IB Diploma Chemistry equations and key facts

Structure 1: Models of the particulate nature of matter

The particulate nature of matter

• temperature in kelvin = temperature in °C + 273 (T = θ + 273)
• Average kinetic energy of the particles is proportional to the temperature in kelvin
• Endothermic changes (energy absorbed): melting, vaporization, sublimation
• Exothermic changes (energy released): freezing, condensation, deposition
• Filtration: insoluble solid from a liquid. Evaporation or crystallization: dissolved solid from its solution
• Distillation: a solvent from a solution, or liquids with different boiling points (fractional distillation)
• Solvent extraction: a solute that dissolves much better in one of two liquids that do not mix. Paper chromatography: small amounts of dissolved substances such as dyes

The nuclear atom

• Relative mass: proton 1, neutron 1, electron about 1/1836 (negligible)
• Relative charge: proton +1, neutron 0, electron −1
• number of neutrons = mass number − atomic number (A − Z)
• number of electrons = Z − charge on the ion (a 3+ ion has 3 fewer electrons, a 2− ion has 2 more)
• In a nuclear symbol the mass number A is the top number and the atomic number Z is the bottom number
• relative atomic mass = sum of (isotope mass × % abundance) ÷ 100

Electron configurations

• Hydrogen: transitions down to n = 1 give ultraviolet lines, to n = 2 visible lines, to n = 3 infrared lines
• maximum number of electrons in level n = 2n² (2, 8, 18, 32)
• s sublevel: 1 orbital, 2 electrons. p: 3 orbitals, 6 electrons. d: 5 orbitals, 10 electrons. f: 7 orbitals, 14 electrons
• An s orbital is spherical; a p orbital is dumbbell-shaped
• Filling order up to Z = 36: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p
• Exceptions: Cr is [Ar] 3d⁵ 4s¹ and Cu is [Ar] 3d¹⁰ 4s¹
• When a d-block atom forms a positive ion, the 4s electrons are removed before the 3d electrons

Counting particles by mass: the mole

• number of particles = amount × Avogadro constant (N = n × L, L = 6.02 × 10²³ mol⁻¹)
• amount = mass ÷ molar mass (n = m ÷ M), with m in g and M in g mol⁻¹
• concentration = amount ÷ volume (c = n ÷ V), with V in dm³; 1 dm³ = 1000 cm³
• Dilution: the amount of solute does not change, so c₁ × V₁ = c₂ × V₂
• Empirical formula: divide each mass or % by A_r, then divide every answer by the smallest
• molecular formula = empirical formula × (molar mass ÷ empirical formula mass)
• Avogadro's law: at the same temperature and pressure, equal volumes of gases contain equal amounts, so gas volumes react in the same ratio as the moles in the equation

Ideal gases

• pressure × volume = amount × gas constant × temperature (PV = nRT), R = 8.31 J K⁻¹ mol⁻¹
• Units for PV = nRT: P in Pa with V in m³, or P in kPa with V in dm³; T in K
• 1 dm³ = 1 × 10⁻³ m³ and 1 cm³ = 1 × 10⁻⁶ m³
• Combined gas law for a fixed amount: P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂
• At constant T, volume is inversely proportional to pressure. At constant P, volume is proportional to T in kelvin
• At STP (273 K, 100 kPa) one mole of an ideal gas occupies 22.7 dm³: amount = volume ÷ 22.7
• molar mass = mass ÷ amount, with the amount found from n = PV ÷ RT

Structure 2: Models of bonding and structure

The ionic model

• Ion charges by group: group 1 is 1+, group 2 is 2+, group 13 is 3+, group 15 is 3−, group 16 is 2−, group 17 is 1−
• Polyatomic ions: NH₄⁺, OH⁻, NO₃⁻, HCO₃⁻, CO₃²⁻, SO₄²⁻, PO₄³⁻
• In a formula the total positive charge equals the total negative charge; put brackets round a polyatomic ion that is used more than once
• Lattice enthalpy is larger when the ions have higher charges and smaller radii
• Ionic solids do not conduct (ions fixed in the lattice); they conduct when molten or dissolved in water (ions free to move)
• Many ionic compounds dissolve in polar solvents such as water but not in non-polar solvents such as hexane

