Physical Chemistry

The basic building blocks of all matter. Protons (positive charge, found in nucleus), neutrons (neutral, found in nucleus), and electrons (negative charge, orbiting nucleus). Protons and neutrons have roughly equal mass (~1 amu), while electrons are much lighter (~1/2000 amu). The number of protons defines the element; the number of electrons determines the overall charge of an atom or ion. All a

Physical Chemistry

Physical Chemistry

The mass number (A) is the total number of protons and neutrons in a nucleus. Isotopes are atoms of the same element (same proton number) with different numbers of neutrons, and therefore different mass numbers. Isotopes have identical chemical properties because they have the same electron configuration, but different physical properties (e.g., density, melting point). Relative atomic mass is the

Physical Chemistry

Physical Chemistry

The arrangement of electrons in an atom, described using shells (energy levels) and subshells (s, p, d, f orbitals). Electrons fill orbitals in order of increasing energy, following the Aufbau principle. For example, nitrogen (N, atomic number 7) has configuration 1s² 2s² 2p³. Configuration determines an element's chemical properties and bonding behaviour. Electrons occupy orbitals in shells arou

Physical Chemistry

Physical Chemistry

The energy required to remove one mole of electrons from one mole of gaseous atoms or ions. First ionisation energy (IE₁) removes the first electron; second ionisation energy (IE₂) removes the second, etc. Measured in kJ mol⁻¹. Ionisation energies increase across a period (increased nuclear charge) and decrease down a group (increased atomic radius, shielding effect). Ionisation energy reflects h

Physical Chemistry

Physical Chemistry

An analytical technique that measures the mass-to-charge ratio of ions by timing how long they take to travel a fixed distance. Atoms/molecules are ionised (usually by electron impact), accelerated through an electric field, then drift along a field-free region. Lighter ions reach the detector faster than heavier ones. Time of flight correlates with mass, producing a mass spectrum showing relative

Physical Chemistry

Physical Chemistry

A region of space where there is a high probability of finding an electron. Orbitals are described by quantum numbers and have characteristic shapes: s orbitals are spherical, p orbitals are dumbbell-shaped, d orbitals are more complex. Each orbital can hold a maximum of 2 electrons (with opposite spins). Orbitals are grouped into subshells (s, p, d, f) and shells (n=1, 2, 3...). Quantum mechanic

Physical Chemistry

Physical Chemistry

The weighted average mass of all isotopes of an element, relative to one-twelfth of the mass of carbon-12 (which is assigned exactly 12). Denoted Ar. For example, chlorine has Ar = 35.5 because it's a mixture of Cl-35 (75.8%) and Cl-37 (24.2%). Relative atomic masses are found on the periodic table and are dimensionless (no units, though sometimes 'u' for atomic mass units is used). Relative atom

Physical Chemistry

Physical Chemistry

The sum of the relative atomic masses of all atoms in a molecule. Denoted Mr. For example, H₂O has Mr = (2 × 1) + 16 = 18. Relative molecular mass is dimensionless but numerically equals the molar mass in g mol⁻¹. Used to convert between mass and number of moles, and to calculate percentage composition. Relative molecular mass is simply the sum of Ar values weighted by atom counts. For glucose C₆

Physical Chemistry

Physical Chemistry

The mole is the SI unit of amount of substance. One mole contains 6.02 × 10²³ particles (atoms, molecules, ions, electrons, etc.)—Avogadro's constant (NA). The number of moles in a sample is calculated as: n = mass/Mr (for compounds) or n = mass/Ar (for elements). One mole of any gas at RTP occupies 24 dm³ (or 24,000 cm³). The mole connects the atomic scale to the laboratory scale. One mole of ca

Physical Chemistry

Physical Chemistry

The equation PV = nRT relates pressure (P in Pa), volume (V in m³), number of moles (n), and absolute temperature (T in K). R is the gas constant (8.31 J K⁻¹ mol⁻¹). Rearranged forms: P = ρRT/M (where ρ is density, M is molar mass), or used to find moles: n = PV/RT. Ideal gases obey this equation perfectly; real gases approximate it except at very high pressures or low temperatures. The ideal gas

