UEE Chemistry cheat sheet

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

Quantum numbers: n = 1,2,3…; l = 0…n−1 (s,p,d,f); m_l = −l…+l; m_s = ±1/2. Pauli exclusion forbids identical sets.

Orbital filling follows Aufbau order 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p; Cr and Cu are exceptions (3d5 4s1, 3d10 4s1).

Hund's rule: degenerate orbitals are singly occupied with parallel spins before pairing.

Effective nuclear charge Z_eff = Z − S (Slater); across a period Z_eff rises, so atomic radius falls and ionisation energy rises.

First ionisation energy increases across a period and decreases down a group; large jumps reveal noble-gas core shells.

Electron affinity is most negative for Group 17; noble gases have near-zero or positive values.

Periodic trends: metallic character increases down a group; electronegativity (Pauling) rises up and to the right, F = 4.0.

Emission line spectra arise from quantised transitions: ΔE = hν = hc/λ; Rydberg 1/λ = R(1/n1² − 1/n2²).

Electronegativity difference Δχ > ~1.8 suggests ionic character; < 0.4 is essentially nonpolar covalent.

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

Lone-pair repulsion order: lp–lp > lp–bp > bp–bp; CH4 109.5°, NH3 107°, H2O 104.5°.

Hybridisation from steric number: 2 sp, 3 sp2, 4 sp3, 5 sp3d, 6 sp3d2.

Bond order = (bonding electrons − antibonding electrons)/2 in MO theory; O2 has bond order 2 and is paramagnetic.

Formal charge = valence electrons − nonbonding electrons − ½ bonding electrons; minimise formal charges to choose structures.

Bond polarity plus geometry determines molecular dipole; CO2 and CCl4 are nonpolar despite polar bonds.

Hydrogen bonding requires H bonded to N, O or F; it raises boiling point (H2O 100 °C vs H2S −60 °C).

Resonance delocalises electrons; bond length and energy are intermediate between contributing structures.

n = m/M; for gases at STP (0 °C, 1 atm) molar volume = 22.4 L mol⁻¹; at 25 °C, 24.5 L mol⁻¹.

Avogadro constant N_A = 6.022 × 10²³ mol⁻¹; number of particles = n × N_A.

Balance equations by atom conservation; use mole ratios from coefficients, never mass ratios.

Limiting reagent: divide moles of each reactant by its coefficient; the smallest quotient limits.

Percentage yield = (actual/theoretical) × 100; atom economy = (M of desired product / ΣM of reactants) × 100.

Concentration c = n/V (mol L⁻¹); dilution: c1V1 = c2V2.

Empirical formula from % composition: divide by atomic mass, then by the smallest ratio; molecular formula = empirical × n.

Percent by mass of element = (atoms × A_r of element / M_r of compound) × 100.

Titration relation: c_aV_a/n_a = c_bV_b/n_b for an acid–base neutralisation.

Ideal gas: PV = nRT with R = 8.314 J mol⁻¹ K⁻¹ = 0.0821 L atm mol⁻¹ K⁻¹; T must be in kelvin.

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

Dalton's law: P_total = ΣP_i; partial pressure P_i = x_i P_total.

Average kinetic energy = (3/2)kT per molecule; v_rms = √(3RT/M), so lighter gases effuse faster (Graham's law).

Van der Waals: (P + an²/V²)(V − nb) = nRT; a corrects attractions, b corrects molecular volume.

Real gases deviate most at high pressure and low temperature, near condensation.

Critical temperature is the highest temperature at which a gas can be liquefied by pressure alone.

Phase diagrams: triple point is where solid, liquid and gas coexist; the fusion curve for water slopes negatively.

Ideal solubility of gases follows Henry's law: solubility ∝ partial pressure of the gas.

ΔH = q_p at constant pressure; q = mcΔT with c(water) = 4.18 J g⁻¹ K⁻¹.

Exothermic reactions have ΔH < 0; bond formation releases energy, bond breaking absorbs it.

Hess's law: ΔH is path-independent; sum step enthalpies to obtain the overall value.

ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants); ΔH°f of an element in its standard state is zero.

Mean bond enthalpy route: ΔH = Σ(bonds broken) − Σ(bonds formed); values are averages, so results are approximate.

Calorimetry: heat lost by reaction = heat gained by solution + calorimeter; q_cal = CΔT.

Second law: ΔS_universe > 0 for a spontaneous process; ΔS increases with gas moles and temperature.

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

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

K_c uses equilibrium concentrations; K_p uses partial pressures with K_p = K_c(RT)^Δn.

Reaction quotient Q: if Q < K the reaction proceeds forward; if Q > K it proceeds in reverse.

Le Chatelier: raising pressure favours the side with fewer gas moles; heating favours the endothermic direction.

A catalyst lowers E_a and speeds attainment of equilibrium but changes neither K nor yield.

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

pH = −log[H⁺]; for a weak acid K_a = [H⁺]²/[HA] and pH ≈ ½(pK_a − log c).

Henderson–Hasselbalch: pH = pK_a + log([A⁻]/[HA]) for a buffer.