The covalent model

• Bond strength: single < double < triple. Bond length: triple is shortest, single is longest
• 2 domains: linear, 180°. 3 domains: trigonal planar, 120°. 4 domains: tetrahedral, 109.5°
• 4 domains with 1 lone pair: trigonal pyramidal, about 107° (NH₃). With 2 lone pairs: bent, about 105° (H₂O)
• A bond is polar when the two atoms differ in electronegativity. A molecule is non-polar if its shape makes the bond dipoles cancel (CO₂, CCl₄)
• Strength of intermolecular forces: London (dispersion) < dipole–dipole < hydrogen bonding. London forces are stronger with more electrons; hydrogen bonding needs H bonded directly to N, O or F
• Diamond and SiO₂: four bonds per C or Si, hard, non-conductors. Graphite and graphene: three bonds per C, delocalized electrons, conductors. C₆₀ is molecular
• R_f = distance moved by the spot ÷ distance moved by the solvent front (never more than 1)

The metallic model

• Metallic bond: electrostatic attraction between a lattice of cations and delocalized electrons
• Stronger bonding with a higher cation charge, more delocalized electrons per atom and a smaller cation radius
• Electrical conductivity: delocalized electrons move when a potential difference is applied (the cations do not move)
• Thermal conductivity: delocalized electrons pass kinetic energy quickly through the lattice
• Across period 3, melting point rises: Na < Mg < Al (ions 1+, 2+, 3+ and getting smaller)
• Down group 1, melting point falls: the ions get larger, so the attraction for the delocalized electrons is weaker

From models to materials

• Δχ = higher electronegativity − lower electronegativity; average χ = (sum of the two values) ÷ 2
• Large Δχ (about 1.8 or more): ionic. Small Δχ with high average χ: covalent. Small Δχ with low average χ: metallic
• For an element Δχ = 0, so it lies on the base of the triangle: metals on the left, non-metals on the right
• The smaller the Δχ, the more covalent character an ionic compound has
• Alloys are mixtures, not compounds: no fixed formula, metallic bonding kept, so they still conduct
• Addition polymerization: the C=C bond of each alkene monomer opens and the monomers join; no other product forms
• Repeating unit of an addition polymer: the two C atoms of the C=C, now joined by a single bond, with one open bond at each end

Structure 3: Classification of matter

The periodic table: classification of elements

• Across a period: atomic radius decreases; first ionization energy and electronegativity increase. Down a group: radius increases; ionization energy and electronegativity decrease
• Ions with the same number of electrons: the more protons, the smaller the ion (N³⁻ > O²⁻ > F⁻ > Na⁺)
• First electron affinity: X(g) + e⁻ → X⁻(g). First ionization energy: X(g) → X⁺(g) + e⁻
• Group 1 with water: 2Na(s) + 2H₂O(l) → 2NaOH(aq) + H₂(g); more vigorous down the group
• A halogen higher in group 17 displaces a lower one from its halide: Cl₂(aq) + 2Br⁻(aq) → 2Cl⁻(aq) + Br₂(aq)
• Metal oxides are basic: Na₂O + H₂O → 2NaOH. Non-metal oxides are acidic: SO₃ + H₂O → H₂SO₄; CO₂ + H₂O ⇌ H₂CO₃. Al₂O₃ is amphoteric
• Oxidation states add up to zero in a compound and to the charge in an ion; O is usually −2 and H is usually +1

