United Grade 11 AP Chemistry
Chapters: 9
1. Atomic Structure and Properties
Moles and Molar Mass · Mass Spectra of Elements · Elemental Composition of Pure Substances · Composition of Mixtures · Atomic Structure and Electron Configuration · Photoelectron Spectroscopy · Periodic Trends · Valence Electrons and Ionic Compounds
- Mole Concept, Molar Mass and Chemical Formulas – Atoms are far too small to count one by one, so chemists count them by weighing. Atomic masses are given in u, where 1 u is one-twelfth the mass of a carbon-12 atom. One mole is 6.022 × 10²³ particles, and its mass in grams equals the formula mass in u. With moles we can find the percentage of each element in a compound, and work back from percentages to the empirical and molecular formulas.
- Atoms and Molecules – In a chemical reaction mass is neither created nor destroyed (conservation of mass), and a compound always has its elements in the same ratio by mass (constant proportions). Dalton explained both: matter is made of tiny atoms that join in small whole numbers. Atoms join to form molecules; charged atoms or groups are ions. Formulae are written by crossing valencies. Molecular mass (or formula unit mass for ionic compounds) is the sum of the atomic masses in the formula, in u.
- Quantum Mechanical Model: Quantum Numbers, Orbitals and Configuration – Moving electrons also behave like waves: λ = h/mv (de Broglie). Because of this we cannot know exact position and momentum together: Δx·Δp ≥ h/4π (Heisenberg). So we drop sharp orbits and use orbitals: regions where the electron is likely to be, from the Schrödinger equation (ψ² gives probability). Four quantum numbers describe each electron: n (shell, size, energy), l (subshell, shape: 0 to n−1), mₗ (orientation: −l to +l) and mₛ (spin: +½ or −½). s is spherical, p is dumbbell, d is mostly four-lobed. Electrons fill by the Aufbau (n + l) rule, Pauli principle (max 2, opposite spins) and Hund's rule (single first). Half-filled and fully filled subshells are extra stable, so Cr is 3d⁵4s¹ and Cu is 3d¹⁰4s¹.
- Periodic Trends in Properties – Two forces decide almost every trend: the pull of the nucleus (effective nuclear charge) and the distance of the outer shell. Across a period the nuclear pull grows while the shell stays the same, so atoms shrink, ionisation enthalpy rises, electron gain enthalpy becomes more negative and electronegativity rises. Down a group a new shell is added, so atoms grow and these values fall. Cations are smaller and anions bigger than their atoms. Valence follows the outer electrons; metallic reactivity is highest at the bottom left and non-metallic reactivity at the top right.
- Kossel-Lewis Approach and the Ionic Bond – Atoms join so that each gets a stable outer shell of 8 electrons (an octet), like a noble gas. Kossel said atoms can give or take electrons to make ions (ionic bond). Lewis said atoms can also share pairs of electrons (covalent bond). Lewis structures show these electrons as dots and lines. Formal charge (V − L − B/2) helps pick the best Lewis structure. Ions pack into a crystal, and the energy released is linked to the lattice enthalpy.
2. Compound Structure and Properties
Types of Chemical Bonds · Intramolecular Force and Potential Energy · Structure of Ionic Solids · Structure of Metals and Alloys · Lewis Diagrams · Resonance and Formal Charge · VSEPR and Hybridization
- Kossel-Lewis Approach and the Ionic Bond – Atoms join so that each gets a stable outer shell of 8 electrons (an octet), like a noble gas. Kossel said atoms can give or take electrons to make ions (ionic bond). Lewis said atoms can also share pairs of electrons (covalent bond). Lewis structures show these electrons as dots and lines. Formal charge (V − L − B/2) helps pick the best Lewis structure. Ions pack into a crystal, and the energy released is linked to the lattice enthalpy.
- Atoms and Molecules – In a chemical reaction mass is neither created nor destroyed (conservation of mass), and a compound always has its elements in the same ratio by mass (constant proportions). Dalton explained both: matter is made of tiny atoms that join in small whole numbers. Atoms join to form molecules; charged atoms or groups are ions. Formulae are written by crossing valencies. Molecular mass (or formula unit mass for ionic compounds) is the sum of the atomic masses in the formula, in u.
- Mole Concept, Molar Mass and Chemical Formulas – Atoms are far too small to count one by one, so chemists count them by weighing. Atomic masses are given in u, where 1 u is one-twelfth the mass of a carbon-12 atom. One mole is 6.022 × 10²³ particles, and its mass in grams equals the formula mass in u. With moles we can find the percentage of each element in a compound, and work back from percentages to the empirical and molecular formulas.