Salt hydrolysis: strong acid–weak base salts are acidic; weak acid–strong base salts are basic.

Solubility product K_sp applies to saturated solutions; common ions lower solubility (Le Chatelier).

Rate = −(1/a)d[A]/dt = (1/b)d[B]/dt; rates are defined per stoichiometric coefficient.

Rate law is determined experimentally, not from coefficients: rate = k[A]^m[B]^n; overall order = m + n.

First-order: t½ = ln2/k = 0.693/k, independent of initial concentration.

Zero-order: [A] = [A]0 − kt; second-order: 1/[A] = 1/[A]0 + kt.

Arrhenius: k = A e^(−E_a/RT); ln(k2/k1) = (E_a/R)(1/T1 − 1/T2).

A catalyst provides an alternative pathway with lower E_a; enzymes are highly selective biological catalysts.

Rate-determining step is the slowest elementary step; it controls the observed rate law.

Collision theory requires sufficient energy (≥ E_a) and correct orientation; steric factor reduces A.

Temperature increase of 10 K roughly doubles many reaction rates near room temperature.

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

Oxidation number rules: elements 0, monatomic ion = charge, O usually −2, H usually +1, sum equals overall charge.

Balance redox in acid: balance atoms, add H2O for O, H⁺ for H, then electrons; in base add OH⁻ to neutralise H⁺.

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

Standard hydrogen electrode (SHE) is assigned E° = 0.00 V; potentials are reduction potentials.

ΔG° = −nFE°cell with F = 96 485 C mol⁻¹; Nernst equation E = E° − (0.0592/n)log Q at 25 °C.

In electrolysis the cathode attracts cations; in a galvanic cell the cathode is positive.

Amount deposited: m = (MIt)/(nF), from Faraday's laws.

Disproportionation: the same element is simultaneously oxidised and reduced (e.g. Cl2 in cold alkali).

Group 1 metals react with water giving MOH + H2; reactivity increases down the group.

Group 2 oxides are basic; hydroxides become more soluble down the group, sulfates less soluble (BaSO4 insoluble).

Group 17 reactivity decreases down the group; oxidising power falls Cl2 > Br2 > I2.

Halide tests with AgNO3: AgCl white, AgBr cream, AgI yellow; solubility in dilute and concentrated NH3 distinguishes them.

Group 16: H2O vs H2S boiling points differ because only water hydrogen-bonds.

Transition metals show variable oxidation states, form coloured complexes, and act as catalysts (Fe, V2O5, Ni).

Ligand substitution and coordination number: [Cu(H2O)6]²⁺ blue, [Cu(NH3)4(H2O)2]²⁺ deep blue, [CuCl4]²⁻ yellow-green.

MnO4⁻ in acid is reduced to Mn²⁺ (purple to colourless); Cr2O7²⁻ to Cr³⁺ (orange to green).

Inert pair effect: heavier p-block elements prefer oxidation states two below the group maximum (Pb²⁺, Bi³⁺).

Homologous series differ by CH2; functional group determines chemical properties.

IUPAC naming: longest chain, lowest locants, suffix by priority (acid > ester > amide > aldehyde > ketone > alcohol > amine).

Alkanes undergo free-radical substitution: initiation, propagation, termination.

Alkenes: electrophilic addition with HBr, Br2, H2O/H⁺; Markovnikov's rule places H on the carbon with more H.

Benzene is aromatic (4n+2 π electrons) and undergoes electrophilic substitution, not addition.

Alcohols: primary oxidise to aldehydes then carboxylic acids; secondary to ketones; tertiary resist oxidation.

Nucleophilic substitution: SN1 proceeds via carbocation (racemisation, tertiary favoured); SN2 is concerted with inversion (primary favoured).

Carbonyls undergo nucleophilic addition; aldehydes are oxidised by Tollens' and Fehling's reagents, ketones are not.

Esters form from acid + alcohol with H2SO4 catalyst; hydrolysis is acid- or base-catalysed (saponification with NaOH).

Filtration separates insoluble solid from liquid; decantation and centrifugation serve similar purposes.

Simple distillation separates a volatile solvent from non-volatile solute; fractional distillation separates liquids with close boiling points.

Separating funnel separates immiscible liquids by density; the denser layer is drained from the bottom.

Paper and thin-layer chromatography separate by differential adsorption/partition; Rf = distance travelled by solute / distance travelled by solvent.

Recrystallisation purifies solids: dissolve in hot minimal solvent, cool slowly, filter crystals.

Titration: rinse burette with titrant, use a white tile, read the bottom of the meniscus, take concordant results.

Qualitative tests: flame tests (Na yellow, K lilac, Ca brick-red, Cu blue-green); limewater turns milky with CO2.

Drying agents: anhydrous CaCl2, MgSO4, Na2SO4; never use CaCl2 for alcohols or amines because it forms complexes.

Safety and accuracy: use a fume cupboard for toxic vapours, never pipette by mouth, and record apparatus precision (±0.05 cm³ burette).