FSc Part 1 Chemistry equations and key facts

Basic concepts

Atoms, molecules, ions and isotopes

• Relative atomic mass = mass of one atom of the element compared with one atom of carbon-12 taken as 12 amu (1 amu = 1/12 of the mass of a carbon-12 atom)
• Relative molecular mass = sum of the relative atomic masses of all the atoms in the formula
• Cation = positive ion (Na⁺, Ca²⁺); anion = negative ion (Cl⁻, SO₄²⁻); molecular ion = a whole molecule that has lost or gained an electron (CH₄⁺, N₂⁺)
• Free radical = an atom or group of atoms with an unpaired electron and usually no charge (Cl•, CH₃•)
• Isotopes: same atomic number and same chemical properties, different mass number. Elements with even atomic number usually have more isotopes; tin has the most, while F, I, As and Au have only one
• Mass spectrometer: vaporise the sample, ionise it to positive ions, accelerate them with an electric field, deflect them with a magnetic field according to m/e, then detect them. Lighter ions are deflected more
• Relative atomic mass = sum of (isotopic mass × % abundance) ÷ 100

The mole and Avogadro's number

• number of moles = mass in grams ÷ molar mass (n = m/M)
• number of particles = number of moles × 6.02 × 10²³
• volume of a gas at STP = number of moles × 22.414 dm³ (22.4 dm³ is used in most questions)
• number of atoms = number of molecules × number of atoms in one molecule
• number of ions = number of formula units × number of that ion in the formula, e.g. 1 mol of CaCl₂ gives 2 mol of Cl⁻ ions
• Equal numbers of moles mean equal numbers of particles, whatever the masses are
• 1 dm³ = 1000 cm³

Stoichiometry, limiting reactant and yield

• Steps: mass → moles (÷ molar mass) → mole ratio from the balanced equation → mass (× molar mass) or volume at STP (× 22.4 dm³)
• Limiting reactant = the reactant that gives the smallest number of moles of product
• To find it: work out the moles of product from each reactant separately and take the smaller value
• percentage yield = (actual yield ÷ theoretical yield) × 100
• Actual yield is lower because of side reactions, reversible reactions that do not go to completion, and loss of product during filtration, crystallisation and transfer
• Percentage yield can never be more than 100% for a pure, dry product

Experimental techniques in chemistry

Filtration, crystallisation and sublimation

• Filter paper: folded so it sits well in the funnel; a fluted paper filters faster. The stem of the funnel should stay full of liquid and touch the side of the beaker
• Gooch crucible: porcelain with a perforated bottom, covered with filter paper or an asbestos mat, used with suction. With asbestos it can filter liquids that attack paper, such as concentrated HCl and KMnO₄ solution
• Sintered glass crucible: has a porous glass disc sealed into the bottom, so it needs no preparation
• A good crystallisation solvent dissolves a lot of the substance when hot and very little when cold, does not react with it, dissolves the impurities well or not at all, and is cheap, safe and easy to remove
• Coloured impurities are removed by boiling the solution with animal charcoal and filtering hot
• Crystals are dried between filter papers, in an oven, or in a vacuum desiccator over anhydrous CaCl₂, silica gel or P₂O₅
• Solids that sublime: iodine, ammonium chloride, naphthalene, benzoic acid

Solvent extraction and chromatography

• Distribution law: at a constant temperature, a solute distributes itself between two immiscible liquids so that the ratio of its concentrations is constant
• distribution coefficient K = concentration in organic solvent ÷ concentration in water
• Several extractions with small portions of solvent remove more solute than one extraction with the same total volume
• Adsorption chromatography: stationary phase is a solid. Partition chromatography: stationary phase is a liquid. Paper chromatography is partition chromatography
• R_f = distance moved by the component ÷ distance moved by the solvent front, both measured from the base line
• R_f has no unit and is always less than 1. It identifies a substance for a given solvent and temperature
• Paper chromatography can be ascending, descending or radial (circular)

