particles must collide with each other
  • 2. Collisions must have proper geometric orientation
  • 3. Collisions must have energy ≥ activation energy (Ea)
  • Effective collision: meets all three conditions → products form
  • Ineffective collision: wrong orientation OR insufficient energy → no reaction
Factors affecting reaction rate
  • Temperature ↑: particles move faster → more frequent AND higher-energy collisions
  • Concentration ↑ (or pressure ↑ for gases): more particles per volume → more frequent collisions
  • Surface area ↑ (grinding/crushing): more exposed particles for collisions
  • Catalyst: provides alternate lower-Ea pathway → more collisions succeed (does NOT change ΔH)
  • Nature of reactants: ionic reactions in solution are faster than molecular reactions
Physical vs chemical equilibrium
Both involve a balance of opposing processes in a closed system. Regents tests both.
  • Physical equilibrium: balance between opposing physical processes — no chemical reaction occurring
  • Example: sealed flask with liquid water → evaporation rate = condensation rate → liquid-vapor equilibrium
  • Evidence of physical equilibrium: liquid level stays constant in a sealed container; no net change observed
  • Chemical equilibrium: balance between forward and reverse chemical reactions at equal rates
  • Both types: occur in CLOSED systems, appear static but are dynamic, concentrations/amounts stay constant
Reading concentration vs. time graphs
A concentration-vs-time graph shows equilibrium when the lines become FLAT and stop changing.
  • Before equilibrium: concentrations changing (reactants decreasing, products increasing, or vice versa)
  • At equilibrium: ALL concentration lines become horizontal (flat) — no further net change
  • The time at which lines flatten = the time equilibrium is reached
  • After equilibrium: concentrations remain constant (flat lines) unless a stress is applied
  • Key: look for where the curves level off and stay flat — that is when equilibrium is established
Chemical equilibrium
A dynamic equilibrium: both forward and reverse reactions occur simultaneously at EQUAL rates.
  • Forward rate = reverse rate at equilibrium
  • Concentrations remain CONSTANT (not necessarily equal to each other)
  • Requires a CLOSED system (nothing enters or leaves)
  • Equilibrium does NOT mean the reaction stopped — both directions still occurring
  • Keq = [products]^coefficients / [reactants]^coefficients (pure solids/liquids excluded)
Le Chatelier's Principle
A system at equilibrium, when stressed, will shift to RELIEVE that stress. Treat heat as a reactant (endo) or product (exo).
  • Add reactant → shifts RIGHT (toward products)
  • Remove reactant → shifts LEFT (toward reactants)
  • Add product → shifts LEFT | Remove product → shifts RIGHT
  • Exothermic + add heat → heat is a product → shifts LEFT
  • Endothermic + add heat → heat is a reactant → shifts RIGHT
  • ↑ Pressure (gas) → shifts toward side with FEWER moles of gas
  • ↓ Pressure → shifts toward MORE moles of gas
  • Catalyst → does NOT shift equilibrium, only reaches it FASTER
  • Inert gas added at constant volume → NO shift (doesn't affect partial pressures of reactants/products)
Equilibrium means RATES are equal, not CONCENTRATIONS.
Catalyst speeds both directions equally — does NOT shift equilibrium position.
Pressure changes only affect GAS-phase equilibria.
Inert gas added at constant volume has NO effect on equilibrium.
A catalyst does NOT appear in the equilibrium constant expression.
Keq = [C]^c[D]^d / [A]^a[B]^b
Le Chatelier: treat heat as substance; exo: product; endo: reactant
Diagram
A + B ⇌ C + D + heat (exothermic) Shift RIGHT if: + more A or B − remove C or D ↓ temperature Shift LEFT if: + more C or D − remove A or B ↑ temperature

Le Chatelier stresses: adding reactant → shift right; adding product → shift left; ↑T for exo → shift left; ↑P → shift toward fewer gas moles.

