GACE Chemistry (712) cheat sheet

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

Accuracy = closeness to the true value; precision = reproducibility among repeated measurements. Random error scatters results and reduces precision; systematic error shifts results consistently and reduces accuracy.

Significant figures: multiplication/division results carry the fewest sig figs of any factor; addition/subtraction results carry the fewest decimal places. Exact counting numbers have unlimited sig figs.

Percent error = |measured − accepted| / accepted × 100%. Percent yield is a separate calculation using stoichiometric predicted mass.

Scientific method sequence: observation, question, hypothesis, controlled experiment, data analysis, conclusion, peer review and replication. A hypothesis must be falsifiable.

A theory is a well-tested explanatory framework supported by many lines of evidence; a law describes a consistent relationship, often mathematically. Neither is a guess.

Lab safety: add acid to water (never water to acid) when diluting; use fume hoods for volatile reagents; know SDS hazard categories and eyewash/shower locations.

Graph choice: line graph for continuous change, bar graph for categorical comparison, scatter plot with regression for correlation between two measured variables.

Bias controls include random assignment, blinding, placebos, adequate sample size, and calibration of instruments before use.

Atomic number Z = protons; mass number A = protons + neutrons; isotopes share Z but differ in neutron count; ions differ in electron count.

Electron configuration follows Aufbau order, Pauli exclusion (two electrons per orbital, opposite spins), and Hund's rule (maximize unpaired spins within a subshell).

Orbital shapes: s spherical, p dumbbell (three orientations), d four-lobed (five orientations); each orbital holds two electrons.

Periodic trends: atomic radius decreases left-to-right and increases top-to-bottom; ionization energy and electronegativity increase left-to-right and decrease down a group.

Effective nuclear charge increases across a period, contracting the electron cloud; added shells down a group outweigh Z increase, expanding radius.

Nuclear decay: alpha (⁴₂He, A−4, Z−2), beta-minus (neutron to proton, A unchanged, Z+1), positron emission (proton to neutron, Z−1), gamma (photon only).

Half-life: remaining amount = initial × (1/2)^n, where n = elapsed time / half-life. After n half-lives the fraction remaining is 2^−n.

Nuclear binding energy: mass defect converts to energy via E = mc²; fission splits heavy nuclei, fusion combines light nuclei, both release energy toward higher binding energy per nucleon.

Balancing nuclear equations: conserve mass number A and atomic number Z on both sides; gamma emission changes neither.

Bond type follows electronegativity difference: <0.4 nonpolar covalent, 0.4–1.7 polar covalent, >1.7 largely ionic (metals plus nonmetals typically ionic).

Ionic compounds form from cation/anion electrostatic attraction, have high melting points, conduct when molten or dissolved, and form crystal lattices.

Lewis structures: sum valence electrons, connect atoms, complete octets, minimize formal charge, expand octets only for period 3 and below.

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

Molecular polarity requires polar bonds plus an asymmetric geometry; symmetric shapes (CO₂ linear, CCl₄ tetrahedral) cancel bond dipoles.

Intermolecular forces ranked: ion-dipole > hydrogen bonding > dipole-dipole > London dispersion; dispersion grows with polarizability and molecular size.

Hybridization from steric number: 2 sp, 3 sp², 4 sp³; sp² systems have one unhybridized p orbital for pi bonding.

Metallic bonding: delocalized electron sea explains conductivity, malleability, and luster; alloys are solid solutions of metals.

Formal charge = valence electrons − nonbonding electrons − (bonding electrons / 2); resonance structures differ only in electron placement.

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

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

Mole conversions: moles = mass / molar mass; moles = molarity × volume (L); at STP one mole of ideal gas occupies 22.4 L.

Limiting reactant: convert each reactant to product moles via the balanced equation; the smallest product amount identifies the limiting reagent; excess remains unreacted.

Percent yield = actual yield / theoretical yield × 100%; percent composition = (mass of element / molar mass) × 100%.

Enthalpy: ΔH_rxn = Σ ΔH_f(products) − Σ ΔH_f(reactants); Hess's law allows summing stepwise reactions; bond breaking absorbs energy, bond forming releases it.