Physical Chemistry

Physical Chemistry

The empirical formula shows the simplest whole-number ratio of atoms in a compound. The molecular formula shows the actual number of atoms. For example, ethene (C₂H₄) and benzene (C₆H₁₂) both have empirical formula CH₂, but different molecular formulas. Finding empirical formula requires: convert mass percentages (or masses) to moles, divide by the smallest value to find whole-number ratios. Findi

Physical Chemistry

Physical Chemistry

A chemical equation with equal numbers of each type of atom on both sides (conserving mass). Coefficients show the mole ratio of reactants to products. For example, 2Na + Cl₂ → 2NaCl shows that 2 moles of sodium react with 1 mole of chlorine to produce 2 moles of sodium chloride. Balancing is essential for stoichiometric calculations. A balanced equation shows equal numbers of each atom type on b

Physical Chemistry

Physical Chemistry

The ratio of actual yield to theoretical yield, expressed as a percentage: % yield = (actual mass / theoretical mass) × 100%. Theoretical yield assumes complete reaction with no losses; actual yield is what's obtained in the lab. Percentage yield is typically less than 100% due to incomplete reactions, side reactions, or product loss during isolation and purification. Theoretical yield is calcula

Physical Chemistry

Physical Chemistry

A measure of how efficiently a reaction uses raw materials, calculated as: atom economy (%) = (Mr of desired product / Σ Mr of all reactants) × 100%. High atom economy (close to 100%) means minimal waste; low atom economy means significant by-products. Unlike percentage yield, atom economy depends on the reaction stoichiometry, not lab performance. Important in green chemistry and industrial proce

Physical Chemistry

Physical Chemistry

The amount of solute per unit volume of solution, typically expressed in mol dm⁻³ (or M, molar). Concentration (c) = n/V, where n is moles of solute and V is volume of solution in dm³. Standard solutions are prepared by dissolving a known mass of solute in distilled water, transferring to a volumetric flask, and diluting to the mark. Dilution formula: c₁V₁ = c₂V₂. Concentration is crucial for rea

Physical Chemistry

Physical Chemistry

The electrostatic attraction between oppositely charged ions. Forms when electrons are transferred from a metal (low ionisation energy) to a nonmetal (high electron affinity). Ionic compounds contain discrete cations and anions arranged in crystal lattices. Common in compounds like NaCl, MgO, and CaCO₃. Ionic compounds conduct electricity when molten or dissolved (mobile ions). Ionic bonds result

Physical Chemistry

Physical Chemistry

The sharing of a pair of electrons between two atoms. Single bonds share 2 electrons; double bonds share 4; triple bonds share 6. Covalent bonds are strong (typically 150-1000 kJ mol⁻¹) and form between nonmetals or between nonmetals and metalloids. Covalent compounds exist as discrete molecules (simple covalent) or giant networks (covalent lattices). Covalent bonds form when two atoms share elec

Physical Chemistry

Physical Chemistry

A covalent bond in which both electrons come from the same atom (the donor), which has a lone pair, while the other atom (acceptor) provides the empty orbital. Also called a coordinate bond. Denoted by an arrow A→B. Once formed, dative bonds are indistinguishable from ordinary covalent bonds. Common in complexes, adducts, and compounds with boron or aluminium. A dative bond (coordinate covalent b

Physical Chemistry

Physical Chemistry

The electrostatic attraction between delocalized electrons and metal cations arranged in a lattice. Metal atoms lose valence electrons to form a 'sea' of mobile electrons that delocalizes across the entire structure. Metallic bonding explains metals' properties: electrical conductivity (mobile electrons), thermal conductivity, malleability, ductility, and lustre (light absorption and re-emission b

