FY13CE Chemistry cheat sheet

Atomic number Z = protons = electrons in a neutral atom; mass number A = protons + neutrons; neutrons N = A − Z.

Isotopes share Z but differ in N; relative atomic mass = Σ(isotopic abundance × isotope mass) / 100 when abundances are percentages.

Electron configuration follows Aufbau order 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p; 4s fills before 3d.

Hund's rule: degenerate orbitals are singly occupied with parallel spins before pairing; Pauli exclusion forbids identical quantum numbers.

Exceptions to fill order: Cr = [Ar]3d5 4s1 and Cu = [Ar]3d10 4s1 because half-filled and fully filled d subshells are stabilized.

Ion formation: cations lose the highest-n shell first (4s electrons leave before 3d for transition metals); anions gain electrons into the lowest-energy vacancy.

Periodic trends across a period: atomic radius decreases, ionization energy and electronegativity increase, metallic character decreases.

Down a group: atomic radius and shielding increase, first ionization energy decreases, electronegativity decreases, metallic character increases.

Quantum numbers: n (shell, n ≥ 1), l (0 to n−1), ml (−l to +l), ms (±½); maximum electrons per shell = 2n².

Electronegativity difference ΔEN > ~1.7 gives predominantly ionic bonding; 0.4–1.7 polar covalent; < 0.4 essentially nonpolar covalent.

Lewis structures: total valence electrons, form single bonds, complete octets on terminal atoms, place remaining electrons on the central atom, then form multiple bonds if octet is short.

Formal charge = (valence electrons) − (nonbonding electrons) − ½(bonding electrons); the structure with formal charges closest to zero is preferred.

VSEPR electron-domain geometries: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral.

Lone pairs compress bond angles: CH4 109.5°, NH3 ~107°, H2O ~104.5°; a lone pair occupies more space than a bonding pair.

Hybridization from steric number: 2 = sp (linear), 3 = sp² (trigonal planar), 4 = sp³ (tetrahedral), 5 = sp³d, 6 = sp³d².

Bond order = (bonding electrons − antibonding electrons)/2; higher bond order means shorter, stronger bond (O2 bond order 2, N2 bond order 3).

A molecule is polar if it has polar bonds and an asymmetric geometry so bond dipoles do not cancel (CO2 nonpolar, H2O polar).

Resonance structures differ only in electron placement, not atom positions; the real structure is a hybrid with bond orders between the contributing forms.

Intermolecular force strength: ion–dipole > hydrogen bonding > dipole–dipole > London dispersion; dispersion increases with polarizability and molecular size.

Hydrogen bonding requires H bonded to N, O, or F; it explains water's high boiling point, high surface tension, and ice being less dense than liquid water.

Ideal gas law: PV = nRT with R = 8.314 J mol⁻¹ K⁻¹ or 0.08206 L atm mol⁻¹ K⁻¹; temperature must be in kelvin.

Combined gas law P1V1/T1 = P2V2/T2; Dalton's law Ptotal = ΣPi; mole fraction xi = ni/ntotal and Pi = xiPtotal.

Van der Waals equation [P + a(n/V)²](V − nb) = nRT corrects for attractive forces (a) and molecular volume (b).

Phase changes: melting and vaporization absorb heat; freezing and condensation release heat; sublimation is solid to gas directly.

Heating-curve plateaus occur at melting and boiling points because added energy breaks intermolecular forces rather than raising kinetic energy.

Critical temperature is the highest temperature at which a gas can be liquefied by pressure alone; above it no liquid phase exists.

Solubility follows 'like dissolves like': polar solutes dissolve in polar solvents, nonpolar in nonpolar; ion–dipole interactions drive ionic dissolution in water.

Balance equations by conserving each element and charge; coefficients apply to the whole formula, subscripts never change during balancing.

Mole conversions: n = m/M, n = N/NA (NA = 6.022 × 10²³ mol⁻¹), n = V/22.4 L at STP for gases.

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

Limiting reactant: divide each reactant's moles by its stoichiometric coefficient; the smallest quotient limits the reaction.