Exothermic reactions have negative ΔH and release heat; endothermic reactions have positive ΔH and absorb heat.

Gibbs free energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0. Entropy increases with gas production, temperature, and dispersal of matter.

Oxidation is loss of electrons (anode), reduction is gain (cathode); balance redox half-reactions for atoms and charge.

Concentration units: molarity M = mol solute / L solution; molality m = mol solute / kg solvent; mole fraction; mass percent.

Dilution: M₁V₁ = M₂V₂. Adding solvent changes volume but not moles of solute.

Colligative properties depend on particle count: boiling point elevation ΔT = i·Kb·m, freezing point depression ΔT = i·Kf·m, vapor pressure lowering, and osmotic pressure π = iMRT.

Raoult's law: vapor pressure of a solution equals the sum of component vapor pressures weighted by mole fraction; nonvolatile solutes lower vapor pressure.

Solubility depends on temperature and pressure; Henry's law states gas solubility is proportional to partial pressure; gases dissolve less as temperature rises.

Rate law expresses rate = k[A]^m[B]^n; reaction order is determined experimentally, not from coefficients. Factors affecting rate: concentration, temperature, surface area, catalysts.

Arrhenius equation k = A·e^(−Ea/RT): higher temperature and lower activation energy increase rate constant; catalysts lower Ea without changing ΔH or equilibrium position.

Equilibrium constant expressions use products over reactants raised to coefficients, excluding pure solids and liquids; K > 1 favors products.

Le Chatelier's principle: increasing concentration of a reactant shifts right; increasing pressure shifts toward fewer gas moles; heating favors the endothermic direction.

Functional groups: hydroxyl (alcohol), carbonyl (aldehyde/ketone), carboxyl (acid), amino, ester, ether, amide, and phosphate; each dictates characteristic reactivity.

IUPAC naming: longest carbon chain, lowest locants for substituents, suffix by highest-priority functional group (acid > ester > amide > aldehyde > ketone > alcohol > amine).

Isomerism: structural isomers differ in connectivity; stereoisomers include enantiomers (mirror images, chiral centers) and diastereomers (cis/trans, ring geometry).

Reaction patterns: alkanes substitution, alkenes addition, alcohols oxidation/dehydration, carboxylic acids esterification with alcohols, esters hydrolysis.

Polymers form by addition (alkene monomers, no byproduct) or condensation (loss of water or small molecule, e.g., peptide and ester linkages).

Biomolecules: carbohydrates (monosaccharides, energy), lipids (fatty acids, glycerol, hydrophobic membranes), proteins (amino acids joined by peptide bonds, folded structure determines function), nucleic acids (nucleotides, DNA/RNA information storage).

Enzymes are biological catalysts that lower activation energy and are specific to substrates; activity depends on pH, temperature, and cofactors.

Greenhouse gases include CO₂, CH₄, N₂O, and water vapor; ozone depletion is driven by CFCs releasing chlorine radicals in the stratosphere.

Water quality indicators: pH, dissolved oxygen, BOD, nitrates/phosphates (eutrophication), and heavy metal concentrations; acid rain forms from SO₂ and NOx emissions.

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

Accuracy = closeness to the true value; precision = reproducibility among repeated measurements. Random error scatters results and reduces precision; systematic error shifts results consistently and reduces accuracy.

Significant figures: multiplication/division results carry the fewest sig figs of any factor; addition/subtraction results carry the fewest decimal places. Exact counting numbers have unlimited sig figs.

Percent error = |measured − accepted| / accepted × 100%. Percent yield is a separate calculation using stoichiometric predicted mass.

Scientific method sequence: observation, question, hypothesis, controlled experiment, data analysis, conclusion, peer review and replication. A hypothesis must be falsifiable.

A theory is a well-tested explanatory framework supported by many lines of evidence; a law describes a consistent relationship, often mathematically. Neither is a guess.

Lab safety: add acid to water (never water to acid) when diluting; use fume hoods for volatile reagents; know SDS hazard categories and eyewash/shower locations.

Graph choice: line graph for continuous change, bar graph for categorical comparison, scatter plot with regression for correlation between two measured variables.