Physical Chemistry

Physical Chemistry

The three-dimensional arrangement of atoms, ions, or molecules in a repeating lattice pattern. Crystal structures include ionic (e.g., NaCl with octahedral coordination), covalent (e.g., diamond with tetrahedral bonding), molecular (e.g., ice with hydrogen bonding), and metallic (e.g., copper with metal cations in electron sea). Properties depend on structure: ionic crystals are hard and brittle;

Physical Chemistry

Physical Chemistry

Molecular geometry predicted by Valence Shell Electron Pair Repulsion (VSEPR) theory: electron pairs (bonding and lone pairs) around a central atom repel each other, arranging themselves to maximize distance. Electron geometry (including lone pairs) differs from molecular geometry (only atoms). Common shapes: tetrahedral (CH₄), trigonal planar (BF₃), linear (CO₂), bent (H₂O), trigonal pyramidal (N

Physical Chemistry

Physical Chemistry

Electronegativity is an atom's ability to attract electrons in a covalent bond (Pauling scale, 0.7-4.0). Bond polarity arises from unequal electron sharing when atoms have different electronegativities. In polar covalent bonds (e.g., HCl), electrons shift toward the more electronegative atom, creating a dipole (δ+ and δ-). Polar molecules have a permanent dipole moment; nonpolar molecules have dip

Physical Chemistry

Physical Chemistry

Weak attractions between separate molecules (or atoms): London dispersion forces (induced dipoles, present in all substances), permanent dipole-dipole forces (in polar molecules), and hydrogen bonding (O-H, N-H, F-H groups with lone pairs). Much weaker than covalent/ionic bonds (typically 0.5-50 kJ mol⁻¹ vs. 100-500 kJ mol⁻¹), but critical for melting/boiling points, solubility, and viscosity. Lo

Physical Chemistry

Physical Chemistry

The heat energy change at constant pressure during a reaction, denoted ΔH (kJ mol⁻¹). Exothermic reactions (ΔH < 0) release heat; endothermic reactions (ΔH > 0) absorb heat. Standard enthalpy change (ΔH°) refers to conditions where all substances are in standard states (298 K, 100 kPa, 1 M solutions). Measured using calorimetry or calculated from bond enthalpies and Hess's law. Enthalpy change ΔH

Physical Chemistry

Physical Chemistry

Experimental measurement of heat energy change. Simple calorimeter: insulated container holding the reaction, thermometer to measure temperature change, heat generated/absorbed by reaction changes the temperature of the liquid (usually water). Heat (q) = mcΔT, where m is mass (g), c is specific heat capacity (J g⁻¹ K⁻¹), ΔT is temperature change. For water, c = 4.18 J g⁻¹ K⁻¹. Calorimetry measure

Physical Chemistry

Physical Chemistry

The enthalpy change of a reaction is independent of the route taken, depending only on initial and final states. If a target reaction is the sum of known reactions, its ΔH is the sum of the individual ΔH values. Hess's law cycles (Hess cycles) manipulate thermochemical equations to find unknown enthalpy changes without direct measurement. Hess's Law states that the enthalpy change of a reaction i

Physical Chemistry

Physical Chemistry

The energy required to break one mole of a covalent bond in gaseous atoms (bond dissociation energy), typically 150-1000 kJ mol⁻¹. Bond enthalpy is always positive (breaking requires energy). Enthalpy change for a reaction: ΔH = Σ(bond enthalpies broken) - Σ(bond enthalpies formed). Average bond enthalpies account for multiple environments (C-H in different molecules) by averaging. Bond enthalpy

Physical Chemistry

Physical Chemistry

The enthalpy change (ΔHc) when one mole of a substance completely burns in excess oxygen under standard conditions (298 K, 100 kPa), measured in kJ mol⁻¹. Combustion is always exothermic, so ΔHc is negative. For example, the standard enthalpy of combustion of methane is ΔHc = -890 kJ mol⁻¹ for the reaction CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l). Standard enthalpy values allow calculation of reaction e