Acid-base theories
Arrhenius is the most restrictive (water only). Brønsted-Lowry is broader (non-aqueous too).
  • Arrhenius acid: releases H⁺ (H₃O⁺) in aqueous solution (HCl, HNO₃, H₂SO₄, HF)
  • Arrhenius base: releases OH⁻ in aqueous solution (NaOH, KOH, Ca(OH)₂)
  • Brønsted-Lowry acid: proton (H⁺) DONOR
  • Brønsted-Lowry base: proton (H⁺) ACCEPTOR
  • Conjugate acid-base pair: differ by one H⁺ (HCl / Cl⁻; NH₄⁺ / NH₃; H₂O / OH⁻)
  • Amphoteric substances: can act as BOTH acid and base — water (H₂O), bicarbonate (HCO₃⁻)
Properties & identification
  • Acids: sour taste; turn blue litmus RED; pH < 7; react with metals → H₂ gas; react with bases
  • Bases: bitter taste, slippery feel; turn red litmus BLUE; pH > 7; react with acids
  • Strong acids (100% ionized in water): HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄ (memorize these 6)
  • Strong bases: NaOH, KOH, Ca(OH)₂, Ba(OH)₂, LiOH
  • Weak acids/bases: partially ionize — reach equilibrium (HF, CH₃COOH/acetic acid, NH₃)
  • Strength = % ionization; concentration = mol/L (a dilute strong acid is still 100% ionized)
pH scale & calculations
pH scale runs 0–14 at 25°C. Logarithmic — each unit = 10× change in [H⁺].
  • pH = −log[H⁺] → [H⁺] = 10^(−pH)
  • pOH = −log[OH⁻] → [OH⁻] = 10^(−pOH)
  • pH + pOH = 14 (at 25°C)
  • Kw = [H⁺][OH⁻] = 1×10⁻¹⁴ (at 25°C)
  • pH < 7 = acidic; pH = 7 = neutral; pH > 7 = basic
  • How much more acidic: pH 3 vs pH 5 → difference of 2 → 10² = 100× more acidic
Neutralization & titration
Acid + Base → Salt + Water. In a titration, a solution of known concentration (titrant) is added to determine unknown concentration.
  • Equivalence point: moles H⁺ = moles OH⁻ (complete neutralization)
  • Indicator selection: choose an indicator whose range brackets the equivalence point pH
  • Titration formula (1:1 molar ratio): M_A × V_A = M_B × V_B
  • Salt formed = cation from base + anion from acid
  • Example: HCl + NaOH → NaCl + H₂O
  • Indicators from Table M: phenolphthalein (colorless→pink at pH 8.2–10); litmus (red→blue at 4.5–8.3)
Strength ≠ concentration — a dilute HCl solution is still a strong acid (100% ionized).
pH scale is LOGARITHMIC — a pH difference of 2 = 100× concentration difference, not 2×.
Titration formula only works for 1:1 molar ratios; adjust for H₂SO₄ (2 H⁺) etc.
Conjugate pairs differ by exactly one H⁺.
pH = −log[H⁺]
pH + pOH = 14
[H⁺][OH⁻] = 1×10⁻¹⁴
M_A × V_A = M_B × V_B (1:1 ratio)
ppm = (mass solute/mass solution) × 10⁶
Oxidation & reduction
OIL RIG: Oxidation Is Loss (of electrons), Reduction Is Gain (of electrons). They always occur together.
  • Oxidation: loss of electrons → oxidation number INCREASES → species becomes more positive
  • Reduction: gain of electrons → oxidation number DECREASES → species becomes more negative
  • Oxidizing agent: accepts electrons (gets REDUCED itself) — causes oxidation of the other
  • Reducing agent: donates electrons (gets OXIDIZED itself) — causes reduction of the other
  • LEO the lion says GER: Loses Electrons Oxidation | Gains Electrons Reduction
Oxidation number rules
Follow in priority order:
  • Rule 1: Free elements = 0 (Na, O₂, Fe, Cl₂)
  • Rule 2: Monatomic ions = ion charge (Na⁺ = +1, O²⁻ = −2)
  • Rule 3: Group 1 in compounds = +1 always
  • Rule 4: Group 2 in compounds = +2 always
  • Rule 5: F in compounds = −1 always (most electronegative)
  • Rule 6: H = +1 usually; −1 in metal hydrides (NaH, CaH₂)
  • Rule 7: O = −2 usually; −1 in peroxides (H₂O₂, Na₂O₂)
  • Rule 8: Sum of oxidation numbers = 0 for neutral compound; = ion charge for polyatomic ion
Half-reactions & balancing
Split redox into oxidation half-reaction and reduction half-reaction. Balance electrons gained = electrons lost.
  • Write the two half-reactions separately
  • Balance atoms (add H⁺ or H₂O if needed for acidic; OH⁻ and H₂O for basic)
  • Balance charge by adding electrons (e⁻)
  • Multiply each half-reaction so e⁻ lost = e⁻ gained (LCM of electrons)
  • Add the two half-reactions; cancel spectators and electrons that appear on both sides
Electrochemical cells
  • Voltaic (galvanic) cell: SPONTANEOUS redox reaction → converts chemical energy to electrical energy (batteries)
  • Anode = oxidation (both start with vowels) — in voltaic cell: NEGATIVE terminal
  • Cathode = reduction (both start with consonants... remember RED-CAT) — in voltaic cell: POSITIVE terminal
  • Electrons flow: anode → external wire → cathode
  • Salt bridge: allows ion flow to maintain electrical neutrality of each half-cell
  • Electrolytic cell: NONSPONTANEOUS reaction driven by external power source — electroplating, electrolysis of water
  • In electrolytic cell: anode = POSITIVE terminal, cathode = NEGATIVE (signs FLIP from voltaic)
  • Oxidation is ALWAYS at the anode; reduction ALWAYS at the cathode (regardless of cell type)
Anode signs flip between voltaic and electrolytic cells — but oxidation is ALWAYS at the anode.
Reducing agent is the species that gets oxidized (it reduces something else by giving up electrons).
In oxidation, the oxidation number INCREASES (more positive).
Electrons flow through the wire from anode to cathode — ions flow through the salt bridge.
e⁻ lost by reducing agent = e⁻ gained by oxidizing agent
Table J activity series: higher = more active = more easily oxidized
Diagram
V salt bridge ANODE (−) CATHODE (+) e⁻ → oxidation reduction

Voltaic cell: anode (−) = oxidation; cathode (+) = reduction. Electrons flow anode→cathode via wire; ions flow through salt bridge.