Bias controls include random assignment, blinding, placebos, adequate sample size, and calibration of instruments before use.

Atomic number Z = protons; mass number A = protons + neutrons; isotopes share Z but differ in neutron count; ions differ in electron count.

Electron configuration follows Aufbau order, Pauli exclusion (two electrons per orbital, opposite spins), and Hund's rule (maximize unpaired spins within a subshell).

Orbital shapes: s spherical, p dumbbell (three orientations), d four-lobed (five orientations); each orbital holds two electrons.

Periodic trends: atomic radius decreases left-to-right and increases top-to-bottom; ionization energy and electronegativity increase left-to-right and decrease down a group.

Effective nuclear charge increases across a period, contracting the electron cloud; added shells down a group outweigh Z increase, expanding radius.

Nuclear decay: alpha (⁴₂He, A−4, Z−2), beta-minus (neutron to proton, A unchanged, Z+1), positron emission (proton to neutron, Z−1), gamma (photon only).

Half-life: remaining amount = initial × (1/2)^n, where n = elapsed time / half-life. After n half-lives the fraction remaining is 2^−n.

Nuclear binding energy: mass defect converts to energy via E = mc²; fission splits heavy nuclei, fusion combines light nuclei, both release energy toward higher binding energy per nucleon.

Balancing nuclear equations: conserve mass number A and atomic number Z on both sides; gamma emission changes neither.

Bond type follows electronegativity difference: <0.4 nonpolar covalent, 0.4–1.7 polar covalent, >1.7 largely ionic (metals plus nonmetals typically ionic).

Ionic compounds form from cation/anion electrostatic attraction, have high melting points, conduct when molten or dissolved, and form crystal lattices.

Lewis structures: sum valence electrons, connect atoms, complete octets, minimize formal charge, expand octets only for period 3 and below.

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

Molecular polarity requires polar bonds plus an asymmetric geometry; symmetric shapes (CO₂ linear, CCl₄ tetrahedral) cancel bond dipoles.

Intermolecular forces ranked: ion-dipole > hydrogen bonding > dipole-dipole > London dispersion; dispersion grows with polarizability and molecular size.

Hybridization from steric number: 2 sp, 3 sp², 4 sp³; sp² systems have one unhybridized p orbital for pi bonding.

Metallic bonding: delocalized electron sea explains conductivity, malleability, and luster; alloys are solid solutions of metals.

Formal charge = valence electrons − nonbonding electrons − (bonding electrons / 2); resonance structures differ only in electron placement.

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

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

Mole conversions: moles = mass / molar mass; moles = molarity × volume (L); at STP one mole of ideal gas occupies 22.4 L.

Limiting reactant: convert each reactant to product moles via the balanced equation; the smallest product amount identifies the limiting reagent; excess remains unreacted.

Percent yield = actual yield / theoretical yield × 100%; percent composition = (mass of element / molar mass) × 100%.

Enthalpy: ΔH_rxn = Σ ΔH_f(products) − Σ ΔH_f(reactants); Hess's law allows summing stepwise reactions; bond breaking absorbs energy, bond forming releases it.

Exothermic reactions have negative ΔH and release heat; endothermic reactions have positive ΔH and absorb heat.

Gibbs free energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0. Entropy increases with gas production, temperature, and dispersal of matter.

Oxidation is loss of electrons (anode), reduction is gain (cathode); balance redox half-reactions for atoms and charge.

Concentration units: molarity M = mol solute / L solution; molality m = mol solute / kg solvent; mole fraction; mass percent.

Dilution: M₁V₁ = M₂V₂. Adding solvent changes volume but not moles of solute.

Colligative properties depend on particle count: boiling point elevation ΔT = i·Kb·m, freezing point depression ΔT = i·Kf·m, vapor pressure lowering, and osmotic pressure π = iMRT.

Raoult's law: vapor pressure of a solution equals the sum of component vapor pressures weighted by mole fraction; nonvolatile solutes lower vapor pressure.

Solubility depends on temperature and pressure; Henry's law states gas solubility is proportional to partial pressure; gases dissolve less as temperature rises.