Gases

Gas laws and the ideal gas equation

• Boyle's law: at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure (P₁V₁ = P₂V₂)
• Charles's law: at constant pressure, volume is directly proportional to absolute temperature (V₁/T₁ = V₂/T₂). A gas changes by 1/273 of its volume at 0 °C for each 1 °C
• T in kelvin = temperature in °C + 273
• Avogadro's law: equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules (V ∝ n)
• General gas equation: PV = nRT. For a fixed amount of gas, P₁V₁/T₁ = P₂V₂/T₂
• R = 0.0821 dm³ atm K⁻¹ mol⁻¹ = 62.4 dm³ torr K⁻¹ mol⁻¹ = 8.314 J K⁻¹ mol⁻¹ (SI) = 1.987 cal K⁻¹ mol⁻¹
• molar mass M = mRT ÷ PV; density d = PM ÷ RT

Dalton's law, Graham's law and kinetic molecular theory

• Dalton's law: total pressure = sum of the partial pressures (P_t = p_A + p_B + p_C)
• partial pressure of a gas = its mole fraction × total pressure (p_A = X_AP_t), where mole fraction = moles of the gas ÷ total moles
• Gas collected over water: pressure of dry gas = total pressure − vapour pressure of water
• Graham's law: rate of diffusion or effusion is inversely proportional to the square root of the molar mass or density (r₁/r₂ = √(M₂/M₁))
• Time taken is the opposite of rate: t₁/t₂ = √(M₁/M₂) for the same volume of gas
• Postulates: molecules have negligible volume; no forces of attraction or repulsion between them; collisions are perfectly elastic; pressure comes from collisions with the walls
• Average kinetic energy ∝ absolute temperature T. Root mean square speed = √(3RT/M), so speed ∝ √T

Non-ideal behaviour, liquefaction and plasma

• Real gases are nearly ideal at high temperature and low pressure
• Z = PV/nRT. Z < 1: attractive forces dominate. Z > 1: the volume of the molecules dominates. H₂ and He have very weak attractions
• van der Waals equation: (P + an²/V²)(V − nb) = nRT. The constant a corrects for attractive forces; b is the excluded volume of one mole of molecules
• Critical temperature T_c = the temperature above which a gas cannot be liquefied, however high the pressure. Critical pressure = the pressure needed to liquefy the gas at T_c
• Stronger intermolecular forces give a higher T_c, so the gas is easier to liquefy (approximately: NH₃ 406 K, CO₂ 304 K, O₂ 154 K, N₂ 126 K)
• Joule-Thomson effect: a highly compressed gas cools when it expands suddenly through a jet into a region of low pressure. Linde's method repeats compression, cooling and expansion until the air liquefies
• Plasma, the fourth state of matter: a mixture of free electrons, positive ions and neutral atoms. It is neutral overall, conducts electricity, and is found in the sun, stars, lightning, neon signs and fluorescent tubes

Liquids and solids

Intermolecular forces and hydrogen bonding

• Dipole-dipole forces: between the permanent dipoles of polar molecules, e.g. HCl, CHCl₃
• Dipole-induced dipole (Debye) forces: a polar molecule induces a dipole in a non-polar molecule or atom, e.g. HCl and argon
• London forces: an instantaneous dipole in one molecule induces a dipole in the next. They act between all atoms and molecules
• London forces increase with polarisability, that is with the size of the electron cloud (boiling points rise from F₂ to I₂ and from He to Rn), with the number of atoms in the molecule, and with surface area (a straight chain boils higher than a branched isomer)
• Hydrogen bonding makes the boiling points of NH₃, H₂O and HF much higher than those of the other hydrides in their groups
• Each water molecule can form up to four hydrogen bonds. In ice these give an open tetrahedral structure with empty spaces, so ice is less dense than water and floats
• Water has its maximum density at 4 °C

Evaporation, vapour pressure, boiling point and liquid crystals

• Vapour pressure = the pressure exerted by the vapour in equilibrium with its liquid at a given temperature
• Vapour pressure depends on temperature and on the strength of the intermolecular forces. It does not depend on the amount of liquid, its surface area or the size of the container
• Boiling point = the temperature at which vapour pressure equals external pressure. Water boils at 100 °C at 760 torr
• Lower external pressure gives a lower boiling point (water boils at about 98 °C at Murree; vacuum distillation). Higher pressure gives a higher boiling point (pressure cooker)
• Molar heat of fusion (ΔH_f), vaporisation (ΔH_v) and sublimation (ΔH_s): the heat absorbed when 1 mole of solid melts, 1 mole of liquid becomes vapour, or 1 mole of solid becomes vapour, at 1 atm
• ΔH_s = ΔH_f + ΔH_v, and ΔH_v is much larger than ΔH_f
• Liquid crystals change colour with temperature. Uses: strip thermometers and temperature sensors, displays of watches and calculators, finding faults in electrical circuits, locating tumours, veins and infections