Functional groups: classification of organic compounds

• Groups: halogeno –X, hydroxyl –OH, carbonyl C=O, carboxyl –COOH, alkoxy –OR, amino –NH₂, amido –CONH₂, ester –COO–, phenyl –C₆H₅
• Chain names: meth 1, eth 2, prop 3, but 4, pent 5, hex 6 carbon atoms
• Naming: find the longest carbon chain, then number it so that the functional group and branches get the lowest numbers
• Alcohols and halogenoalkanes: primary, secondary or tertiary = 1, 2 or 3 carbon atoms bonded to the carbon that carries the –OH or halogen
• Amines: primary, secondary or tertiary = 1, 2 or 3 carbon atoms bonded to the nitrogen atom
• Isomers: chain (different carbon skeleton), position (same group in a different place), functional group (different group, such as alcohol and ether, or aldehyde and ketone)
• Compounds that can form hydrogen bonds (alcohols, carboxylic acids) boil at higher temperatures than alkanes of similar molar mass

Reactivity 1: What drives chemical reactions?

Measuring enthalpy changes

• heat = mass of water or solution × specific heat capacity × temperature change (Q = mcΔT), with c = 4.18 J g⁻¹ K⁻¹
• enthalpy change = −heat ÷ moles reacted (ΔH = −Q ÷ n), in kJ mol⁻¹, so change Q from J to kJ first
• Temperature rises: exothermic, ΔH negative. Temperature falls: endothermic, ΔH positive
• On an energy profile: ΔH = enthalpy of products − enthalpy of reactants
• activation energy (E_a) = enthalpy of the transition state − enthalpy of the reactants
• Lower enthalpy means more stable
• Standard conditions for ΔH^⦵: 100 kPa, usually 298 K, solutions at 1 mol dm⁻³

Energy cycles in reactions

• ΔH = total bond enthalpy of bonds broken − total bond enthalpy of bonds formed
• Bond breaking is endothermic (+). Bond forming is exothermic (−)
• Count every bond: CH₄ has four C–H, CO₂ has two C=O, H₂O has two O–H, and multiply by the coefficients
• Bond enthalpies are averages and apply to gases only, so the result differs from the experimental value
• Hess's law: ΔH is the same for every route from the same reactants to the same products
• Reverse an equation: change the sign of ΔH. Multiply an equation: multiply ΔH by the same number

Energy from fuels

• Complete combustion: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O
• Incomplete combustion: 2C₃H₈ + 7O₂ → 6CO + 8H₂O
• Metals and non-metals: 2Mg + O₂ → 2MgO and S + O₂ → SO₂
• Carbon monoxide binds to haemoglobin, so the blood carries less oxygen
• Greenhouse gases absorb infrared radiation given out by the Earth's surface and send some of it back
• Hydrogen fuel cell, acidic electrolyte. Anode: H₂ → 2H⁺ + 2e⁻. Cathode: O₂ + 4H⁺ + 4e⁻ → 2H₂O
• Hydrogen fuel cell overall: 2H₂ + O₂ → 2H₂O

Reactivity 2: How much, how fast and how far?

How much? The amount of chemical change

• moles = mass ÷ molar mass (n = m ÷ M)
• moles = concentration × volume in dm³ (n = cV), and 1 dm³ = 1000 cm³
• moles of gas = volume ÷ molar volume; molar volume at STP = 22.7 dm³ mol⁻¹
• Limiting reactant: divide the moles of each reactant by its coefficient; the smallest result is limiting
• percentage yield = (actual yield ÷ theoretical yield) × 100
• atom economy = (molar mass of desired product ÷ total molar mass of all reactants) × 100, using the coefficients
• Ionic equation: leave out spectator ions, e.g. Ag⁺(aq) + Cl⁻(aq) → AgCl(s)

How fast? The rate of chemical change

• rate = change in concentration ÷ time taken, in mol dm⁻³ s⁻¹
• Rate at a given time = gradient of the tangent to the curve at that time
• Higher concentration, higher gas pressure or larger surface area: more frequent collisions
• Higher temperature: collisions are slightly more frequent, but mainly a much larger proportion have energy ≥ E_a
• Maxwell–Boltzmann curve: starts at the origin, never touches the energy axis again, and the area under it is the total number of particles
• At a higher temperature the peak is lower and further right; the area stays the same
• A catalyst lowers E_a but does not change ΔH or the energy distribution, and it is not used up

