NYSTCE Chemistry cheat sheet

Independent variable is manipulated by the experimenter; dependent variable is measured; controlled variables are held constant to prevent confounding.

Scientific claim strength follows evidence hierarchy: controlled experiment > observational correlation; correlation alone never establishes causation.

Accuracy is closeness to the true value; precision is reproducibility among repeated trials. Random error affects precision, systematic error shifts accuracy.

Percent error = |experimental − accepted| / accepted × 100; percent yield = actual / theoretical × 100.

Significant figures: all nonzero digits count; zeros between nonzero digits count; leading zeros never count; trailing zeros after a decimal point count.

For multiplication/division, round to the least number of significant figures; for addition/subtraction, round to the least number of decimal places.

SI base units: meter (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount), candela (luminous intensity).

A hypothesis must be falsifiable; a theory is a well-tested explanatory framework; a law describes a consistent relationship, often mathematically.

Peer review and replication are the mechanisms that filter error and bias from the scientific literature.

Pure substances have fixed composition (elements or compounds); mixtures are physically combined and separable by physical means (filtration, distillation, chromatography).

Homogeneous mixture (solution) has uniform composition throughout; heterogeneous mixture has visibly distinct phases.

Intensive properties (density, boiling point, color) do not depend on amount; extensive properties (mass, volume, heat capacity) do.

Physical change alters state or form without changing identity; chemical change produces new substances, signaled by gas evolution, precipitate, color change, or heat release.

Density = mass / volume; specific gravity = density of substance / density of water at 4 °C.

Law of definite proportions: a compound always has the same mass ratio of elements. Law of multiple proportions: ratios of masses of one element combining with a fixed mass of another are small whole numbers.

Percent composition by mass = (mass of element in one mole / molar mass of compound) × 100.

Separation decision rule: differing boiling points → distillation; differing particle size/solubility → filtration; differing affinity for mobile vs stationary phase → chromatography.

Balance equations by changing coefficients only, never subscripts; total atoms of each element must match on both sides.

Mole conversions: moles = mass / molar mass; moles = particles / 6.022 × 10²³; at STP, moles = volume / 22.4 L.

Limiting reactant is identified by converting each reactant to product moles; the smallest product yield sets the theoretical yield.

Percent yield = (actual yield / theoretical yield) × 100; excess reactant remains after the limiting reactant is consumed.

Reaction types: synthesis, decomposition, single replacement, double replacement (metathesis), combustion, acid–base neutralization.

Solubility rules: most nitrates, acetates, and alkali metal salts are soluble; most carbonates, phosphates, and hydroxides are insoluble except with Group 1 or ammonium.

Net ionic equations omit spectator ions; only species that change appear, with charges balanced as well as atoms.

Molarity = moles solute / liters solution; dilution: M₁V₁ = M₂V₂.

Oxidation numbers track electron transfer: free elements 0, monatomic ion equals charge, oxygen usually −2, hydrogen usually +1.

Atomic number Z = protons; mass number A = protons + neutrons; isotopes differ in neutrons only.

Average atomic mass = Σ (isotope mass × fractional abundance).

Electron configuration follows Aufbau (lowest energy first), Pauli exclusion (two electrons per orbital, opposite spin), and Hund's rule (fill degenerate orbitals singly first).

Orbital capacity: s = 2, p = 6, d = 10, f = 14; period number equals highest principal quantum level occupied.

Quantum numbers: n (size/energy), l (shape, 0 to n−1), m_l (−l to +l), m_s (±½).

Periodic trends: atomic radius decreases left→right and increases top→bottom; ionization energy and electronegativity increase left→right and decrease top→bottom.

Group trends: alkali metals (Group 1) most reactive metals; halogens (Group 17) most reactive nonmetals; noble gases (Group 18) have full valence shells.

Valence electrons determine chemical behavior; main-group valence count equals the group number for Groups 1–2 and group number minus 10 for Groups 13–18.

Emission spectra arise when excited electrons relax to lower energy levels, releasing photons of energy ΔE = hν.

Ionic bonds form between metals and nonmetals via electron transfer and electrostatic attraction; covalent bonds share electrons between nonmetals.

Electronegativity difference: <0.4 nonpolar covalent, 0.4–1.7 polar covalent, >1.7 largely ionic (rule of thumb).

Lewis structures: count valence electrons, form octets, minimize formal charge, and place the least electronegative atom centrally.

VSEPR geometries: 2 domains linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral; lone pairs compress bond angles.

Lone-pair repulsion strength: lone pair–lone pair > lone pair–bond pair > bond pair–bond pair.