Crystalline solids

• Isomorphism: different substances with the same crystal form, e.g. NaNO₃ and CaCO₃. Polymorphism: one compound with more than one crystal form, e.g. CaCO₃ as calcite and aragonite. Allotropy: the same idea for an element, e.g. diamond and graphite.
• Transition temperature: the temperature at which two crystalline forms of a substance exist in equilibrium, e.g. rhombic sulphur ⇌ monoclinic sulphur at 95.5 °C.
• Habit is the shape in which a crystal usually grows. Symmetry is the repetition of faces, angles or edges when the crystal is rotated about an axis.
• Seven crystal systems: cubic (a = b = c, all angles 90°), tetragonal (a = b ≠ c, all 90°), orthorhombic (a ≠ b ≠ c, all 90°), monoclinic, hexagonal, rhombohedral (trigonal) and triclinic.
• Ionic solids (NaCl): hard, brittle, high melting point, conduct only when molten or in solution. Covalent solids (diamond, SiC): very hard, very high melting point. Molecular solids (ice, iodine, sugar): soft, low melting point. Metallic solids (Cu): positive ions in a sea of mobile electrons, so they conduct and can be hammered into shape.
• Lattice energy: the energy released when one mole of an ionic crystal is formed from its gaseous ions. For NaCl it is −787 kJ mol⁻¹. It is larger for smaller ions.
• NaCl structure: face-centred cubic. Each Na⁺ is surrounded by 6 Cl⁻ and each Cl⁻ by 6 Na⁺ (coordination number 6). One unit cell holds 4 NaCl formula units.

Atomic structure

Discovery of subatomic particles and Rutherford's model

• Cathode rays: travel in straight lines and cast sharp shadows; are negatively charged (bend towards the positive plate); turn a paddle wheel (they have momentum); make glass glow; produce X-rays when they strike a heavy metal target.
• e/m of the electron = 1.7588 × 10¹¹ C kg⁻¹. It is the same for every gas and every cathode material, so electrons are present in all atoms.
• Positive rays: e/m depends on the gas in the tube and is always much smaller than for cathode rays. It is greatest for hydrogen, whose positive particle is the proton.
• Millikan: charge on an electron = 1.602 × 10⁻¹⁹ C. Mass of electron = e ÷ (e/m) = 9.11 × 10⁻³¹ kg.
• Neutron (Chadwick, 1932): ⁹Be + ⁴He → ¹²C + ¹n. No charge, so not deflected by electric or magnetic fields; mass 1.6749 × 10⁻²⁷ kg, slightly more than a proton.
• Defects of Rutherford's model: a revolving electron should radiate energy continuously and spiral into the nucleus, and the atom should give a continuous spectrum. Real atoms are stable and give line spectra.

Planck's theory, Bohr's model and the hydrogen spectrum

• energy of a photon = Planck's constant × frequency (E = hν). Since c = νλ, E = hc/λ. h = 6.626 × 10⁻³⁴ J s; c = 3.00 × 10⁸ m s⁻¹.
• Higher frequency means shorter wavelength and more energy. Wave number = 1/λ, in m⁻¹.
• Bohr's quantum condition: angular momentum of the electron, mvr = nh/2π, where n = 1, 2, 3 ...
• radius of the nth orbit of hydrogen: r = 0.529 × n² Å.
• energy of the nth orbit: E_n = −1312/n² kJ mol⁻¹. It is negative because the electron is bound; it is zero at n = ∞. Energy of a jump: ΔE = E_higher − E_lower = hν.
• Spectral series, named by the level where the jump ends: Lyman n = 1 (ultraviolet), Balmer n = 2 (visible), Paschen n = 3, Brackett n = 4, Pfund n = 5 (all infrared).
• X-rays form when high-speed cathode rays strike a heavy metal target. Moseley's law: √ν = a(Z − b), so X-ray frequency depends on atomic number Z.