Rate law expresses rate = k[A]^m[B]^n; reaction order is determined experimentally, not from coefficients. Factors affecting rate: concentration, temperature, surface area, catalysts.

Arrhenius equation k = A·e^(−Ea/RT): higher temperature and lower activation energy increase rate constant; catalysts lower Ea without changing ΔH or equilibrium position.

Equilibrium constant expressions use products over reactants raised to coefficients, excluding pure solids and liquids; K > 1 favors products.

Le Chatelier's principle: increasing concentration of a reactant shifts right; increasing pressure shifts toward fewer gas moles; heating favors the endothermic direction.

Functional groups: hydroxyl (alcohol), carbonyl (aldehyde/ketone), carboxyl (acid), amino, ester, ether, amide, and phosphate; each dictates characteristic reactivity.

IUPAC naming: longest carbon chain, lowest locants for substituents, suffix by highest-priority functional group (acid > ester > amide > aldehyde > ketone > alcohol > amine).

Isomerism: structural isomers differ in connectivity; stereoisomers include enantiomers (mirror images, chiral centers) and diastereomers (cis/trans, ring geometry).

Reaction patterns: alkanes substitution, alkenes addition, alcohols oxidation/dehydration, carboxylic acids esterification with alcohols, esters hydrolysis.

Polymers form by addition (alkene monomers, no byproduct) or condensation (loss of water or small molecule, e.g., peptide and ester linkages).

Biomolecules: carbohydrates (monosaccharides, energy), lipids (fatty acids, glycerol, hydrophobic membranes), proteins (amino acids joined by peptide bonds, folded structure determines function), nucleic acids (nucleotides, DNA/RNA information storage).

Enzymes are biological catalysts that lower activation energy and are specific to substrates; activity depends on pH, temperature, and cofactors.

Greenhouse gases include CO₂, CH₄, N₂O, and water vapor; ozone depletion is driven by CFCs releasing chlorine radicals in the stratosphere.

Water quality indicators: pH, dissolved oxygen, BOD, nitrates/phosphates (eutrophication), and heavy metal concentrations; acid rain forms from SO₂ and NOx emissions.

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

Accuracy = closeness to the true value; precision = reproducibility among repeated measurements. Random error scatters results and reduces precision; systematic error shifts results consistently and reduces accuracy.

Significant figures: multiplication/division results carry the fewest sig figs of any factor; addition/subtraction results carry the fewest decimal places. Exact counting numbers have unlimited sig figs.

Percent error = |measured − accepted| / accepted × 100%. Percent yield is a separate calculation using stoichiometric predicted mass.

Scientific method sequence: observation, question, hypothesis, controlled experiment, data analysis, conclusion, peer review and replication. A hypothesis must be falsifiable.

A theory is a well-tested explanatory framework supported by many lines of evidence; a law describes a consistent relationship, often mathematically. Neither is a guess.

Lab safety: add acid to water (never water to acid) when diluting; use fume hoods for volatile reagents; know SDS hazard categories and eyewash/shower locations.

Graph choice: line graph for continuous change, bar graph for categorical comparison, scatter plot with regression for correlation between two measured variables.

Bias controls include random assignment, blinding, placebos, adequate sample size, and calibration of instruments before use.

Atomic number Z = protons; mass number A = protons + neutrons; isotopes share Z but differ in neutron count; ions differ in electron count.

Electron configuration follows Aufbau order, Pauli exclusion (two electrons per orbital, opposite spins), and Hund's rule (maximize unpaired spins within a subshell).

Orbital shapes: s spherical, p dumbbell (three orientations), d four-lobed (five orientations); each orbital holds two electrons.

Periodic trends: atomic radius decreases left-to-right and increases top-to-bottom; ionization energy and electronegativity increase left-to-right and decrease down a group.

Effective nuclear charge increases across a period, contracting the electron cloud; added shells down a group outweigh Z increase, expanding radius.

Nuclear decay: alpha (⁴₂He, A−4, Z−2), beta-minus (neutron to proton, A unchanged, Z+1), positron emission (proton to neutron, Z−1), gamma (photon only).

Half-life: remaining amount = initial × (1/2)^n, where n = elapsed time / half-life. After n half-lives the fraction remaining is 2^−n.