Polar bonds plus asymmetric geometry yield a polar molecule; symmetric geometry (CO₂, CCl₄) cancels bond dipoles.

Intermolecular forces in increasing strength: London dispersion < dipole–dipole < hydrogen bonding < ion–dipole.

Hydrogen bonding requires H bonded to N, O, or F, and explains the anomalously high boiling point of water.

Resonance delocalizes electrons; the actual structure is a hybrid, not a rapid interconversion of forms.

Kinetic molecular theory: gas particles are in constant random motion, collisions are elastic, and average kinetic energy is proportional to absolute temperature.

Ideal gas law: PV = nRT with R = 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K).

Combined gas law: P₁V₁/T₁ = P₂V₂/T₂; Boyle (P∝1/V), Charles (V∝T), Gay-Lussac (P∝T), Avogadro (V∝n).

Dalton's law of partial pressures: P_total = sum of partial pressures; each gas behaves independently.

Graham's law: rate of effusion is inversely proportional to the square root of molar mass.

Real gases deviate from ideal behavior at high pressure and low temperature, where particle volume and intermolecular attractions matter.

Phase changes: melting, freezing, vaporization, condensation, sublimation, deposition; heat of vaporization exceeds heat of fusion for water.

Heating curves show temperature plateaus during phase changes because added energy breaks intermolecular forces rather than raising kinetic energy.

Boiling occurs when vapor pressure equals external pressure; the normal boiling point is measured at 1 atm.

First law: ΔE = q + w; energy is conserved. Sign convention: q positive when heat enters the system, w positive when work is done on the system.

Exothermic reaction: ΔH < 0, releases heat. Endothermic: ΔH > 0, absorbs heat.

Calorimetry: q = mcΔT; at constant pressure, q equals ΔH.

Hess's law: ΔH for a reaction is the sum of the enthalpy changes of its steps, independent of pathway.

Standard enthalpy of reaction = Σ ΔH_f(products) − Σ ΔH_f(reactants); elements in standard state have ΔH_f = 0.

Bond breaking requires energy; bond formation releases energy; ΔH ≈ Σ bonds broken − Σ bonds formed.

Gibbs free energy: ΔG = ΔH − TΔS. Spontaneous when ΔG < 0; at equilibrium ΔG = 0.

ΔG° = −RT ln K and ΔG° = −nFE°; these link thermodynamics to equilibrium and electrochemistry.

Entropy increases with greater moles of gas, higher temperature, and increased disorder; the second law states total entropy of the universe increases.

Equilibrium constant expression includes products over reactants, each raised to its coefficient; pure solids and liquids are omitted.

Le Chatelier's principle: a system at equilibrium shifts to counteract a stress in concentration, pressure, or temperature.

K > 1 favors products; K < 1 favors reactants; the value depends on temperature.

For water, Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C; pH + pOH = 14.

pH = −log[H⁺]; pOH = −log[OH⁻]; acidic pH < 7, basic pH > 7 at 25 °C.

Strong acids and bases ionize completely; weak acids and bases partially ionize and require Ka or Kb equilibrium expressions.

Henderson–Hasselbalch: pH = pKa + log([base]/[acid]) for buffers.

Buffer resists pH change when it contains a weak acid and its conjugate base in comparable amounts.

Titration equivalence: moles acid × protons = moles base × hydroxide; at the equivalence point of a weak acid with strong base, pH > 7.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons (decrease in oxidation number).

LEO the lion says GER: Loss of Electrons is Oxidation; Gain of Electrons is Reduction.

Oxidizing agent is reduced; reducing agent is oxidized.

Galvanic (voltaic) cell converts chemical energy to electrical energy; electrolytic cell uses electrical energy to drive a nonspontaneous reaction.

Cell notation: anode | anode solution || cathode solution | cathode; oxidation occurs at the anode in both cell types.

Standard cell potential E°cell = E°cathode − E°anode; a positive E°cell indicates a spontaneous reaction.

ΔG° = −nFE°, with F = 96,485 C/mol and n = moles of electrons transferred.

In a galvanic cell, electrons flow from anode to cathode through the external circuit; cations migrate toward the cathode in the salt bridge.

Faraday's law: moles of electrons = charge (C) / 96,485; charge = current × time.

Alkanes are saturated (single bonds), formula CnH2n+2; alkenes have one double bond (CnH2n); alkynes have one triple bond (CnH2n−2).

IUPAC naming: longest carbon chain, number to give lowest locants, name substituents alphabetically.

Functional groups: hydroxyl (alcohol), carbonyl (aldehyde/ketone), carboxyl (carboxylic acid), amino (amine), amide, ester, ether, phosphate.