Quantum numbers, orbitals and electronic configuration

• de Broglie: wavelength = Planck's constant ÷ momentum (λ = h/mv). Heisenberg: Δx × Δp ≥ h/4π.
• Principal quantum number n = 1, 2, 3 ... (K, L, M ...): size and energy of the shell. A shell has n² orbitals and holds at most 2n² electrons.
• Azimuthal quantum number l = 0 to (n − 1): the subshell and its shape. l = 0 is s, 1 is p, 2 is d, 3 is f. A subshell holds 2(2l + 1) electrons: s 2, p 6, d 10, f 14.
• Magnetic quantum number m = −l ... 0 ... +l: (2l + 1) orbitals in a subshell (s 1, p 3, d 5, f 7). Spin quantum number s = +½ or −½.
• An s orbital is spherical. A p orbital is dumbbell-shaped with two lobes and zero electron density at the nucleus; p_x, p_y and p_z lie along the three axes.
• (n + l) rule: the subshell with the lower n + l fills first; if equal, the one with lower n fills first. Order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s.
• Pauli: no two electrons in an atom have the same four quantum numbers, so an orbital holds at most 2 electrons with opposite spins. Hund: orbitals of equal energy are first filled singly, with parallel spins.

Chemical bonding

Periodic trends, ionic and covalent bonds

• Atomic radius decreases across a period (nuclear charge rises, same shell) and increases down a group (more shells, more shielding). A positive ion is smaller than its atom; a negative ion is larger.
• Ionisation energy: the minimum energy needed to remove the most loosely bound electron from a gaseous atom. It increases across a period and decreases down a group. Exception: N is higher than O because of its half-filled 2p subshell.
• Electron affinity: the energy released when an electron is added to a gaseous atom. Chlorine has the most exothermic value (−349 kJ mol⁻¹). Second electron affinities are endothermic.
• Electronegativity: the power of an atom to attract a shared electron pair. It increases across a period and decreases down a group; fluorine is highest (4.0).
• Electronegativity difference: 0 gives a non-polar covalent bond; less than 1.7 a polar covalent bond; 1.7 means 50% ionic character; more than 1.7 a mainly ionic bond.
• An ionic bond is favoured by low ionisation energy of the metal, high electron affinity of the non-metal and high lattice energy.
• Cl₂ has a single bond, O₂ a double bond, N₂ a triple bond. NH₄⁺ and H₃N→BF₃ each contain one coordinate covalent bond.

VSEPR theory, valence bond theory and hybridisation

• Order of repulsion: lone pair–lone pair > lone pair–bond pair > bond pair–bond pair.
• No lone pairs: 2 pairs linear, 180° (BeCl₂); 3 pairs trigonal planar, 120° (BF₃); 4 pairs tetrahedral, 109.5° (CH₄).
• With lone pairs: NH₃ (3 bond pairs, 1 lone pair) trigonal pyramidal, 107.5°; H₂O (2 bond pairs, 2 lone pairs) bent, 104.5°; SnCl₂ (2 bond pairs, 1 lone pair) bent, less than 120°.
• Single bond = 1 σ. Double bond = 1 σ + 1 π. Triple bond = 1 σ + 2 π. A π bond is weaker than a σ bond and forms only after a σ bond.
• sp³: four orbitals, tetrahedral, 109.5°, 25% s character (CH₄, C₂H₆, also NH₃ and H₂O).
• sp²: three orbitals, trigonal planar, 120°, 33% s character (C₂H₄, BF₃). sp: two orbitals, linear, 180°, 50% s character (C₂H₂, BeCl₂).
• Carbon-carbon bond length: ethane 154 pm > ethene 133 pm > ethyne 120 pm.

Molecular orbital theory, bond energy and dipole moment

• bond order = (number of bonding electrons − number of antibonding electrons) ÷ 2.
• H₂: (2 − 0) ÷ 2 = 1. He₂: (2 − 2) ÷ 2 = 0, so it does not exist. N₂: (10 − 4) ÷ 2 = 3. O₂: (10 − 6) ÷ 2 = 2.
• O₂ has two unpaired electrons, one in each of the two π*2p orbitals, so oxygen is paramagnetic.
• A higher bond order means a shorter and stronger bond.
• Bond energy: the average energy needed to break one mole of a given bond in the gaseous state, in kJ mol⁻¹. It is larger for shorter, multiple and more polar bonds: H−F > H−Cl > H−Br > H−I; C≡C > C=C > C−C.
• dipole moment = charge × distance between the charges (μ = q × r). Unit: debye, D. 1 D = 3.336 × 10⁻³⁰ C m.
• Symmetrical molecules have zero dipole moment because the bond dipoles cancel: CO₂ (linear), BF₃ (trigonal planar), CH₄ and CCl₄ (tetrahedral). H₂O (1.85 D, bent) and NH₃ (about 1.5 D, pyramidal) are polar.