Types of radiation
  • Alpha (α, ⁴₂He): helium nucleus; charge +2; mass 4 amu; LOW penetrating power (stopped by paper/skin); mass −4, atomic # −2
  • Beta (β⁻, ⁰₋₁e): high-speed electron; charge −1; mass ≈0; moderate penetrating power (stopped by aluminum); mass unchanged, atomic # +1
  • Gamma (γ, ⁰₀γ): high-energy photon; no charge, no mass; HIGHEST penetrating power (needs lead/concrete); no change to mass or atomic #
  • Positron (β⁺, ⁰₊₁e): antimatter electron; charge +1; mass ≈0; mass unchanged, atomic # −1
  • Neutron emission: ¹₀n released; mass −1, atomic # unchanged (rare in Regents but possible)
Nuclear equations & conservation
In ANY nuclear equation, BOTH must be conserved:
  • Mass number conservation: sum of superscripts (top) equal on both sides
  • Atomic number conservation: sum of subscripts (bottom) equal on both sides
  • Strategy: find the missing particle by subtraction
  • Example: ²³⁸₉₂U → ⁴₂He + ²³⁴₉₀Th (alpha decay: mass 238−4=234; atomic# 92−2=90)
  • Example: ¹⁴₆C → ⁰₋₁e + ¹⁴₇N (beta decay: mass 14−0=14; atomic# 6+1=7)
  • Transmutation: one element changing into another through nuclear decay or bombardment
Half-life calculations
Half-life (t₁/₂) = time for exactly half the sample to decay. It is CONSTANT and independent of temperature, pressure, or chemical state.
  • Amount remaining = original × (½)^(t/t₁/₂) = original × (½)^(number of half-lives)
  • Number of half-lives = total time ÷ t₁/₂
  • Each half-life: 100%→50%→25%→12.5%→6.25%→3.125%
  • Table N on Regents: lists radioisotopes, their half-lives, decay modes, and uses
  • Half-life is NOT affected by temperature, pressure, or the chemical form of the element
Fission, fusion & applications
  • Fission: splitting a HEAVY nucleus into smaller ones + neutrons + energy (U-235, Pu-239 in reactors)
  • Chain reaction: neutrons from one fission trigger more fissions — controlled in reactors, uncontrolled in bombs
  • Fusion: combining LIGHT nuclei into heavier one + energy (H + H → He in the sun); requires extreme T and P
  • Fusion releases MORE energy per gram than fission
  • Nuclear energy comes from mass-energy conversion: E = mc² (small mass loss = huge energy)
  • Medical uses (Table N): I-131 (thyroid treatment/imaging), Tc-99m (diagnostic imaging), Co-60 (cancer radiation)
  • C-14 (t₁/₂ = 5715 yr): carbon dating of organic material; U-238 (t₁/₂ = 4.5×10⁹ yr): geological dating
Both mass numbers AND atomic numbers must balance in nuclear equations — check BOTH.
Half-life is constant regardless of temperature, pressure, or chemical state.
Alpha has LOWEST penetrating power; gamma has HIGHEST.
Fusion powers the sun; fission powers nuclear reactors.
In beta decay: atomic # goes UP by 1 (neutron→proton); in positron emission: atomic # goes DOWN by 1.
Amount remaining = initial × (½)^(t/t₁/₂)
Alpha: mass −4, atomic# −2 | Beta: mass 0, atomic# +1 | Gamma: no change | Positron: mass 0, atomic# −1
Diagram
Penetrating Power Alpha (α): stopped by PAPER — low penetration, high ionization Beta (β): stopped by ALUMINUM sheet — medium penetration Gamma (γ): needs LEAD or CONCRETE — highest penetrating power Ionization power (opposite): α > β > γ

Radioactive decay types: alpha loses ⁴₂He (mass−4, Z−2); beta emits e⁻ (Z+1); gamma emits photon (no change); penetrating power: γ > β > α.