Isomers share a molecular formula but differ in structure: structural, geometric (cis/trans), and optical (enantiomers) isomers.

Addition reactions occur at double/triple bonds; substitution occurs at saturated carbons; elimination forms double bonds.

Carbohydrates (monosaccharides) are polyhydroxy aldehydes or ketones; glucose is C6H12O6.

Proteins are polymers of amino acids joined by peptide bonds; the sequence of amino acids determines primary structure.

Nucleic acids are polymers of nucleotides; DNA contains deoxyribose and thymine, RNA contains ribose and uracil.

Lipids include fats, oils, phospholipids, and steroids; triglycerides are glycerol esterified with three fatty acids.

Alpha decay emits a helium nucleus (⁴₂He), reducing mass number by 4 and atomic number by 2.

Beta-minus decay converts a neutron to a proton, emitting an electron and antineutrino; mass number unchanged, atomic number increases by 1.

Gamma emission releases high-energy photons without changing mass or atomic number.

Positron emission converts a proton to a neutron, decreasing atomic number by 1 with mass number unchanged.

Nuclear equations conserve mass number and atomic number on both sides.

Half-life: after n half-lives, remaining fraction = (1/2)ⁿ; mass remaining = initial mass × (1/2)ⁿ.

Nuclear fission splits a heavy nucleus and releases energy; nuclear fusion combines light nuclei and powers stars.

Mass defect converts to binding energy via E = mc²; the mass of a nucleus is less than the sum of its nucleons.

Radioactive decay follows first-order kinetics; carbon-14 dating uses a half-life of about 5,730 years.

Safety Data Sheets (SDS) provide hazard identification, handling, storage, and first-aid information for each chemical.

Standard PPE: goggles, lab coat or apron, and gloves; never eat, drink, or taste in the laboratory.

Never pipette by mouth; use a pipette bulb or pump.

Dilute acid by adding acid to water slowly, never water to acid, to control exothermic heat.

Heating test tubes: point the mouth away from people and heat gently while moving the tube.

Waft to detect odors; never inhale directly. Report all spills and injuries to the instructor immediately.

Waste disposal follows instructor and local regulations; never pour chemicals down the drain unless explicitly permitted.

Inquiry-based instruction: pose a question, design investigation, collect and analyze data, construct explanation, communicate findings.

Formative assessment informs instruction during learning; summative assessment measures achievement after instruction.

Independent variable is manipulated; dependent variable is measured; controlled variables are held constant.

Accuracy is closeness to the true value; precision is reproducibility of repeated measurements.

Percent error = |experimental − accepted| / accepted × 100.

Significant figures: leading zeros never count; trailing zeros after a decimal point count.

SI base units: meter, kilogram, second, ampere, kelvin, mole, candela.

A hypothesis must be falsifiable; a theory is a well-tested explanatory framework.

Correlation alone does not establish causation; controlled experiments do.

Pure substances have fixed composition; mixtures are physically combined and separable.

Intensive properties (density, boiling point) do not depend on amount; extensive properties do.

Density = mass / volume; specific gravity compares density to water.

Law of definite proportions: a compound has a fixed mass ratio of elements.

Percent composition = (element mass in one mole / molar mass) × 100.

Distillation separates by boiling point; filtration separates by particle size or solubility.

Balance equations by changing coefficients only, never subscripts.

moles = mass / molar mass; at STP, moles = volume / 22.4 L.

Limiting reactant gives the smallest product yield; it sets theoretical yield.

Percent yield = (actual / theoretical) × 100.

Most nitrates and alkali metal salts are soluble; most carbonates and hydroxides are not.

Net ionic equations omit spectator ions and balance both atoms and charge.

Molarity = moles solute / liters solution; dilution: M₁V₁ = M₂V₂.

Atomic number = protons; mass number = protons + neutrons.

Average atomic mass = Σ (isotope mass × fractional abundance).

Orbital capacity: s = 2, p = 6, d = 10, f = 14.

Hund's rule: fill degenerate orbitals singly before pairing.

Atomic radius decreases left→right; ionization energy and electronegativity increase left→right.

Group 1 are the most reactive metals; Group 17 the most reactive nonmetals; Group 18 have full valence shells.

Emission spectra arise when excited electrons relax, releasing photons of energy ΔE = hν.

Ionic bonds transfer electrons; covalent bonds share electrons.

Electronegativity difference <0.4 nonpolar covalent, 0.4–1.7 polar covalent, >1.7 largely ionic.

VSEPR: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral.

Lone pair–lone pair repulsion is strongest and compresses bond angles.