Thermochemistry

Energy, the first law and enthalpy

• First law: change in internal energy = heat + work (ΔE = q + w). q is positive when the system absorbs heat; w is positive when work is done on the system.
• Pressure-volume work: w = −PΔV. At constant volume no such work is done, so ΔE = q_v.
• Enthalpy: H = E + PV. At constant pressure, ΔH = ΔE + PΔV = q_p.
• For reactions involving gases: ΔH = ΔE + ΔnRT, where Δn = moles of gaseous products − moles of gaseous reactants and R = 8.314 J K⁻¹ mol⁻¹. If Δn = 0, ΔH = ΔE.
• Glass calorimeter (constant pressure, reactions in solution): q = m × s × ΔT, where s is the specific heat. This gives ΔH.
• Bomb calorimeter (constant volume, combustion): q = c × ΔT, where c is the heat capacity of the calorimeter. This gives ΔE.
• If the temperature rises, the reaction is exothermic: give the answer a negative sign. Divide by the moles reacted to get kJ mol⁻¹.

Standard enthalpy changes, Hess's law and the Born-Haber cycle

• Enthalpy of formation, ΔH°_f: one mole of a compound is formed from its elements in their standard states. It is zero for an element in its standard state, e.g. O₂(g), C(graphite).
• Enthalpy of combustion, ΔH°_c: one mole of a substance is burned completely in excess oxygen. Always negative.
• Enthalpy of atomisation, ΔH°_at: one mole of gaseous atoms is formed from the element. Always positive.
• Enthalpy of neutralisation: one mole of H⁺ from an acid reacts with one mole of OH⁻ from a base to form one mole of water. About −57.4 kJ mol⁻¹ for any strong acid with any strong base.
• Enthalpy of solution: one mole of a substance dissolves in so much solvent that further dilution causes no heat change.
• ΔH° of reaction = sum of ΔH°_f of products − sum of ΔH°_f of reactants. Multiply each value by its coefficient in the equation.
• Born-Haber cycle for NaCl: ΔH°_f = atomisation of Na + ionisation energy of Na + atomisation of ½Cl₂ + electron affinity of Cl + lattice energy.

Chemical equilibrium

Law of mass action, Kc and Kp

• For aA + bB ⇌ cC + dD: K_c = [C]^c[D]^d ÷ ([A]^a[B]^b), using equilibrium concentrations in mol dm⁻³. Products go on top.
• K_p uses partial pressures of gases, K_x uses mole fractions and K_n uses numbers of moles.
• K_p = K_c(RT)^Δn, where Δn = moles of gaseous products − moles of gaseous reactants. If Δn = 0, K_p = K_c = K_x = K_n.
• Units of K_c come from the expression. If the numbers of moles on both sides are equal, K_c has no units.
• Reaction quotient Q_c: the same expression with the concentrations at any instant. Q_c < K_c: net reaction goes forward. Q_c > K_c: it goes in reverse. Q_c = K_c: equilibrium.
• Very large K_c: the reaction goes almost to completion. Very small K_c: very little product forms.
• K_c changes only with temperature, not with concentration, pressure or a catalyst.

Le Chatelier's principle and industrial applications

• Concentration: adding a reactant (or removing a product) shifts the equilibrium to the right; K_c does not change.
• Pressure: higher pressure shifts the equilibrium to the side with fewer moles of gas; no effect when the moles of gas are equal on both sides.
• Temperature: heating favours the endothermic direction, cooling favours the exothermic direction.
• Exothermic forward reaction: K_c decreases as temperature rises. Endothermic forward reaction: K_c increases.
• Haber process: N₂(g) + 3H₂(g) ⇌ 2NH₃(g), ΔH = −92 kJ mol⁻¹; about 200 atm, 400–450 °C, finely divided iron catalyst; ammonia is removed by liquefying it.
• Contact process: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), exothermic; 400–500 °C, V₂O₅ catalyst, pressure only slightly above atmospheric.
• The temperature used in both processes is a compromise: low temperature gives a better yield but too slow a rate.