What makes a compound organic
Organic compounds contain carbon. Carbon is unique because it forms 4 covalent bonds and can bond to itself in long chains and rings.
  • All organic compounds contain carbon (and usually hydrogen)
  • Carbon always forms 4 covalent bonds — never more, never less
  • The backbone of organic molecules is a chain or ring of carbon-carbon bonds
  • Organic chemistry is the chemistry of carbon-containing compounds
  • Exceptions that are NOT considered organic: CO, CO₂, carbonates (CO₃²⁻), cyanides (CN⁻)
Homologous series & naming prefixes (Table Q)
A homologous series is a family of organic compounds with the same general formula, differing by one CH₂ unit. Each member has similar chemical properties.
  • Prefix meth- = 1 carbon | eth- = 2 | prop- = 3 | but- = 4 | pent- = 5 | hex- = 6 | hept- = 7 | oct- = 8
  • Alkanes (CₙH₂ₙ₊₂): single bonds only; -ane suffix (methane, ethane, propane...)
  • Alkenes (CₙH₂ₙ): one double bond; -ene suffix (ethene, propene, butene...)
  • Alkynes (CₙH₂ₙ₋₂): one triple bond; -yne suffix (ethyne = acetylene)
  • Cycloalkanes (CₙH₂ₙ): carbon ring with all single bonds
  • Each successive member differs by one CH₂ unit (14 g/mol higher molar mass)
Functional groups (Table P)
A functional group is an atom or group of atoms that determines the chemical properties of an organic compound.
  • Alcohol (−OH): R−OH; suffix -ol; e.g., ethanol (CH₃CH₂OH). Formed by: fermentation, substitution of halogen.
  • Aldehyde (−CHO): R−CHO; suffix -al; e.g., methanal (formaldehyde). Contains C=O at end of chain.
  • Ketone (C=O in chain): R−CO−R; suffix -one; e.g., propanone (acetone).
  • Carboxylic acid (−COOH): R−COOH; suffix -oic acid; e.g., methanoic acid (formic), ethanoic acid (acetic).
  • Ester (−COO−): R−COO−R'; suffix -anoate; e.g., ethyl ethanoate. Formed from acid + alcohol.
  • Ether (−O−): R−O−R'; e.g., diethyl ether.
  • Amine (−NH₂): R−NH₂; e.g., methylamine. Weak bases.
  • Amide (−CONH₂): R−CONH₂; found in proteins and nylon.
  • Halide: one or more H replaced by halogen (F, Cl, Br, I)
Organic reactions (Table R)
  • Fermentation: C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ (glucose → ethanol + CO₂; yeast catalyst; no O₂ — anaerobic)
  • Esterification: carboxylic acid + alcohol → ester + water (R−COOH + HO−R' → R−COO−R' + H₂O)
  • Saponification: ester + base (NaOH) → soap (salt of fatty acid) + alcohol
  • Substitution: one atom replaces another; e.g., alkane + Cl₂ → chloroalkane + HCl
  • Addition: atoms added across a double or triple bond; alkene + H₂ → alkane (hydrogenation)
  • Combustion: CₓHᵧ + O₂ → CO₂ + H₂O + energy
  • Polymerization: many monomers join → polymer; e.g., ethene → polyethylene; nylon, proteins, DNA
Isomers
Isomers have the SAME molecular formula but DIFFERENT structural formulas — the atoms are connected differently.
  • Same: molecular formula (same # of each atom), molar mass
  • Different: structural formula (arrangement), physical properties (BP, MP), sometimes chemical properties
  • Example: C₄H₁₀ → butane (straight chain) and 2-methylpropane (branched) are isomers
  • Example: propanoic acid (CH₃CH₂COOH) and ethyl methanoate (HCOOCH₂CH₃) are isomers — both C₃H₆O₂
  • To identify: count atoms in each formula; if totals match, they are isomers
Organic naming rules
Use Table Q for prefixes. Name the longest continuous carbon chain, then number from the end closest to a branch.
  • Step 1: Find the longest continuous C chain → gives base name (hex = 6 carbons)
  • Step 2: Number from end closest to branches/substituents (gives them lowest numbers)
  • Step 3: Name substituents with number: 2-methyl (CH₃ on C2), 3-ethyl, etc.
  • Multiple substituents: alphabetical order (ethyl before methyl); di/tri if same substituent twice
  • Example: 3-methylhexane = 6-carbon chain with a CH₃ branch on carbon 3
  • Example: 2,3-dimethylpentane = 5-carbon chain with CH₃ on C2 and C3
CₙH₂ₙ is ALKENES (one double bond) — not alkanes (CₙH₂ₙ₊₂).
Fermentation produces ETHANOL (alcohol), not just any product.
Esterification = acid + alcohol → ester + WATER (not H₂).
Isomers have the SAME molecular formula but different structural formulas.
Carbon is always in organic compounds — but CO and CO₂ are NOT organic.
When naming: pick the LONGEST chain, then number from end closest to the branch.
Alkanes: CₙH₂ₙ₊₂ | Alkenes: CₙH₂ₙ | Alkynes: CₙH₂ₙ₋₂
Fermentation: C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂
Esterification: acid + alcohol → ester + H₂O
Term
Definition
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Core Formulas (Table T)

