MTTC Chemistry (018) cheat sheet

SI base units: length meter (m), mass kilogram (kg), amount mole (mol), temperature kelvin (K), time second (s); derived units include the newton (kg·m/s²) and the joule (kg·m²/s²).

Density d = m/V serves as a conversion factor between mass and volume (water ≈ 1.00 g/mL at 4 °C).

Percent error = |measured − accepted| ÷ accepted × 100%; the result is reported as a positive value.

Significant figures: addition and subtraction keep the fewest decimal places; multiplication and division keep the fewest significant figures; exact counting numbers have unlimited significant figures.

Scientific notation N × 10ⁿ: only the coefficient digits are significant; round only once, at the final step of a multistep calculation.

Random error degrades precision and scatters results in both directions; systematic error (miscalibrated balance, contaminated reagent) shifts results consistently and degrades accuracy.

Uncertainty propagation: absolute uncertainties add for sums and differences; relative (percent) uncertainties add for products and quotients.

Safety rules: add acid to water, never water to acid; use a fume hood for volatile or toxic reagents; never pipette by mouth; know the location of the eyewash and shower.

Experimental design: the independent variable is manipulated, the dependent variable is measured, controlled variables are held constant, and a control group isolates the effect of the treatment.

Quantum numbers: n = 1, 2, 3…; l = 0 to n − 1 (s, p, d, f); m_l = −l to +l; m_s = ±½. The Pauli exclusion principle forbids two electrons from sharing all four values.

Subshell capacities: s = 2 electrons, p = 6, d = 10, f = 14; a shell holds a maximum of 2n² electrons.

Aufbau filling order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p; exceptions include Cr [Ar]3d⁵4s¹ and Cu [Ar]3d¹⁰4s¹.

Photon energy E = hν = hc/λ, with h = 6.626 × 10⁻³⁴ J·s and c = 3.00 × 10⁸ m/s; the photoelectric effect requires photon energy above the work function.

Periodic trends: atomic radius decreases left to right across a period and increases down a group; first ionization energy and electronegativity increase across a period and decrease down a group.

Effective nuclear charge rises across a period while shielding stays roughly constant, contracting the atom; added shells down a group outweigh the larger nuclear charge and expand it.

Average atomic mass = Σ (isotopic mass × fractional abundance); mass spectrometry supplies the abundances.

Group names: alkali metals (1), alkaline earth metals (2), halogens (17), noble gases (18); metals lie left of the metalloid staircase and nonmetals to the right.

Ion formation: metals lose electrons to reach the preceding noble-gas configuration; nonmetals gain electrons to reach the following noble-gas configuration.

Electronegativity difference rule (Pauling): ΔEN < 0.4 nonpolar covalent; 0.4–1.7 polar covalent; > 1.7 predominantly ionic.

VSEPR geometries: 2 domains linear 180°; 3 trigonal planar 120°; 4 tetrahedral 109.5°; 5 trigonal bipyramidal 90°/120°; 6 octahedral 90°.

Lone pairs occupy more space than bonding pairs, so each lone pair compresses neighboring angles: CH₄ 109.5°, NH₃ 107°, H₂O 104.5°.

Formal charge = valence electrons − (nonbonding electrons + ½ bonding electrons); the preferred resonance structure minimizes formal charge and places negative charge on the more electronegative atom.

Hybridization from steric number: 2 → sp (linear), 3 → sp² (trigonal planar), 4 → sp³ (tetrahedral); each double bond contributes one π bond from an unhybridized p orbital.

Intermolecular force strength order: ion–dipole > hydrogen bond > dipole–dipole > London dispersion; dispersion strengthens with molar mass and surface area.

Hydrogen bonds require H covalently bonded to N, O, or F interacting with a lone pair on another N, O, or F atom.

Molecular polarity requires polar bonds whose dipoles do not cancel: CO₂ is nonpolar (linear) while H₂O and NH₃ are polar (bent, trigonal pyramidal).

Bond order increases from single to double to triple, with bond length decreasing and bond dissociation energy increasing.

Mole relationships: 1 mol = 6.022 × 10²³ particles; molar mass is expressed in g/mol; 1 mol of an ideal gas occupies 22.4 L at STP (0 °C, 1 atm).

Percent composition = (mass of the element in 1 mol ÷ molar mass of the compound) × 100%.

Empirical formula from percent composition: divide each percent by the atomic mass, divide every quotient by the smallest, then multiply to reach whole numbers; the molecular formula is a whole-number multiple of the empirical formula.

Balancing equations: change coefficients only, never subscripts; atoms and total charge must be conserved on both sides.

Limiting reactant: convert each reactant amount to moles of a chosen product using the mole ratio; the smallest product amount identifies the limiting reactant and the theoretical yield.

Percent yield = (actual yield ÷ theoretical yield) × 100%; a result above 100% signals an impure or wet product.

Reaction classes: synthesis (A + B → AB), decomposition, single replacement (A + BC → AC + B), double replacement (AB + CD → AD + CB), combustion (hydrocarbon + O₂ → CO₂ + H₂O).

Oxidation numbers: free elements 0; monatomic ions equal their charge; O is usually −2; H is usually +1; the sum equals the overall species charge; oxidation is loss of electrons, reduction is gain.

Net ionic equations: write soluble strong electrolytes as separated ions, keep weak electrolytes, gases, and precipitates intact, then cancel spectator ions.

Calorimetry: q = mcΔT with c(H₂O) = 4.18 J/(g·°C); for a reaction run in solution, q_reaction = −q_solution.

First law: ΔE = q + w, and w = −PΔV for gas expansion; ΔE is a state function while q and w are path dependent.