Nuclear binding energy: mass defect converts to energy via E = mc²; fission splits heavy nuclei, fusion combines light nuclei, both release energy toward higher binding energy per nucleon.

Balancing nuclear equations: conserve mass number A and atomic number Z on both sides; gamma emission changes neither.

Bond type follows electronegativity difference: <0.4 nonpolar covalent, 0.4–1.7 polar covalent, >1.7 largely ionic (metals plus nonmetals typically ionic).

Ionic compounds form from cation/anion electrostatic attraction, have high melting points, conduct when molten or dissolved, and form crystal lattices.

Lewis structures: sum valence electrons, connect atoms, complete octets, minimize formal charge, expand octets only for period 3 and below.

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

Molecular polarity requires polar bonds plus an asymmetric geometry; symmetric shapes (CO₂ linear, CCl₄ tetrahedral) cancel bond dipoles.

Intermolecular forces ranked: ion-dipole > hydrogen bonding > dipole-dipole > London dispersion; dispersion grows with polarizability and molecular size.

Hybridization from steric number: 2 sp, 3 sp², 4 sp³; sp² systems have one unhybridized p orbital for pi bonding.

Metallic bonding: delocalized electron sea explains conductivity, malleability, and luster; alloys are solid solutions of metals.

Formal charge = valence electrons − nonbonding electrons − (bonding electrons / 2); resonance structures differ only in electron placement.

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

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

Mole conversions: moles = mass / molar mass; moles = molarity × volume (L); at STP one mole of ideal gas occupies 22.4 L.

Limiting reactant: convert each reactant to product moles via the balanced equation; the smallest product amount identifies the limiting reagent; excess remains unreacted.

Percent yield = actual yield / theoretical yield × 100%; percent composition = (mass of element / molar mass) × 100%.

Enthalpy: ΔH_rxn = Σ ΔH_f(products) − Σ ΔH_f(reactants); Hess's law allows summing stepwise reactions; bond breaking absorbs energy, bond forming releases it.

Exothermic reactions have negative ΔH and release heat; endothermic reactions have positive ΔH and absorb heat.

Gibbs free energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0. Entropy increases with gas production, temperature, and dispersal of matter.

Oxidation is loss of electrons (anode), reduction is gain (cathode); balance redox half-reactions for atoms and charge.

Concentration units: molarity M = mol solute / L solution; molality m = mol solute / kg solvent; mole fraction; mass percent.

Dilution: M₁V₁ = M₂V₂. Adding solvent changes volume but not moles of solute.

Colligative properties depend on particle count: boiling point elevation ΔT = i·Kb·m, freezing point depression ΔT = i·Kf·m, vapor pressure lowering, and osmotic pressure π = iMRT.

Raoult's law: vapor pressure of a solution equals the sum of component vapor pressures weighted by mole fraction; nonvolatile solutes lower vapor pressure.

Solubility depends on temperature and pressure; Henry's law states gas solubility is proportional to partial pressure; gases dissolve less as temperature rises.

Rate law expresses rate = k[A]^m[B]^n; reaction order is determined experimentally, not from coefficients. Factors affecting rate: concentration, temperature, surface area, catalysts.

Arrhenius equation k = A·e^(−Ea/RT): higher temperature and lower activation energy increase rate constant; catalysts lower Ea without changing ΔH or equilibrium position.

Equilibrium constant expressions use products over reactants raised to coefficients, excluding pure solids and liquids; K > 1 favors products.

Le Chatelier's principle: increasing concentration of a reactant shifts right; increasing pressure shifts toward fewer gas moles; heating favors the endothermic direction.

Functional groups: hydroxyl (alcohol), carbonyl (aldehyde/ketone), carboxyl (acid), amino, ester, ether, amide, and phosphate; each dictates characteristic reactivity.

IUPAC naming: longest carbon chain, lowest locants for substituents, suffix by highest-priority functional group (acid > ester > amide > aldehyde > ketone > alcohol > amine).

Isomerism: structural isomers differ in connectivity; stereoisomers include enantiomers (mirror images, chiral centers) and diastereomers (cis/trans, ring geometry).