How far? The extent of chemical change

• For aA + bB ⇌ cC + dD: K_c = ([C]^c × [D]^d) ÷ ([A]^a × [B]^b)
• K much greater than 1: equilibrium lies to the right. K much less than 1: it lies to the left
• Add a reactant or remove a product: position shifts right. K is unchanged
• Increase the pressure: position shifts to the side with fewer moles of gas. K is unchanged
• Increase the temperature: position shifts in the endothermic direction, and K changes
• Exothermic forward reaction: K falls as temperature rises. Endothermic forward reaction: K rises
• Catalyst: equilibrium is reached sooner; position and K stay the same

Reactivity 3: What are the mechanisms of chemical change?

Proton transfer reactions

• pH = −log₁₀[H⁺] and [H⁺] = 10^−pH, with [H⁺] in mol dm⁻³
• K_w = [H⁺][OH⁻] = 1.00 × 10⁻¹⁴ at 298 K
• Conjugate pair: acid and base differ by one H⁺, e.g. NH₄⁺ / NH₃ and H₂O / OH⁻
• Strong acids: HCl, HNO₃, H₂SO₄. Weak acids: ethanoic acid, carbonic acid
• Strong bases: NaOH, KOH. Weak base: NH₃
• acid + base → salt + water; acid + carbonate or hydrogencarbonate → salt + water + CO₂
• Strong acid with strong base: the pH curve has a steep vertical section with the equivalence point at pH 7

Electron transfer reactions

• Oxidation Is Loss of electrons, Reduction Is Gain (OIL RIG)
• Half-equation in acid: balance the main atoms, add H₂O for O, add H⁺ for H, then add e⁻ to balance the charge
• In every cell, oxidation is at the anode and reduction is at the cathode
• Voltaic cell: the anode is negative, electrons flow through the wire from anode to cathode, chemical energy → electrical energy
• Electrolytic cell: the anode is positive. Molten salt: metal forms at the cathode, non-metal at the anode
• Oxidation with acidified K₂Cr₂O₇: primary alcohol → aldehyde (distil) → carboxylic acid (reflux); secondary alcohol → ketone; tertiary alcohol: no reaction
• Reduction reverses this: aldehyde or carboxylic acid → primary alcohol, ketone → secondary alcohol. Alkene + H₂ → alkane

Electron sharing reactions

• Initiation (UV light): Cl₂ → 2Cl•
• Propagation 1: CH₄ + Cl• → CH₃• + HCl
• Propagation 2: CH₃• + Cl₂ → CH₃Cl + Cl•
• Termination: two radicals join, e.g. 2Cl• → Cl₂, CH₃• + Cl• → CH₃Cl, 2CH₃• → C₂H₆
• Overall: CH₄ + Cl₂ → CH₃Cl + HCl
• Excess halogen gives further substitution: CH₂Cl₂, CHCl₃, CCl₄
• Count radicals to name a step: none → radicals is initiation; one → one is propagation; two → none is termination

Electron-pair sharing reactions

• Nucleophiles have a lone pair or a negative charge: OH⁻, H₂O, NH₃, CN⁻, Cl⁻
• Electrophiles have a positive or partial positive charge: H⁺, H^δ+ in HBr, Br^δ+ in a polarized Br₂ molecule
• Nucleophilic substitution: CH₃CH₂Br + OH⁻ → CH₃CH₂OH + Br⁻ (the leaving group is the halide ion)
• Alkene + halogen → dihalogenoalkane: C₂H₄ + Br₂ → CH₂BrCH₂Br
• Alkene + hydrogen halide → halogenoalkane: C₂H₄ + HBr → CH₃CH₂Br
• Alkene + steam, with an acid catalyst → alcohol: C₂H₄ + H₂O → CH₃CH₂OH
• Bromine water turns from orange to colourless with an alkene