Density
D = m / V
% Error
|meas − accept| / accept × 100
Moles
n = m / GFM
Avogadro
1 mol = 6.02×10²³ particles
Kelvin
K = °C + 273
q = mCΔT
Sloped sections — T changing
q = mH_f
Melting/freezing (flat at MP)
q = mH_v
Boiling/condensing (flat at BP)
pH
pH = −log[H⁺]
pH + pOH
= 14 (at 25°C)
Kw
[H⁺][OH⁻] = 1×10⁻¹⁴
Titration (1:1)
M_A × V_A = M_B × V_B
Molarity
M = mol solute / L solution
ppm
(m_solute / m_solution) × 10⁶
Dilution
M₁V₁ = M₂V₂
Combined Gas
P₁V₁/T₁ = P₂V₂/T₂
% Composition
(mass part / total mass) × 100
Half-Life
A = A₀ × (½)^(t/t₁/₂)
ΔH (bonds)
ΔH = bonds broken − bonds formed
Atomic Mass
Σ(mass × fractional abundance)
Molar Volume (STP)
1 mol gas = 22.4 L
% Yield
actual / theoretical × 100
ΔG (Gibbs)
ΔG = ΔH − TΔS (spont. if < 0)
Stoichiometry
g ÷ GFM_given × ratio × GFM_want

Nuclear Particle Changes

Decay TypeSymbolMass # ChangeAtomic # ChangePenetration
Alpha (α)⁴₂He−4−2Stopped by paper
Beta⁻ (β⁻)⁰₋₁e0+1Stopped by aluminum
Positron (β⁺)⁰₊₁e0−1Stopped by aluminum
Gamma (γ)⁰₀γ00Needs lead/concrete

Indicator Table (Table M)

IndicatorTransition pHAcid ColorBase Color
Methyl orange3.1–4.4RedYellow
Bromcresol green3.8–5.4YellowBlue
Litmus4.5–8.3RedBlue
Bromthymol blue6.0–7.6YellowBlue
Thymol blue8.0–9.6YellowBlue
Phenolphthalein8.2–10.0ColorlessPink/Fuchsia

Oxidation Number Rules (Priority Order)

  1. Free elements: any uncombined element = 0 (Na, O₂, Cl₂, Fe)
  2. Monatomic ions: oxidation # = ion charge (Na⁺=+1, Cl⁻=−1, Fe³⁺=+3)
  3. Group 1 in compounds: always +1 (Li, Na, K, Rb, Cs)
  4. Group 2 in compounds: always +2 (Mg, Ca, Ba, Sr)
  5. Fluorine: always −1 (most electronegative element)
  6. Hydrogen: +1 usually; −1 in metal hydrides (NaH, CaH₂, LiH)
  7. Oxygen: −2 usually; −1 in peroxides (H₂O₂, Na₂O₂); +2 with F only
  8. Sum rule: sum of all oxidation numbers = 0 (neutral) or = ion charge (polyatomic)

Half-Life Reference Table

# Half-LivesFraction Left% Remaining% Decayed
01100%0%
11/250%50%
21/425%75%
31/812.5%87.5%
41/166.25%93.75%
51/323.125%96.875%

VSEPR Molecular Geometry

Bonding PairsLone PairsGeometryBond AngleExample
20Linear180°CO₂, BeCl₂
30Trigonal planar120°BF₃, SO₃
40Tetrahedral109.5°CH₄, CCl₄
31Trigonal pyramidal107°NH₃
22Bent/V-shaped104.5°H₂O

Electrochemistry Summary

PropertyVoltaic (Galvanic) CellElectrolytic Cell
Energy conversionChemical → ElectricalElectrical → Chemical
Spontaneous?YesNo (needs external power)
Anode signNegative (−)Positive (+)
Cathode signPositive (+)Negative (−)
At anodeOxidation (always)Oxidation (always)
At cathodeReduction (always)Reduction (always)
Electron flowAnode → Cathode (wire)Cathode ← Anode (wire)

Strong Acids & Bases (Memorize)

Strong Acids (6)
HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄
Strong Bases
NaOH, KOH, Ca(OH)₂, Ba(OH)₂, LiOH
Weak Acid examples
HF, CH₃COOH, H₂CO₃, H₃PO₄
Weak Base examples
NH₃, Al(OH)₃

Reference Table Guide (All Tables)

Table A
STP: 273 K, 101.3 kPa, 1 atm, 760 mmHg
Table B
Water constants: C=4.18 J/g·K, H_f=334 J/g, H_v=2260 J/g
Table C
Selected polyatomic ions (NH₄⁺, OH⁻...)
Table D
Selected units and measurements
Table E
Polyatomic ions (NO₃⁻, SO₄²⁻, CO₃²⁻, PO₄³⁻...)
Table F
Solubility rules — predicts precipitates
Table G
Solubility curves (g/100g H₂O vs temp)
Table H
Vapor pressure curves (BP = where VP = 101.3 kPa)
Table I
Heats of reaction (ΔH values in kJ/mol)
Table J
Activity series — metal/halogen reactivity ranking
Table K
Common acids and their formulas
Table L
Common bases and their formulas
Table M
Indicators — pH ranges and color changes
Table N
Radioisotopes — half-lives, decay modes, medical uses
Table O
Nuclear symbols (α, β, γ, positron)
Table P
Organic functional groups
Table Q
Organic prefixes (meth=1, eth=2, prop=3...)
Table R
Organic reactions
Table S
Properties of selected elements (EN, radius, ionization E)
Table T
Important formulas (density, gas laws, pH, etc.)