Reaction patterns: alkanes substitution, alkenes addition, alcohols oxidation/dehydration, carboxylic acids esterification with alcohols, esters hydrolysis.

Polymers form by addition (alkene monomers, no byproduct) or condensation (loss of water or small molecule, e.g., peptide and ester linkages).

Biomolecules: carbohydrates (monosaccharides, energy), lipids (fatty acids, glycerol, hydrophobic membranes), proteins (amino acids joined by peptide bonds, folded structure determines function), nucleic acids (nucleotides, DNA/RNA information storage).

Enzymes are biological catalysts that lower activation energy and are specific to substrates; activity depends on pH, temperature, and cofactors.

Greenhouse gases include CO₂, CH₄, N₂O, and water vapor; ozone depletion is driven by CFCs releasing chlorine radicals in the stratosphere.

Water quality indicators: pH, dissolved oxygen, BOD, nitrates/phosphates (eutrophication), and heavy metal concentrations; acid rain forms from SO₂ and NOx emissions.

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

Accuracy = closeness to the true value; precision = reproducibility among repeated measurements. Random error scatters results and reduces precision; systematic error shifts results consistently and reduces accuracy.

Significant figures: multiplication/division results carry the fewest sig figs of any factor; addition/subtraction results carry the fewest decimal places. Exact counting numbers have unlimited sig figs.

Percent error = |measured − accepted| / accepted × 100%. Percent yield is a separate calculation using stoichiometric predicted mass.

Scientific method sequence: observation, question, hypothesis, controlled experiment, data analysis, conclusion, peer review and replication. A hypothesis must be falsifiable.

A theory is a well-tested explanatory framework supported by many lines of evidence; a law describes a consistent relationship, often mathematically. Neither is a guess.

Lab safety: add acid to water (never water to acid) when diluting; use fume hoods for volatile reagents; know SDS hazard categories and eyewash/shower locations.

Graph choice: line graph for continuous change, bar graph for categorical comparison, scatter plot with regression for correlation between two measured variables.

Bias controls include random assignment, blinding, placebos, adequate sample size, and calibration of instruments before use.

Atomic number Z = protons; mass number A = protons + neutrons; isotopes share Z but differ in neutron count; ions differ in electron count.

Electron configuration follows Aufbau order, Pauli exclusion (two electrons per orbital, opposite spins), and Hund's rule (maximize unpaired spins within a subshell).

Orbital shapes: s spherical, p dumbbell (three orientations), d four-lobed (five orientations); each orbital holds two electrons.

Periodic trends: atomic radius decreases left-to-right and increases top-to-bottom; ionization energy and electronegativity increase left-to-right and decrease down a group.

Effective nuclear charge increases across a period, contracting the electron cloud; added shells down a group outweigh Z increase, expanding radius.

Nuclear decay: alpha (⁴₂He, A−4, Z−2), beta-minus (neutron to proton, A unchanged, Z+1), positron emission (proton to neutron, Z−1), gamma (photon only).

Half-life: remaining amount = initial × (1/2)^n, where n = elapsed time / half-life. After n half-lives the fraction remaining is 2^−n.

Nuclear binding energy: mass defect converts to energy via E = mc²; fission splits heavy nuclei, fusion combines light nuclei, both release energy toward higher binding energy per nucleon.

Balancing nuclear equations: conserve mass number A and atomic number Z on both sides; gamma emission changes neither.

Bond type follows electronegativity difference: <0.4 nonpolar covalent, 0.4–1.7 polar covalent, >1.7 largely ionic (metals plus nonmetals typically ionic).

Ionic compounds form from cation/anion electrostatic attraction, have high melting points, conduct when molten or dissolved, and form crystal lattices.

Lewis structures: sum valence electrons, connect atoms, complete octets, minimize formal charge, expand octets only for period 3 and below.

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

Molecular polarity requires polar bonds plus an asymmetric geometry; symmetric shapes (CO₂ linear, CCl₄ tetrahedral) cancel bond dipoles.

Intermolecular forces ranked: ion-dipole > hydrogen bonding > dipole-dipole > London dispersion; dispersion grows with polarizability and molecular size.