Theoretical yield comes from the limiting reactant; percent yield = (actual yield / theoretical yield) × 100.

Combustion of a hydrocarbon CxHy: CxHy + (x + y/4)O2 → xCO2 + (y/2)H2O.

Common reaction classes: synthesis, decomposition, single replacement, double replacement (precipitation), and combustion.

Net ionic equations remove spectator ions; only species that change appear, and charges must balance on both sides.

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

First law: ΔU = q + w; at constant pressure qp = ΔH, and w = −PΔV for gas expansion work.

Exothermic reactions have ΔH < 0 (energy released); endothermic reactions have ΔH > 0 (energy absorbed).

Calorimetry: q = mcΔT; for a bomb calorimeter q = CΔT where C is the heat capacity of the calorimeter.

Hess's law: the enthalpy change of a reaction is independent of pathway, so ΔHrxn = ΣΔHf(products) − ΣΔHf(reactants).

Standard enthalpy of formation of an element in its standard state is zero; ΔHf° of a compound is for forming one mole from elements.

Bond enthalpy method: ΔHrxn = Σ(bonds broken) − Σ(bonds formed); bond breaking is endothermic, bond making is exothermic.

Gibbs free energy: ΔG = ΔH − TΔS; ΔG < 0 spontaneous, ΔG = 0 at equilibrium, ΔG > 0 nonspontaneous.

Entropy increases with more gas moles, higher temperature, and greater disorder (solid → liquid → gas).

Reaction spontaneity depends on both ΔH and ΔS; a reaction with ΔH > 0 can be spontaneous if ΔS is sufficiently positive at high T.

Rate = −Δ[reactant]/Δt = Δ[product]/Δt divided by the stoichiometric coefficient; units are mol L⁻¹ s⁻¹.

Rate law rate = k[A]^m[B]^n; reaction order is determined experimentally, not from stoichiometry.

Integrated forms: zero order [A] = [A]0 − kt; first order ln[A] = ln[A]0 − kt (half-life 0.693/k); second order 1/[A] = 1/[A]0 + kt.

Arrhenius equation k = Ae^(−Ea/RT); ln(k2/k1) = (Ea/R)(1/T1 − 1/T2); higher Ea means stronger temperature dependence.

A catalyst lowers activation energy and speeds both forward and reverse rates without changing ΔH or the equilibrium position.

Equilibrium constant Kc uses product concentrations over reactant concentrations, each raised to its coefficient; pure solids and liquids are omitted.

Reaction quotient Q compared with K: Q < K shifts right, Q > K shifts left, Q = K at equilibrium.

Le Chatelier's principle: adding reactant shifts right; increasing pressure shifts toward fewer gas moles; increasing temperature favors the endothermic direction.

Kp = Kc(RT)^Δn, where Δn is the change in moles of gas between products and reactants.

Brønsted–Lowry: acids donate protons, bases accept protons; conjugate pairs differ by one H⁺.

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

Strong acids (HCl, HBr, HI, HNO3, H2SO4, HClO4) and strong bases (group 1 hydroxides, Ca(OH)2, Ba(OH)2) dissociate completely.

Weak acid equilibrium Ka = [H⁺][A⁻]/[HA]; larger Ka means stronger acid; pKa = −log Ka.

Percent ionization = ([H⁺]/[HA]initial) × 100; it increases on dilution for a weak acid.

Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]); a buffer works best when pH is within about ±1 of pKa.

Salt hydrolysis: a salt of a weak acid and strong base is basic; a salt of a strong acid and weak base is acidic; strong acid–strong base salts are neutral.

Titration: at the equivalence point moles acid = moles base adjusted by stoichiometry; strong acid–strong base equivalence pH = 7.

Ksp expresses sparingly soluble salt solubility; for AB, Ksp = s², for AB2, Ksp = 4s³.

Oxidation is loss of electrons (anode); reduction is gain of electrons (cathode); remembered as OIL RIG.