Electronegativity & Bond Type

ΔEN RangeBond TypeExample
0 – 0.4Nonpolar covalentCl-Cl, C-H, H-H
0.4 – 1.7Polar covalentH-O, H-N, H-Cl
≥ 1.7IonicNa-Cl, Mg-O, Ca-F

Gas Laws Quick Reference

LawFormulaConstantRelationship
Boyle'sP₁V₁ = P₂V₂T, nP and V inverse
Charles'sV₁/T₁ = V₂/T₂P, nV and T direct
Gay-Lussac'sP₁/T₁ = P₂/T₂V, nP and T direct
CombinedP₁V₁/T₁ = P₂V₂/T₂nAll three
Avogadro'sEqual V at same T,P = equal nT, PV and n direct

Organic Chemistry Quick Reference

SeriesGeneral FormulaBond TypeExample
AlkanesCₙH₂ₙ₊₂Single only (saturated)CH₄, C₂H₆, C₃H₈
AlkenesCₙH₂ₙOne double bondC₂H₄, C₃H₆
AlkynesCₙH₂ₙ₋₂One triple bondC₂H₂ (acetylene)
CycloalkanesCₙH₂ₙRing, single bondsC₃H₆ (cyclopropane)
Functional GroupName ClassSuffixExample
−OHAlcohol-olethanol (C₂H₅OH)
−COOHCarboxylic acid-oic acidethanoic acid (CH₃COOH)
−COO−Ester-anoateethyl ethanoate
−CHOAldehyde-almethanal (formaldehyde)
C=O (chain)Ketone-onepropanone (acetone)
−NH₂Amine-aminemethylamine
Reaction (Table R)ReactantsProductsKey fact
FermentationC₆H₁₂O₆2C₂H₅OH + 2CO₂Yeast, anaerobic, makes alcohol
EsterificationAcid + AlcoholEster + H₂OReversible
SaponificationEster + NaOHSoap + AlcoholReverse of esterification
AdditionAlkene + H₂/Cl₂Saturated productBreaks double bond
SubstitutionAlkane + halogenHaloalkane + HXReplaces H with halogen
CombustionCₓHᵧ + O₂CO₂ + H₂OComplete combustion always
Polymerizationn(monomer)PolymerEthene → polyethylene
Naming prefixes
meth=1, eth=2, prop=3, but=4, pent=5, hex=6, hept=7, oct=8
Isomers rule
Same molecular formula, different structural formula → isomers
Allotropes (Q7 exam)
O₂ vs O₃: same element, different structure → different properties
Organic = contains C
Exceptions: CO, CO₂, CO₃²⁻, CN⁻ are inorganic

Crystallization & Stoichiometry Quick Reference

Crystallization trigger
Cool saturated solution OR evaporate solvent → supersaturated → crystals form
Amount crystallized
Solubility(T_high) − Solubility(T_low) per 100 g H₂O
Seed crystal
Nucleation surface; triggers crystallization from supersaturated solution
Best candidate for recrystallization
Substance with steep solubility curve (e.g., KNO₃)
Stoichiometry roadmap
g ÷ GFM_given × (mol wanted/mol given) × GFM_wanted
Limiting reagent test
Convert both reactants to mol of product → smaller answer = limiting
% yield
actual ÷ theoretical × 100 (never > 100%)
Gas stoichiometry (STP)
Volumes react in same ratio as coefficients; 1 mol = 22.4 L

Periodic Trends Summary

PropertyAcross Period (L→R)Down Group (↓)Largest Value
Atomic radiusDecreasesIncreasesFr (bottom-left)
Ionization energyIncreasesDecreasesHe (top-right)
ElectronegativityIncreasesDecreasesF (4.0)
Metallic characterDecreasesIncreasesFr (bottom-left)
Ionic radius (cations)DecreasesIncreasesCs⁺

Table I — Heats of Dissolving (Tested on Regents!)