Physical Chemistry

Physical Chemistry

The enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions (298 K, 100 kPa). Denoted ΔH°f. By definition, ΔH°f of elements in their standard states = 0. Used to calculate reaction enthalpy: ΔH°rxn = Σ(ΔH°f products) - Σ(ΔH°f reactants). Standard enthalpy of formation (ΔH°f) is ΔH for forming one mole of compound from elements in

Physical Chemistry

Physical Chemistry

A model explaining reaction mechanisms: a reaction occurs when reactant molecules collide with sufficient kinetic energy (exceeding the activation energy, Ea) and appropriate orientation. Not all collisions produce reaction—only those with energy ≥ Ea in the correct geometry react. Reaction rate increases with temperature (more energetic collisions), concentration (more frequent collisions), and u

Physical Chemistry

Physical Chemistry

The minimum kinetic energy that colliding molecules must have to react (Ea, in kJ mol⁻¹). Energy diagram shows reactants at one level, products at another (lower for exothermic, higher for endothermic), with an energy barrier (activation energy) between them. Ea is independent of whether the reaction is exothermic or endothermic; it depends only on the reaction mechanism. Activation energy is the

Physical Chemistry

Physical Chemistry

A probability distribution showing the fraction of molecules at each kinetic energy (or velocity) in a gas/liquid at a given temperature. The distribution is skewed: most molecules have near-average energy, a tail extends to very high energies. The area under the curve above Ea equals the fraction of molecules with E ≥ Ea (able to react). As temperature increases, the curve flattens and shifts rig

Physical Chemistry

Physical Chemistry

Reaction rate increases with temperature. Typically, a 10°C increase roughly doubles the rate (rate ≈ 2 × rate at T-10). Two effects: collision frequency increases slightly (~2% per °C), but the fraction of collisions with E ≥ Ea increases exponentially. The exponential factor dominates, explaining the roughly-doubling rule. Quantified by the Arrhenius equation. Temperature strongly increases rea

Physical Chemistry

Physical Chemistry

Increasing reactant concentration increases the rate of reaction (in the absence of saturating conditions). The relationship is quantified by the rate equation: rate = k[A]ⁿ[B]ᵐ, where n and m are orders of reaction (often 0, 1, or 2, determined experimentally). Doubling concentration of a first-order reactant doubles the rate; doubling a second-order reactant increases rate by 4x. Concentration

Physical Chemistry

Physical Chemistry

A substance that increases reaction rate by lowering the activation energy, without being consumed in the reaction. A catalyst speeds up both forward and reverse reactions equally (increases equilibrium approach rate, doesn't shift equilibrium position). Homogeneous catalysts (same phase as reactants, e.g., I⁻ in H₂O₂ decomposition) work by forming intermediates; heterogeneous catalysts (different

Physical Chemistry

Physical Chemistry

When a system at equilibrium is disturbed (by changing concentration, pressure, or temperature), the equilibrium shifts to counteract the disturbance and re-establish equilibrium. Increasing a reactant's concentration shifts equilibrium right (increases products); increasing pressure shifts toward the side with fewer moles of gas; increasing temperature shifts toward the endothermic direction. Le

Physical Chemistry

Physical Chemistry

A state where the forward and reverse reactions occur simultaneously at equal rates, so concentrations of reactants and products remain constant (but not necessarily equal). Equilibrium is dynamic: both reactions continue, but net composition doesn't change. Reached when forward rate = reverse rate (after sufficient time). Represented by ↔ (double arrow). In a reversible reaction aA + bB ⇌ cC + d

Physical Chemistry

Physical Chemistry

A constant (at a given temperature) expressing the ratio of product to reactant concentrations at equilibrium. For aA + bB ↔ cC + dD, Kc = [C]^c[D]^d / [A]^a[B]^b. Kc units depend on stoichiometry (often mol⁻¹ dm³ or unitless). Large Kc (>1) favors products; small Kc (<1) favors reactants. Kc changes with temperature but not with concentration, pressure, or catalysts. Kc is derived from the equil