Ionic equilibria: pH, buffers and solubility product

• K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 25 °C; K_w increases with temperature.
• pH = −log[H⁺], pOH = −log[OH⁻], and pH + pOH = 14 at 25 °C.
• pK_a = −log K_a; a larger K_a means a smaller pK_a and a stronger acid. For a conjugate acid-base pair, K_a × K_b = K_w.
• Henderson equation for an acidic buffer: pH = pK_a + log([salt] ÷ [acid]).
• For a basic buffer: pOH = pK_b + log([salt] ÷ [base]).
• When [salt] = [acid], pH = pK_a; this is where the buffer works best.
• Solubility product for solubility S mol dm⁻³: K_sp = S² for a salt like AgCl; K_sp = 4S³ for a salt like PbCl₂.

Solutions

Concentration units

• Percentage weight/weight = (mass of solute ÷ mass of solution) × 100. Mass of solution = mass of solute + mass of solvent.
• Percentage weight/volume = mass of solute in g per 100 cm³ of solution; percentage volume/volume = volume of solute per 100 cm³ of solution.
• Molarity (M) = moles of solute ÷ volume of solution in dm³; unit mol dm⁻³.
• Molality (m) = moles of solute ÷ mass of solvent in kg; unit mol kg⁻¹.
• Mole fraction of A (X_A) = moles of A ÷ total moles; it has no unit and all the mole fractions add up to 1.
• Parts per million (ppm) = (mass of solute ÷ mass of solution) × 10⁶.
• Dilution: M₁V₁ = M₂V₂.

Raoult's law, ideal and non-ideal solutions

• Raoult's law: p = p° × X₁, where X₁ is the mole fraction of the solvent. Relative lowering of vapour pressure: Δp ÷ p° = X₂, the mole fraction of the solute.
• Two volatile liquids: total vapour pressure P = p°_AX_A + p°_BX_B. The vapour is richer in the more volatile component.
• Ideal (nearly): benzene and toluene; no heat change and no volume change on mixing.
• Positive deviation: A−B attractions are weaker, vapour pressure is higher than predicted, e.g. ethanol and water. They form a minimum-boiling azeotrope with about 95.6% ethanol.
• Negative deviation: A−B attractions are stronger, vapour pressure is lower than predicted, e.g. acetone and chloroform, or HCl and water (maximum-boiling azeotrope).
• An azeotrope cannot be separated by fractional distillation, because the liquid and the vapour have the same composition.
• Solubility rises with temperature if dissolving absorbs heat (e.g. KNO₃); NaCl changes very little; Na₂SO₄·10H₂O shows a break at 32.4 °C.

Colligative properties, hydration and hydrolysis

• Elevation of boiling point: ΔT_b = K_b × m. Depression of freezing point: ΔT_f = K_f × m (m = molality).
• For water, K_b = 0.52 K kg mol⁻¹ and K_f = 1.86 K kg mol⁻¹.
• Molar mass of solute: M₂ = (K × 1000 × W₂) ÷ (ΔT × W₁), with W₂ = mass of solute in g and W₁ = mass of solvent in g.
• Electrolytes give more particles: at equal molality, NaCl (2 ions) and CaCl₂ (3 ions) have a bigger effect than glucose or urea.
• Osmotic pressure: the pressure that must be applied to a solution to stop solvent flowing into it through a semipermeable membrane.
• Water of crystallisation: water molecules held in a crystal, e.g. CuSO₄·5H₂O (blue); heating drives it off to leave white CuSO₄.
• Hydrolysis: salt of strong acid + weak base is acidic (NH₄Cl); salt of weak acid + strong base is basic (CH₃COONa, Na₂CO₃); strong + strong is neutral (NaCl).

Electrochemistry

Oxidation numbers and balancing redox equations

• Free elements have oxidation number 0 (Zn, Cl₂, S₈). For a simple ion it equals the charge.
• In compounds: Group I metals +1, Group II metals +2, fluorine always −1.
• Hydrogen is +1, except −1 in metal hydrides such as NaH.
• Oxygen is −2, except −1 in peroxides such as H₂O₂ and +2 in OF₂.
• The oxidation numbers add up to 0 in a neutral compound and to the charge in an ion.
• Oxidising agent: its oxidation number decreases (it is reduced). Reducing agent: its oxidation number increases (it is oxidised).
• Ion-electron method: write two half-equations, balance atoms, add H₂O and H⁺, add electrons to balance charge, make the electrons equal, then add.