Hybridization from steric number: 2 sp, 3 sp², 4 sp³; sp² systems have one unhybridized p orbital for pi bonding.

Metallic bonding: delocalized electron sea explains conductivity, malleability, and luster; alloys are solid solutions of metals.

Formal charge = valence electrons − nonbonding electrons − (bonding electrons / 2); resonance structures differ only in electron placement.

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

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

Mole conversions: moles = mass / molar mass; moles = molarity × volume (L); at STP one mole of ideal gas occupies 22.4 L.

Limiting reactant: convert each reactant to product moles via the balanced equation; the smallest product amount identifies the limiting reagent; excess remains unreacted.

Percent yield = actual yield / theoretical yield × 100%; percent composition = (mass of element / molar mass) × 100%.

Enthalpy: ΔH_rxn = Σ ΔH_f(products) − Σ ΔH_f(reactants); Hess's law allows summing stepwise reactions; bond breaking absorbs energy, bond forming releases it.

Exothermic reactions have negative ΔH and release heat; endothermic reactions have positive ΔH and absorb heat.

Gibbs free energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0. Entropy increases with gas production, temperature, and dispersal of matter.

Oxidation is loss of electrons (anode), reduction is gain (cathode); balance redox half-reactions for atoms and charge.

Concentration units: molarity M = mol solute / L solution; molality m = mol solute / kg solvent; mole fraction; mass percent.

Dilution: M₁V₁ = M₂V₂. Adding solvent changes volume but not moles of solute.

Colligative properties depend on particle count: boiling point elevation ΔT = i·Kb·m, freezing point depression ΔT = i·Kf·m, vapor pressure lowering, and osmotic pressure π = iMRT.

Raoult's law: vapor pressure of a solution equals the sum of component vapor pressures weighted by mole fraction; nonvolatile solutes lower vapor pressure.

Solubility depends on temperature and pressure; Henry's law states gas solubility is proportional to partial pressure; gases dissolve less as temperature rises.

Rate law expresses rate = k[A]^m[B]^n; reaction order is determined experimentally, not from coefficients. Factors affecting rate: concentration, temperature, surface area, catalysts.

Arrhenius equation k = A·e^(−Ea/RT): higher temperature and lower activation energy increase rate constant; catalysts lower Ea without changing ΔH or equilibrium position.

Equilibrium constant expressions use products over reactants raised to coefficients, excluding pure solids and liquids; K > 1 favors products.

Le Chatelier's principle: increasing concentration of a reactant shifts right; increasing pressure shifts toward fewer gas moles; heating favors the endothermic direction.

Functional groups: hydroxyl (alcohol), carbonyl (aldehyde/ketone), carboxyl (acid), amino, ester, ether, amide, and phosphate; each dictates characteristic reactivity.

IUPAC naming: longest carbon chain, lowest locants for substituents, suffix by highest-priority functional group (acid > ester > amide > aldehyde > ketone > alcohol > amine).

Isomerism: structural isomers differ in connectivity; stereoisomers include enantiomers (mirror images, chiral centers) and diastereomers (cis/trans, ring geometry).

Reaction patterns: alkanes substitution, alkenes addition, alcohols oxidation/dehydration, carboxylic acids esterification with alcohols, esters hydrolysis.

Polymers form by addition (alkene monomers, no byproduct) or condensation (loss of water or small molecule, e.g., peptide and ester linkages).

Biomolecules: carbohydrates (monosaccharides, energy), lipids (fatty acids, glycerol, hydrophobic membranes), proteins (amino acids joined by peptide bonds, folded structure determines function), nucleic acids (nucleotides, DNA/RNA information storage).

Enzymes are biological catalysts that lower activation energy and are specific to substrates; activity depends on pH, temperature, and cofactors.

Greenhouse gases include CO₂, CH₄, N₂O, and water vapor; ozone depletion is driven by CFCs releasing chlorine radicals in the stratosphere.

Water quality indicators: pH, dissolved oxygen, BOD, nitrates/phosphates (eutrophication), and heavy metal concentrations; acid rain forms from SO₂ and NOx emissions.