Physical Chemistry

Physical Chemistry

Temperature changes alter Kc according to the reaction's enthalpy. For exothermic reactions (ΔH° < 0), increasing T decreases Kc (equilibrium shifts left, favoring reactants). For endothermic reactions (ΔH° > 0), increasing T increases Kc (equilibrium shifts right, favoring products). Quantified by van 't Hoff equation: ln(K₂/K₁) = -(ΔH°/R)(1/T₂ - 1/T₁). Temperature directly affects Kc (equilibri

Physical Chemistry

Physical Chemistry

Large-scale production optimizes equilibrium position using Le Chatelier's principle. Haber process (N₂ + 3H₂ ↔ 2NH₃): high pressure favors products (fewer moles); moderate T (~450°C) balances yield (higher T increases rate but decreases Kc for exothermic reaction). Contact process (2SO₂ + O₂ ↔ 2SO₃, exothermic): high pressure, moderate T (~450°C), catalyst increases rate without affecting equilib

Physical Chemistry

Physical Chemistry

A number assigned to an element in a compound that represents electrons lost, gained, or shared. Rules: (1) elements in standard state = 0; (2) monoatomic ions = charge; (3) O = -2 (except peroxides -1); (4) H = +1 (except hydrides -1); (5) Group 1 = +1, Group 2 = +2; (6) sum = zero (neutral) or charge (ions). Used to identify redox reactions (oxidation states change). Oxidation states track elec

Physical Chemistry

Physical Chemistry

Reactions involving transfer of electrons between species. Oxidation is loss of electrons or increase in oxidation state; reduction is gain of electrons or decrease in oxidation state. Oxidizing agents accept electrons (are reduced); reducing agents donate electrons (are oxidized). Redox reactions power batteries, fuel cells, and many industrial processes. Half-equations separate oxidation and red

Physical Chemistry

Physical Chemistry

Separate equations for oxidation and reduction components of a redox reaction. The oxidation half-equation shows species losing electrons; the reduction half-equation shows species gaining electrons. Half-equations must be balanced for atoms and charge. Multiplying half-equations by integers ensures equal electron transfer, then adding gives the overall balanced redox equation. Half-equations clar

Physical Chemistry

Physical Chemistry

An oxidising agent gains electrons (is reduced); a reducing agent loses electrons (is oxidized). Identified by oxidation state change: if a species' oxidation state increases, it's oxidized (by the oxidising agent); if it decreases, it's reduced (by the reducing agent). Example: in Mg + Cl₂ → MgCl₂, Mg is the reducing agent (0 → +2), Cl₂ is the oxidising agent (+0 → -1). The terms 'oxidising agen

Physical Chemistry

Physical Chemistry

A thermochemical cycle used to calculate lattice enthalpy of an ionic compound. Depicts the formation of a solid ionic compound from its elements via two routes: (1) direct formation (ΔH°f), (2) via gaseous ions. Both routes have the same overall enthalpy change (Hess's law), allowing calculation of unmeasurable lattice enthalpy. Born-Haber cycle is a thermochemical cycle combining measured entha

Physical Chemistry

Physical Chemistry

The enthalpy change required to convert one mole of solid ionic compound into gaseous ions: MX(s) → M⁺(g) + X⁻(g), ΔH(lattice). Always positive (energy required to break the ionic lattice). Measured via Born-Haber cycles (cannot be directly calorimetered). Depends on ionic charge and size (higher charge, smaller ions → larger lattice enthalpy). Lattice enthalpy (enthalpy of lattice formation) is

Physical Chemistry

Physical Chemistry

The enthalpy change when one mole of gaseous ions dissolves in water to form an aqueous ion: M⁺(g) + aq → M⁺(aq), ΔH(hydration). Always negative (energy released when water molecules surround ions). Related to lattice enthalpy: solubility depends on competition between lattice enthalpy (positive, unfavourable) and hydration enthalpy (negative, favourable). When an ionic solid dissolves, the latti