Symmetric geometry (CO₂, CCl₄) cancels bond dipoles, giving nonpolar molecules.

Intermolecular forces: London dispersion < dipole–dipole < hydrogen bonding < ion–dipole.

Hydrogen bonding requires H bonded to N, O, or F.

Ideal gas law: PV = nRT with R = 0.0821 L·atm/(mol·K).

Combined gas law: P₁V₁/T₁ = P₂V₂/T₂.

Dalton's law: P_total = sum of partial pressures.

Graham's law: effusion rate is inversely proportional to √molar mass.

Real gases deviate from ideal behavior at high pressure and low temperature.

Boiling occurs when vapor pressure equals external pressure.

Temperature plateaus on a heating curve occur during phase changes.

First law: ΔE = q + w; q is positive when heat enters the system.

Exothermic: ΔH < 0; endothermic: ΔH > 0.

Calorimetry: q = mcΔT.

Hess's law: ΔH is the sum of the steps and is path-independent.

ΔH°rxn = Σ ΔH_f(products) − Σ ΔH_f(reactants); elements have ΔH_f = 0.

ΔG = ΔH − TΔS; spontaneous when ΔG < 0; equilibrium when ΔG = 0.

ΔG° = −RT ln K and ΔG° = −nFE°.

K expression: products over reactants, each raised to its coefficient; omit solids and liquids.

Le Chatelier's principle: a system shifts to counteract a stress.

Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C; pH + pOH = 14.

pH = −log[H⁺]; acidic pH < 7, basic pH > 7 at 25 °C.

Henderson–Hasselbalch: pH = pKa + log([base]/[acid]).

A buffer contains a weak acid and its conjugate base in comparable amounts.

At the equivalence point of a weak acid with a strong base, pH > 7.

Oxidation is loss of electrons; reduction is gain of electrons.

The oxidizing agent is reduced; the reducing agent is oxidized.

Galvanic cells convert chemical energy to electrical energy; electrolytic cells use electrical energy.

Oxidation occurs at the anode in both cell types.

E°cell = E°cathode − E°anode; positive E°cell means spontaneous.

ΔG° = −nFE°, with F = 96,485 C/mol.

In a galvanic cell, electrons flow anode → cathode externally; cations migrate toward the cathode.

Alkanes: CnH2n+2; alkenes: CnH2n; alkynes: CnH2n−2.

IUPAC naming: longest chain, lowest locants, substituents alphabetical.

Functional groups: hydroxyl, carbonyl, carboxyl, amino, amide, ester, ether, phosphate.

Isomers share a molecular formula but differ in structure: structural, geometric, optical.

Addition occurs at double/triple bonds; substitution at saturated carbons; elimination forms double bonds.

Proteins are amino acid polymers joined by peptide bonds.

DNA contains deoxyribose and thymine; RNA contains ribose and uracil.

Alpha decay: mass number −4, atomic number −2.

Beta-minus decay: mass number unchanged, atomic number +1.

Gamma emission changes neither mass number nor atomic number.

Positron emission: atomic number −1, mass number unchanged.

Nuclear equations conserve mass number and atomic number.

Remaining fraction after n half-lives = (1/2)ⁿ.

E = mc² relates mass defect to binding energy.

SDS sheets list hazard identification, handling, storage, and first aid.

Standard PPE: goggles, lab coat or apron, gloves.

Never pipette by mouth; use a bulb or pump.

Add acid to water slowly, never water to acid.

Point test-tube mouths away from people when heating.

Waft to detect odors; never inhale directly.

Inquiry cycle: question, investigation, data analysis, explanation, communication.

Independent variable is manipulated; dependent variable is measured; controlled variables are held constant.

Accuracy is closeness to true value; precision is reproducibility.

Percent error = |experimental − accepted| / accepted × 100.

Leading zeros never count as significant; trailing zeros after a decimal point do.

SI base units: meter, kilogram, second, ampere, kelvin, mole, candela.

A hypothesis must be falsifiable; a theory is a well-tested explanatory framework.

Correlation alone does not establish causation.

Pure substances have fixed composition; mixtures are physically combined and separable.

Intensive properties (density, boiling point) do not depend on amount; extensive properties do.

Density = mass / volume.

Law of definite proportions: a compound has a fixed mass ratio of elements.

Percent composition = (element mass in one mole / molar mass) × 100.

Distillation separates by boiling point; filtration separates by particle size.

Balance equations by changing coefficients only, never subscripts.

moles = mass / molar mass; at STP, moles = volume / 22.4 L.

Limiting reactant gives the smallest product yield and sets theoretical yield.

Percent yield = (actual / theoretical) × 100.