CompoundΔH (dissolving)TypeEffect on solution
NaOH(s)Negative (−)ExothermicSolution gets WARM
NH₄NO₃(s)Positive (+)EndothermicSolution gets COLD (cold packs)
KNO₃(s)Positive (+)EndothermicSolution gets COLD
NH₄Cl(s)Positive (+)EndothermicSolution gets COLD

Physical vs Chemical Equilibrium

TypeExampleWhat's equalClosed system?
Physical equilibriumSealed flask with liquid H₂OEvaporation rate = condensation rateYes
Chemical equilibriumN₂ + 3H₂ ⇌ 2NH₃Forward rate = reverse rateYes
Reading conc-vs-time graph
Equilibrium = where ALL lines become flat and stay flat
PE during evaporation
PE INCREASES as molecules escape IMFs; KE (temp) of remaining liquid DECREASES → cooling
Heat flow direction
Always flows from HIGH temperature to LOW temperature
Control group (lab)
The unchanged baseline — e.g., dry towel in evaporation experiment

Top 15 Exam Traps

  1. Always convert °C to Kelvin before using gas law formulas (K = °C + 273).
  2. Dissolving is a PHYSICAL change — NaCl can be recovered by evaporation.
  3. Activation energy (Ea) is measured from REACTANTS up to the peak — not from zero.
  4. Catalyst lowers Ea but does NOT change ΔH or shift equilibrium position.
  5. CO₂ has polar bonds but is a nonpolar MOLECULE — linear geometry cancels dipoles.
  6. Ionic solids do NOT conduct electricity — only when molten or dissolved (ions mobile).
  7. Saturated ≠ concentrated. Saturated = at maximum capacity (on the solubility curve line).
  8. pH scale is LOGARITHMIC: each 1-unit difference = 10× change in [H⁺].
  9. Single replacement: check Table J first. If replacing element is lower → NR.
  10. Only COEFFICIENTS can be changed when balancing — never subscripts.
  11. Voltaic vs. electrolytic: anode terminal signs flip, but oxidation is ALWAYS at the anode.
  12. Nuclear equations: BOTH mass numbers AND atomic numbers must balance.
  13. Half-life is constant — unaffected by temperature, pressure, or chemical form.
  14. Excited state still has the correct number of electrons — they're just not in lowest levels.
  15. Strength ≠ concentration — a dilute HCl solution is still a STRONG acid (100% ionized).

Exam Day Checklist

  • Use Table T first — it lists all the formulas you'll need.
  • Know which Reference Table to use: J (activity series), F (precipitates), M (indicators), N (radioisotopes), G (solubility curves).
  • Show all work with units. Dimensional analysis prevents errors.
  • Start with questions you know best; circle and skip difficult ones.
  • Gas laws: write down given values, identify what's constant, pick the right formula.
  • Nuclear equations: always verify mass numbers AND atomic numbers balance.
  • For PE diagrams: mark reactants, peak, and products before reading Ea or ΔH.
  • Treat heat as a substance (reactant or product) for Le Chatelier problems.
  • Oxidation number assignments: use the 8 rules in priority order.
  • Check units in your final answer before moving on.
Quick ways to lock in the facts you keep forgetting. Read the big trick, then the small note tells you what it unlocks. Say them out loud — silly is memorable.

Matter, Measurement & Atoms

Can you get it back?
Physical change: the original substance can be recovered (melt ice, freeze it back). Chemical change: you can't un-burn wood — a genuinely new substance formed.
Fixed = compound, flexible = mixture
Compounds have a fixed ratio of elements (H₂O is always 2:1). Mixtures can be any ratio — that's what makes them physically separable.
Distill by degree, filter what's firm
Distillation separates liquids by different boiling points. Filtration catches an insoluble solid in a filter.
Zeros: leading lies, trailing tells, captive counts
Leading zeros (0.0025) are never significant. Trailing zeros only count WITH a decimal point (1500. = 4 sig figs). Captive zeros (2005) always count.
Add keeps the least decimal, multiply keeps the least digit
Adding/subtracting: round to the fewest decimal places among your numbers. Multiplying/dividing: round to the fewest total sig figs.
Same P, different N = isotope
Isotopes have the same number of protons but a different number of neutrons — mass number varies, atomic number doesn't.

Periodic Table & Bonding

Down gets big, across gets small
Atomic radius increases going down a group (more energy levels) and decreases going across a period (more protons pull electrons in).
Ionization energy is the opposite of radius
Small atom = electrons held tight = high ionization energy. IE increases across a period, decreases down a group — the reverse of atomic radius.
Fluorine is the greediest
Electronegativity peaks at fluorine (top-right of the table, excluding noble gases) — it pulls shared electrons hardest of any element.
Metal + nonmetal = ionic, nonmetal + nonmetal = covalent
Ionic bonds transfer electrons (big electronegativity gap). Covalent bonds share electrons (both nonmetals, similar electronegativity).
Symmetric cancels, lopsided doesn't
A molecule with polar bonds can still be nonpolar overall if its shape is symmetric (like CO₂) — the bond dipoles cancel out.
VSEPR: count the groups around the center
4 bonding groups, 0 lone pairs = tetrahedral. 4 groups, 1 lone pair = trigonal pyramidal. 4 groups, 2 lone pairs = bent.