Hess's law: ΔH°_rxn = Σ ΔH°_f(products) − Σ ΔH°_f(reactants); ΔH°_f of an element in its standard state is zero; reversing a step changes the sign of ΔH and multiplying a step multiplies ΔH.

Bond-energy estimate: ΔH ≈ Σ (bonds broken) − Σ (bonds formed).

Rate definitions: rate = −(1/a)Δ[A]/Δt = (1/c)Δ[C]/Δt; the exponents in the rate law k[A]^m[B]^n come from experiment, not from the balanced coefficients.

Integrated rate laws: zero order [A] = [A]₀ − kt; first order ln[A] = ln[A]₀ − kt with t₁/₂ = 0.693/k; second order 1/[A] = 1/[A]₀ + kt.

Arrhenius equation k = Ae^(−Ea/RT): a plot of ln k versus 1/T has slope −Ea/R; a catalyst lowers Ea and speeds the reaction without changing ΔH or K.

Equilibrium constant Kc uses only gaseous and aqueous species, with pure solids and liquids omitted; Kp = Kc(RT)^Δn, where Δn counts moles of gaseous products minus reactants.

Thermodynamic links: ΔG° = −RT ln K and ΔG = ΔH − TΔS; negative ΔG means spontaneous, and Q < K means the net change proceeds toward products.

Concentration units: molarity M = mol solute ÷ L solution; molality m = mol solute ÷ kg solvent; mole fraction X_A = n_A ÷ n_total.

Dilution: M₁V₁ = M₂V₂, because the moles of solute are conserved and volumes use the same units.

Solubility rules: Group 1 and ammonium salts are soluble; nitrates and acetates are soluble; most chlorides are soluble except Ag⁺, Pb²⁺, Hg₂²⁺; most carbonates, phosphates, and sulfides are insoluble; sulfates are insoluble with Ba²⁺, Pb²⁺, Ca²⁺.

Colligative properties depend on particle count: ΔTb = i·Kb·m, ΔTf = i·Kf·m, and π = iMRT, where i is the number of ions per formula unit for a strong electrolyte.

Gas solubility falls as temperature rises and rises with partial pressure according to Henry's law, S = kP.

Saturation states: saturated solution is at equilibrium with undissolved solute; unsaturated holds less than the maximum; supersaturated holds more and is unstable, crystallizing when seeded.

Like dissolves like: polar and ionic solutes dissolve in polar solvents, while nonpolar solutes dissolve in nonpolar solvents such as hexane.

Raoult's law for a nonvolatile solute: P_solution = X_solvent × P°_solvent, so adding solute lowers the vapor pressure.

Convert percent by mass to molarity: M = (% mass × density in g/mL × 10) ÷ molar mass.

pH = −log[H₃O⁺]; pOH = −log[OH⁻]; pH + pOH = 14.00 at 25 °C because Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴.

Strong acids to memorize: HCl, HBr, HI, HNO₃, HClO₄, and H₂SO₄ (first proton only); strong bases: Group 1 hydroxides and heavy Group 2 hydroxides such as Ba(OH)₂.

Weak-acid equilibrium Ka = [H⁺][A⁻] ÷ [HA]; percent ionization = ([H⁺] ÷ [HA]₀) × 100%; for a conjugate pair, Ka × Kb = Kw.

Buffer equation (Henderson–Hasselbalch): pH = pKa + log([A⁻] ÷ [HA]); buffer capacity is greatest when pH = pKa, that is, [A⁻] = [HA].

Titration stoichiometry: at equivalence, moles H⁺ = moles OH⁻ after adjusting for coefficients; strong acid with strong base gives pH 7, while weak acid with strong base gives pH > 7 and calls for phenolphthalein.

Salt hydrolysis: weak acid with strong base gives a basic solution; strong acid with weak base gives an acidic solution; strong acid with strong base gives a neutral solution.

Lewis definitions: a Lewis acid accepts an electron pair (BF₃, AlCl₃, Ag⁺) and a Lewis base donates one (NH₃, H₂O, OH⁻, F⁻).

Polyprotic acids lose protons in steps with Ka1 > Ka2 > Ka3, so the first dissociation usually controls [H₃O⁺].

Functional groups: alcohol −OH, ether R−O−R, aldehyde −CHO, ketone C=O, carboxylic acid −COOH, ester −COO−, amine −NH₂, amide −CONH₂.

IUPAC naming: find the longest chain, number to give the principal functional group the lowest locant, then list substituents alphabetically; suffix priority is acid > ester > amide > aldehyde > ketone > alcohol > amine.

Isomer classes: structural isomers differ in connectivity; geometric (cis–trans) isomers differ around a restricted-rotation bond; optical isomers are non-superimposable mirror images arising from a chiral carbon bearing four different groups.

Reaction patterns: alkanes undergo radical substitution; alkenes and alkynes undergo electrophilic addition; aromatic rings undergo substitution; alkyl halides undergo substitution or elimination.

Polymers: addition polymerization links monomers containing double bonds (polyethylene, polystyrene); condensation polymerization releases a small molecule such as water (polyesters, polyamides, proteins).

Biomolecule classes: carbohydrates (monosaccharides through polysaccharides), lipids (fatty acid esters of glycerol), proteins (amino acid polymers), nucleic acids (nucleotide polymers).

An amino acid carries an amino group and a carboxyl group on the same carbon; a peptide bond is an amide linkage formed by condensation with loss of water.

Enzymes are highly specific biological catalysts that lower activation energy and stabilize the transition state without altering ΔG or the equilibrium constant.

Hydrocarbon combustion: CₙH₂ₙ₊₂ + O₂ → CO₂ + H₂O; incomplete combustion produces CO and soot.