Most nitrates and alkali metal salts are soluble; most carbonates and hydroxides are not.

Net ionic equations omit spectator ions and balance atoms and charge.

Molarity = moles solute / liters solution; dilution: M₁V₁ = M₂V₂.

Atomic number = protons; mass number = protons + neutrons.

Average atomic mass = Σ (isotope mass × fractional abundance).

Orbital capacity: s = 2, p = 6, d = 10, f = 14.

Hund's rule: fill degenerate orbitals singly before pairing.

Atomic radius decreases left→right; ionization energy and electronegativity increase left→right.

Group 1 most reactive metals; Group 17 most reactive nonmetals; Group 18 full valence shells.

Emission spectra arise when excited electrons relax, releasing photons of energy ΔE = hν.

Ionic bonds transfer electrons; covalent bonds share electrons.

Electronegativity difference <0.4 nonpolar covalent, 0.4–1.7 polar covalent, >1.7 largely ionic.

VSEPR: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral.

Lone pair–lone pair repulsion is strongest and compresses bond angles.

Symmetric geometry (CO₂, CCl₄) cancels bond dipoles, giving nonpolar molecules.

Intermolecular forces: London dispersion < dipole–dipole < hydrogen bonding < ion–dipole.

Hydrogen bonding requires H bonded to N, O, or F.

Ideal gas law: PV = nRT with R = 0.0821 L·atm/(mol·K).

Combined gas law: P₁V₁/T₁ = P₂V₂/T₂.

Dalton's law: P_total = sum of partial pressures.

Graham's law: effusion rate is inversely proportional to √molar mass.

Real gases deviate from ideal behavior at high pressure and low temperature.

Boiling occurs when vapor pressure equals external pressure.

Temperature plateaus on a heating curve occur during phase changes.

First law: ΔE = q + w; q is positive when heat enters the system.

Exothermic: ΔH < 0; endothermic: ΔH > 0.

Calorimetry: q = mcΔT.

Hess's law: ΔH is the sum of the steps and is path-independent.

ΔH°rxn = Σ ΔH_f(products) − Σ ΔH_f(reactants); elements have ΔH_f = 0.

ΔG = ΔH − TΔS; spontaneous when ΔG < 0; equilibrium when ΔG = 0.

ΔG° = −RT ln K and ΔG° = −nFE°.

K expression: products over reactants, each raised to its coefficient; omit solids and liquids.

Le Chatelier's principle: a system shifts to counteract a stress.

Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C; pH + pOH = 14.

pH = −log[H⁺]; acidic pH < 7, basic pH > 7 at 25 °C.

Henderson–Hasselbalch: pH = pKa + log([base]/[acid]).

A buffer contains a weak acid and its conjugate base in comparable amounts.

At the equivalence point of a weak acid with a strong base, pH > 7.

Oxidation is loss of electrons; reduction is gain of electrons.

The oxidizing agent is reduced; the reducing agent is oxidized.

Galvanic cells convert chemical energy to electrical energy; electrolytic cells use electrical energy.

Oxidation occurs at the anode in both cell types.

E°cell = E°cathode − E°anode; positive E°cell means spontaneous.

ΔG° = −nFE°, with F = 96,485 C/mol.

In a galvanic cell, electrons flow anode → cathode externally; cations migrate toward the cathode.

Alkanes: CnH2n+2; alkenes: CnH2n; alkynes: CnH2n−2.

IUPAC naming: longest chain, lowest locants, substituents alphabetical.

Functional groups: hydroxyl, carbonyl, carboxyl, amino, amide, ester, ether, phosphate.

Isomers share a molecular formula but differ in structure: structural, geometric, optical.

Addition occurs at double/triple bonds; substitution at saturated carbons; elimination forms double bonds.

Proteins are amino acid polymers joined by peptide bonds.

DNA contains deoxyribose and thymine; RNA contains ribose and uracil.

Alpha decay: mass number −4, atomic number −2.

Beta-minus decay: mass number unchanged, atomic number +1.

Gamma emission changes neither mass number nor atomic number.

Positron emission: atomic number −1, mass number unchanged.

Nuclear equations conserve mass number and atomic number.

Remaining fraction after n half-lives = (1/2)ⁿ.

E = mc² relates mass defect to binding energy.

SDS sheets list hazard identification, handling, storage, and first aid.

Standard PPE: goggles, lab coat or apron, gloves.

Never pipette by mouth; use a bulb or pump.

Add acid to water slowly, never water to acid.

Point test-tube mouths away from people when heating.

Waft to detect odors; never inhale directly.

Inquiry cycle: question, investigation, data analysis, explanation, communication.