Quantities & Reactions

Moles are always the bridge
Every stoichiometry problem goes grams → moles → moles → grams. You can never skip straight from one substance's grams to another's.
Limiting runs out first, excess is left over
Whichever reactant produces the smaller amount of product is the limiting reagent — it runs out first and stops the reaction.
Yield can't beat 100%
% yield = actual ÷ theoretical × 100. An answer over 100% means a math error somewhere.
One becomes many, many become one
Synthesis: two reactants → one product. Decomposition: one reactant → many products — think of them as opposites.
Higher on the list wins
Table J's activity series: a metal can only replace a less active metal below it. Asking it to replace something above it means "no reaction."
Balance coefficients, never subscripts
Only the big numbers in front of formulas can change when balancing. Changing a subscript changes the substance itself.

Phases & Gases

Flat means it's changing phase
On a heating curve, a flat plateau means energy is breaking intermolecular forces, not raising temperature — melting or boiling in progress.
Gas particles don't care about each other
KMT: gas particles have negligible volume and no attraction to each other — that's why gases compress easily and fill any container.
Tyndall = you can see the beam
A light beam becomes visible passing through a colloid because its particles are big enough to scatter light — true solutions don't do this.
Squeeze it, it heats up pressure-wise
Boyle's Law: P and V are inversely related at constant T — squeeze the volume down, pressure goes up.
Charles says heat it, it grows
Charles's Law: V and T are directly related at constant P — heat a balloon, it expands.
STP is the universal starting line
At STP (0°C, 1 atm), 1 mole of any gas = 22.4 L. Always convert Celsius to Kelvin before plugging into a gas law.

Solutions & Thermochemistry

Above the line, it won't all dissolve
On a solubility curve, a point above the curve means undissolved solid remains — the solution at that point is saturated at most.
Concentrated ≠ saturated
Saturated means at the max the solvent can hold. Concentrated just means "a lot of solute" — a dilute solution can still be saturated if the solute barely dissolves.
Dilution: moles don't change
M₁V₁ = M₂V₂ works because adding water changes concentration, not the actual moles of solute present.
Exo EXits heat, endo takes it IN
Exothermic reactions release heat to the surroundings. Endothermic reactions absorb heat from the surroundings.
Flat parts on a PE diagram are phase changes
Sloped line = temperature changing (q = mCΔT). Flat line = phase changing at constant temperature (q = mH_f or mH_v).
Activation energy is measured from where you start
Ea is measured from the reactants up to the peak of the curve, not from zero — a common exam trap.

Equilibrium & Acids/Bases

Stress it, it shifts away
Le Chatelier's Principle: add stress (more reactant, less product, heat, pressure) and equilibrium shifts to relieve it, away from the stress.
Catalysts speed up, don't show up
A catalyst lowers activation energy and speeds a reaction, but isn't consumed and does NOT change ΔH or shift the equilibrium position.
Down the pH scale, up the acid
Each drop of 1 on the pH scale means [H⁺] is 10× bigger — pH is logarithmic, not linear.
Arrhenius: acids give H⁺, bases give OH⁻
That's the whole definition — an Arrhenius acid donates H⁺ ions in water, an Arrhenius base donates OH⁻ ions.
Strong means it splits all the way
Strong acids/bases ionize 100% in water. A dilute strong acid is still STRONG — don't confuse concentration with strength.
More collisions, more successful hits
Reaction rate increases with more concentration, more surface area, higher temperature, or a catalyst — all mean more effective collisions.

Redox & Nuclear

LEO the lion says GER
Lose Electrons = Oxidation. Gain Electrons = Reduction. Oxidation number goes up when you lose electrons, down when you gain them.
An OX and a RED CAT
Anode = OXidation (always). Cathode = REDuction (always) — true in both voltaic and electrolytic cells, even though the charge signs flip between them.
Free elements start at zero
Any uncombined element (Na, O₂, Fe) has an oxidation number of 0 — rule #1 before anything else.
Alpha is heavy, beta is light, gamma is nothing
Alpha decay: mass −4, atomic number −2. Beta decay: mass unchanged, atomic number +1. Gamma: neither changes — pure energy.
Half-life doesn't care about anything else
Half-life is constant no matter the temperature, pressure, or chemical form the isotope is in — a purely nuclear property.
Fission splits big, fusion joins small
Fission breaks a heavy nucleus (like U-235) into smaller pieces. Fusion joins light nuclei (like hydrogen) into a bigger one — the sun runs on fusion.

Organic Chemistry

Meth-Eth-Prop-But: count the carbons
Methane(1)-Ethane(2)-Propane(3)-Butane(4) — the prefix always tells you the carbon count, no matter the functional group.
-ane is full, -ene has one, -yne has two
Saturated hydrocarbons (all single bonds) end in -ane. One double bond = -ene. One triple bond = -yne.
Same family, one CH₂ apart
A homologous series is a family with the same general formula and functional group, where each member differs from the next by exactly one CH₂ unit.
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