Physical Chemistry

Physical Chemistry

The change in disorder or randomness in a system, denoted ΔS (units: J K⁻¹ mol⁻¹). Positive ΔS indicates increased disorder (favored); negative ΔS indicates decreased disorder (unfavored). Entropy increases when solids dissolve, liquids evaporate, or gases expand. Temperature affects entropy: higher temperature increases molecular motion and disorder. Entropy change is crucial for predicting spont

Physical Chemistry

Physical Chemistry

The thermodynamic quantity determining spontaneity of reactions: ΔG = ΔH − TΔS (units: kJ mol⁻¹). Negative ΔG indicates spontaneity (reaction occurs); positive ΔG indicates non-spontaneity (reaction does not occur under standard conditions). ΔG = 0 at equilibrium. Temperature, enthalpy, and entropy all influence whether a reaction is spontaneous. Gibbs free energy allows prediction of reaction fea

Physical Chemistry

Physical Chemistry

Thermodynamic feasibility determined by ΔG < 0 (spontaneous, will proceed forward). Kinetic feasibility determined by activation energy and reaction rate (some feasible reactions are too slow to observe on reasonable timescales). A reaction can be thermodynamically favorable (ΔG < 0) but kinetically slow (high Ea); conversely, a reaction can be thermodynamically unfavorable (ΔG > 0) but proceeding

Physical Chemistry

Physical Chemistry

An equation expressing reaction rate as a function of reactant concentrations raised to powers (orders). General form: rate = k[A]ⁿ[B]ᵐ, where k is rate constant, [A] and [B] are concentrations, and n and m are orders. Orders are determined experimentally, not from stoichiometry. Overall order (n + m) indicates how many concentration changes double the rate. Rate equations explain why some reactio

Physical Chemistry

Physical Chemistry

The power to which a reactant's concentration is raised in the rate equation. For rate = k[A]ⁿ[B]ᵐ, n is the order with respect to A, m is the order with respect to B. Orders are zero (rate independent of concentration), first (rate doubles when concentration doubles), or second (rate quadruples when concentration doubles). Overall order is n + m. Orders must be determined experimentally, not from

Physical Chemistry

Physical Chemistry

The constant k in the rate equation rate = k[A]ⁿ[B]ᵐ. Units depend on overall reaction order: for zero-order reactions, k has units mol dm⁻³ s⁻¹; for first-order, s⁻¹; for second-order, mol⁻¹ dm³ s⁻¹. Rate constant increases with temperature following the Arrhenius equation k = Ae^(-Ea/RT). A catalyst lowers activation energy and increases k without being consumed. k determines reaction speed at a

Physical Chemistry

Physical Chemistry

The slowest step in a multi-step reaction mechanism. The overall reaction rate equals the rate of the rate-determining step. Elementary steps faster than the rate-determining step don't contribute to rate-limiting. The rate-determining step often involves the reactants (or intermediates from earlier steps), explaining why the experimental rate equation often resembles the rate-determining step's s

Physical Chemistry

Physical Chemistry

An equation describing the temperature-dependence of the rate constant: k = Ae^(-Ea/RT), where A is the pre-exponential factor, Ea is activation energy (J mol⁻¹), R is the gas constant (8.31 J K⁻¹ mol⁻¹), T is absolute temperature. Linear form: ln(k) = ln(A) - (Ea/R)(1/T). Used to calculate k at different temperatures or to find Ea from rate constant data. Arrhenius equation k = Ae^(−Ea/RT) quant

Physical Chemistry

Physical Chemistry

In a mixture of ideal gases, the partial pressure of a gas is the pressure that gas would exert if it alone occupied the container at the same temperature. Dalton's Law: total pressure = sum of partial pressures. For gas i in a mixture, Pi = xi × Ptotal (where xi is mole fraction). Partial pressures explain gas behavior in mixtures: calculating equilibrium constants for gases uses partial pressure