Assign oxidation numbers: free elements 0, monatomic ions equal charge, oxygen usually −2, hydrogen usually +1, sum equals overall charge.

Galvanic cell: oxidation at the anode, reduction at the cathode; electrons flow anode → cathode through the external circuit.

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

ΔG° = −nFE°; with n moles of electrons and F = 96485 C mol⁻¹.

Nernst equation: E = E° − (0.0592/n)log Q at 25 °C; E = 0 at equilibrium.

In electrolysis, the external power source drives a nonspontaneous reaction; oxidation still occurs at the anode.

In a salt bridge, ions migrate to maintain charge neutrality: anions toward the anode, cations toward the cathode.

Balancing redox in acid: separate half-reactions, balance atoms, add H2O for O and H⁺ for H, balance charge with electrons, then equalize electrons and combine.

Alkali metals (group 1) are highly reactive, form +1 ions, and react vigorously with water to give hydroxide and hydrogen gas.

Alkaline earth metals (group 2) form +2 ions; reactivity increases down the group.

Halogens (group 17) are oxidizing agents; reactivity decreases down the group as atomic size increases.

Noble gases (group 18) have full valence shells and are largely inert; their ionization energies are the highest in each period.

Transition metals show variable oxidation states, form colored complexes, and often act as catalysts (Fe in Haber, Pt in catalytic converters).

Periodic table blocks: s (groups 1–2), p (groups 13–18), d (transition metals), f (lanthanides and actinides).

Metal oxides are generally basic, nonmetal oxides acidic; amphoteric oxides such as Al2O3 react with both acids and bases.

Diagonal relationships: Li resembles Mg, Be resembles Al in charge-to-size ratio and chemistry.

Ionic radius: cations are smaller than their parent atoms, anions larger; isoelectronic ions shrink as nuclear charge increases.

Alkanes CnH2n+2 are saturated, sp³, and undergo substitution with halogens; alkenes CnH2n have a C=C double bond and undergo addition.

Alkynes CnH2n−2 contain a C≡C triple bond; terminal alkynes are weakly acidic and react with strong base.

IUPAC naming: longest carbon chain, number from the end nearest the principal functional group, then list substituents alphabetically.

Functional group suffixes: -ol (alcohol), -al (aldehyde), -one (ketone), -oic acid (carboxylic acid), -amine (amine), -amide (amide).

Alcohols (R–OH) can be primary, secondary, or tertiary; oxidation gives aldehydes/ketones (1° and 2°) or resists oxidation (3°).

Carboxylic acids (R–COOH) are weak acids; they react with alcohols under acid catalysis to form esters (Fischer esterification).

Aldehydes are oxidized by Tollens' reagent (silver mirror) and Fehling's solution; ketones are not.

Isomers have the same molecular formula but different structures: structural isomers differ in connectivity, stereoisomers in spatial arrangement.

Aromatic rings such as benzene are planar, conjugated, and follow Hückel's rule (4n+2 π electrons) for aromaticity.

Filtration separates an insoluble solid from a liquid; decantation pours off the liquid; centrifugation speeds separation of fine suspensions.

Distillation separates liquids by boiling point; fractional distillation is used for close boiling points such as petroleum fractions.

Chromatography separates by differential affinity: the mobile phase carries the sample, the stationary phase retards components differently.

Titration procedure: rinse burette with titrant, record initial volume, add indicator, swirl, stop at the endpoint, read the meniscus at eye level.

Significant figures: addition/subtraction keeps the least decimal places; multiplication/division keeps the least significant figures.

Percent error = |experimental − accepted| / accepted × 100; precision refers to reproducibility, accuracy to closeness to the true value.

Qualitative tests: flame tests identify metal ions (Na yellow, K lilac, Cu blue-green, Ca brick red); BaCl2 detects sulfate.

Spectrophotometry uses Beer–Lambert law A = εbc; absorbance is proportional to concentration at a fixed path length.

Safety: add acid to water, never water to acid; use a fume hood for volatile reagents; read the SDS before handling a new chemical.