Electrolysis and electrolytic cells

• Electrolytic cell: cathode is negative, reduction occurs; anode is positive, oxidation occurs.
• Fused NaCl: Na⁺ + e⁻ → Na at the cathode; 2Cl⁻ → Cl₂ + 2e⁻ at the anode.
• Concentrated aqueous NaCl: hydrogen at the cathode (2H₂O + 2e⁻ → H₂ + 2OH⁻), chlorine at the anode, NaOH left in solution.
• Aqueous Na₂SO₄ or NaNO₃ with inert electrodes: hydrogen at the cathode and oxygen at the anode.
• Downs cell: fused NaCl gives sodium and chlorine; CaCl₂ is added to lower the melting point; iron cathode, graphite anode.
• Nelson's cell: electrolysis of brine gives NaOH, H₂ and Cl₂; graphite anode, perforated steel cathode lined with an asbestos diaphragm.
• Electroplating: object = cathode, plating metal = anode, electrolyte = a solution of a salt of the plating metal.

Galvanic cells, electrode potentials and batteries

• Galvanic cell: anode is negative, oxidation occurs; cathode is positive, reduction occurs. Electrons flow from anode to cathode in the wire.
• Daniell cell: Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s); zinc is the anode, copper the cathode, emf 1.10 V.
• Salt bridge: completes the circuit and keeps both solutions electrically neutral by letting ions move.
• Standard hydrogen electrode: platinised platinum, H₂ at 1 atm, 1 mol dm⁻³ H⁺, 25 °C; its potential is taken as 0.00 V.
• E°_cell = E°(cathode) − E°(anode), using standard reduction potentials for both.
• A metal displaces from solution the ions of any metal below it in the series (one with a less negative E°). Metals above hydrogen displace H₂ from acids.
• Lead accumulator (rechargeable, 2 V per cell): Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O on discharge. Alkaline and silver oxide cells use a zinc anode with KOH; a hydrogen-oxygen fuel cell gives only water.

Reaction kinetics

Rate of reaction, order and half-life

• Rate = change in concentration ÷ time taken; unit mol dm⁻³ s⁻¹.
• Specific rate constant: the rate of the reaction when the concentration of each reactant is 1 mol dm⁻³.
• Units of k: zero order mol dm⁻³ s⁻¹; first order s⁻¹; second order dm³ mol⁻¹ s⁻¹; third order dm⁶ mol⁻² s⁻¹.
• Examples: zero order, photochemical H₂ + Cl₂; first order, decomposition of N₂O₅; second order, NO + O₃ → NO₂ + O₂; third order, 2NO + O₂ → 2NO₂.
• Half-life for initial concentration a: first order t_½ = 0.693 ÷ k (independent of a); second order t_½ = 1 ÷ (k × a); in general t_½ is proportional to 1 ÷ aⁿ⁻¹.
• Molecularity is the number of particles taking part in one step; it is always a whole number.
• Measuring rate: physical methods (spectrometry, electrical conductivity, dilatometry, refractometry, optical rotation) or chemical methods (titration). Order is found by the half-life method or the method of large excess.

Activation energy, factors affecting rate and catalysis

• ΔH = E_a(forward) − E_a(reverse). For an exothermic reaction, E_a(reverse) is the larger one.
• Arrhenius equation: k = Ae^−E_a/RT, so ln k = ln A − E_a ÷ (RT), with R = 8.314 J K⁻¹ mol⁻¹ and T in kelvin.
• Graph of ln k against 1/T: straight line, slope = −E_a ÷ R. Graph of log k against 1/T: slope = −E_a ÷ (2.303R).
• A rise of 10 K roughly doubles the rate of many reactions.
• Homogeneous catalysis: catalyst and reactants in the same phase. Heterogeneous catalysis: different phases, e.g. nickel in the hydrogenation of vegetable oils, V₂O₅ in the Contact process.
• Autocatalysis: a product catalyses the reaction, e.g. Mn²⁺ in the reaction of KMnO₄ with oxalic acid. A poison destroys the activity of a catalyst (arsenic compounds poison platinum); a promoter increases it.
• Enzymes are protein catalysts: highly specific, very efficient, and most active at an optimum temperature (about 37 °C) and pH.