Physical Chemistry

Physical Chemistry

The mole fraction (xi) of component i in a mixture is ni / ntotal (moles of i divided by total moles). Mole fractions are dimensionless, ranging 0 to 1, and sum to 1 for all components. Mole fractions relate to partial pressure: Pi = xi × Ptotal (for ideal gases). Mole fractions are useful for non-ideal solutions and gas mixtures where concentrations aren't relevant. Mole fraction is a compositio

Physical Chemistry

Physical Chemistry

For gases in equilibrium, Kp expresses the ratio of partial pressures (in Pa) at equilibrium. For aA(g) + bB(g) ↔ cC(g) + dD(g): Kp = (Pc^c × Pd^d) / (Pa^a × Pb^b) (units depend on stoichiometry, often Pa^Δn). Like Kc (concentration-based), Kp depends only on temperature. Related by: Kp = Kc(RT)^Δn, where Δn = moles products - moles reactants (gaseous only). Kp uses partial pressures instead of c

Physical Chemistry

Physical Chemistry

Changes in pressure, volume, or temperature affect Kp (equilibrium constant in terms of partial pressures). Temperature changes Kp: for endothermic reactions, increasing T increases Kp (shifts equilibrium right); for exothermic reactions, increasing T decreases Kp (shifts left). Pressure and volume changes don't alter Kp value itself, but do shift equilibrium position (Le Chatelier). Catalysts don

Physical Chemistry

Physical Chemistry

The potential (in volts) of a half-cell under standard conditions (298 K, 100 kPa, 1 M solutions) relative to the standard hydrogen electrode (SHE). Denoted E°. Reduction potentials (for reduction reactions) are tabulated. Positive E° indicates a good oxidising agent (reduction is favourable); negative E° indicates a good reducing agent (oxidation is favourable). Electrode potential measures the

Physical Chemistry

Physical Chemistry

A reference electrode with assigned E° = 0 V by definition. Consists of Pt electrode in contact with H₂(g, 1 atm, ~1 bar) and H⁺(aq, 1 M) at 298 K. The half-reaction: 2H⁺ + 2e⁻ ↔ H₂. All other electrode potentials are measured relative to SHE by constructing a galvanic cell with the SHE as one half-cell. Standard hydrogen electrode (SHE, 2H⁺(aq) + 2e⁻ → H₂(g) at 298 K, 100 kPa, [H⁺] = 1 M) is def

Physical Chemistry

Physical Chemistry

A device in which redox reactions occur at two electrodes (anode and cathode) separated by an electrolyte. In a galvanic (voltaic) cell, spontaneous redox reactions produce electrical current (ΔG < 0, E° > 0). In an electrolytic cell, applied external voltage drives non-spontaneous redox reactions. Cell notation: anode | electrolyte | cathode; double line | | represents a salt bridge (in galvanic

Physical Chemistry

Physical Chemistry

The electromotive force (voltage) of a galvanic cell: E°cell = E°(cathode) - E°(anode) under standard conditions. Positive E°cell indicates a spontaneous reaction (ΔG < 0). Related to ΔG° by: ΔG° = -nFE°, where n is moles of electrons, F is Faraday's constant (96,500 C mol⁻¹). Non-standard conditions: Ecell = E°cell - (RT/nF) ln(Q) (Nernst equation). EMF is the driving force for electron flow in

Physical Chemistry

Physical Chemistry

Electrochemical cells generating electricity from continuous supply of fuel (e.g., H₂) and oxidant (e.g., O₂). More efficient than combustion (not limited by Carnot efficiency). The hydrogen fuel cell: anode: 2H₂ + 4OH⁻ → 4H₂O + 4e⁻ (in alkaline), cathode: O₂ + 2H₂O + 4e⁻ → 4OH⁻. Overall: 2H₂ + O₂ → 2H₂O. Clean (product is water), quiet, efficient (~60% theoretical max). Fuel cells are galvanic c

Physical Chemistry

Physical Chemistry

An acid is a proton (H⁺) donor; a base is a proton acceptor. An acid-base reaction is proton transfer: HA + B → A⁻ + HB⁺. The conjugate base of an acid (A⁻) is formed by removing a proton; the conjugate acid of a base (HB⁺) is formed by adding a proton. A conjugate acid-base pair differs by one proton. Bronsted-Lowry theory extends acid-base chemistry beyond aqueous solutions and includes reactio

Physical Chemistry

Physical Chemistry

Strong acids (HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄) completely dissociate in water: HA → H⁺ + A⁻ (100% ionisation). Weak acids (e.g., CH₃COOH, HCN) partially dissociate: HA ↔ H⁺ + A⁻, equilibrium favours reactants. Strength is quantified by Ka (acid dissociation constant). Strong acids have Ka >> 1; weak acids have Ka << 1. Strong acids dissociate completely, so [H⁺] from a strong acid = initial conc

Physical Chemistry

Physical Chemistry

pH = -log₁₀[H⁺], where [H⁺] is hydrogen ion concentration in mol dm⁻³. Neutral solutions (at 298 K): pH = 7. Acidic: pH < 7 ([H⁺] > 10⁻⁷). Basic: pH > 7 ([H⁺] < 10⁻⁷). Related to pOH by: pH + pOH = 14 (at 298 K). Converting between pH and [H⁺]: [H⁺] = 10^(-pH). pH = −log[H⁺] expresses hydrogen ion concentration on logarithmic scale (manageable range 0−14 instead of 10⁻¹⁴ to 10⁻¹). [H⁺] from pH: [

Physical Chemistry

Physical Chemistry

The water ion product Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C (units: mol² dm⁻⁶). Kw is the equilibrium constant for water dissociation: H₂O ⇌ H⁺ + OH⁻. In pure water, [H⁺] = [OH⁻] = 10⁻⁷ M (neutral, pH = 7). Adding acid increases [H⁺], shifting equilibrium left and decreasing [OH⁻] proportionally (product Kw remains constant). Kw enables calculating [OH⁻] from [H⁺]: [OH⁻] = Kw / [H⁺]. Kw increases w

Physical Chemistry

Physical Chemistry

For a weak acid HA ↔ H⁺ + A⁻, Ka = [H⁺][A⁻]/[HA] (mol dm⁻³). Larger Ka indicates stronger acid (more dissociation). Tabulated values at 298 K. Related to strength: strong acids have Ka >> 1 (often>10³); weak acids have Ka < 1. pKa = -log Ka; lower pKa = stronger acid. Ka = [H⁺][A⁻] / [HA] quantifies weak acid strength (HA ⇌ H⁺ + A⁻). Large Ka (weak acid is strong, more dissociation): HCl (very la

Physical Chemistry

Physical Chemistry

Solutions that resist pH changes when small amounts of acid or base are added. Composed of a weak acid and its conjugate base (e.g., CH₃COOH + CH₃COONa) or a weak base and its conjugate acid (e.g., NH₃ + NH₄Cl). Buffer capacity depends on the concentrations of the weak acid and conjugate base. pH is given by Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]). Buffers work by neutralizing a

Physical Chemistry

Physical Chemistry

A pH curve (titration curve) plots pH vs. volume of titrant during an acid-base titration. Shapes differ based on acid/base strengths: strong acid/strong base (sharp vertical at equivalence point), weak acid/strong base (curved, steep portion before equivalence point, buffer region), weak base/strong acid (curved, buffer region before equivalence point). Indicators are weak acids or bases that cha

Physical Chemistry

Physical Chemistry

Quantitative analysis using acid-base titrations. At equivalence point: moles of acid = moles of base (accounting for stoichiometry). For strong acid/strong base: use concentration × volume (n = cV) directly. For weak acids/bases, use the same stoichiometric principle, but pH at equivalence point differs. Standardisation: a standard solution (precisely known concentration) is used as the titrant.

Physical Chemistry