- Chemical Bonding: Ionic, Covalent and Metallic Bonds – Atoms join together (bond) to become more stable. Only their outer electrons take part. Most atoms are most stable with 8 outer electrons: the octet rule. There are three main ways to reach it. In an ionic bond, a metal gives electrons to a non-metal, making oppositely charged ions that attract. In a covalent bond, two non-metals share pairs of electrons to make molecules. In a metallic bond, metal atoms release outer electrons into a shared 'sea' that holds positive ions together. The difference in electronegativity (how strongly an atom pulls shared electrons) tells us which kind of bond forms. The type of bond explains melting points, whether a substance conducts electricity, and whether it dissolves in water.
- Bond Parameters, Resonance and Polarity – A covalent bond is described by four numbers: bond length (distance between nuclei), bond angle (angle between bonds at an atom), bond enthalpy (energy to break 1 mol of bonds) and bond order (number of shared pairs). Higher bond order means a shorter, stronger bond. When one Lewis structure cannot describe a molecule, the real molecule is a resonance hybrid of several structures. Unequal sharing makes a bond polar; the dipole moment μ = q × d measures it, and the shape decides whether bond dipoles cancel.
- VSEPR Theory: Shapes of Molecules – VSEPR stands for Valence Shell Electron Pair Repulsion. The electron pairs around a central atom repel each other and move as far apart as possible. The number of pairs sets the basic arrangement: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral. Lone pairs take more room than bond pairs (lp–lp > lp–bp > bp–bp), so they squeeze bond angles and change the shape we see, for example NH₃ (pyramidal, 107°) and H₂O (bent, 104.5°).
3. Properties of Substances and Mixtures
Intermolecular and Interparticle Forces · Properties of Solids · Solids, Liquids, and Gases · Ideal Gas Law · Kinetic Molecular Theory · Deviation from Ideal Gas Law · Solutions and Mixtures · Representations of Solutions · Separation of Solutions and Mixtures · Solubility · Spectroscopy and the Electromagnetic Spectrum · Properties of Photons · Beer-Lambert Law
- Hydrogen Bonding – A hydrogen bond is a weak attraction between an H atom that is joined to a small, very electronegative atom (F, O or N) and a lone pair on another such atom. It is shown with a dotted line: X–H···Y. It is much weaker than a covalent bond (about 10–40 kJ mol⁻¹) but strong enough to raise boiling points, make ice float and hold DNA together. Intermolecular H-bonds join different molecules; intramolecular H-bonds form inside one molecule.
- Intermolecular Forces – Intermolecular forces are weak attractions BETWEEN molecules. From weakest to strongest (for similar-size molecules): London dispersion < dipole–dipole < hydrogen bond. Stronger forces mean higher melting and boiling points, higher viscosity and surface tension, and they decide what dissolves in what.
- Perfect Gas Equation PV = nRT and Work in Compressing a Gas – A gas is made of countless tiny molecules flying about. Their hits on the walls make pressure. For a low-density gas, three simple laws hold: at fixed temperature, P × V stays constant (Boyle); at fixed pressure, V grows in step with kelvin temperature (Charles); at the same P and T, equal volumes hold equal numbers of molecules (Avogadro). Put together they give the perfect gas equation PV = nRT = N k T. One mole holds Avogadro's number, 6.022 × 10²³, of particles. Pushing a piston in does work on the gas; the work equals the area under the P–V graph, and at fixed temperature W = nRT ln(V₁/V₂).
- Kinetic Theory of Gases: Pressure, Temperature and rms Speed – Kinetic theory explains gas behaviour by picturing a gas as tiny, fast, randomly moving molecules that bounce elastically and do not pull on each other. Each hit on a wall reverses the molecule's velocity and hands the wall momentum 2mvₓ. Adding the hits of all molecules gives the pressure P = ⅓ n m v̄² = ⅓ ρ v̄². Comparing with PV = N k T shows that the average kinetic energy of a molecule is (3/2) k T: temperature is a measure of the average kinetic energy of the molecules. The root mean square speed is v_rms = √(3RT/M) = √(3kT/m), so lighter gases move faster at the same temperature.
- Gas Laws: How Pressure, Volume and Temperature Are Linked – Gas pressure comes from particles hitting the walls. For a fixed amount of gas: Boyle's law P₁V₁ = P₂V₂ (constant T); Charles's law V₁/T₁ = V₂/T₂ (constant P); pressure (Gay-Lussac's) law P₁/T₁ = P₂/T₂ (constant V). Temperature must be in kelvin. Combined: P₁V₁/T₁ = P₂V₂/T₂. Dalton's law: in a mixture, total pressure = sum of partial pressures, and each partial pressure = mole fraction × total pressure.
- Solutions: Types, Concentration and Henry's Law – A solution is an even mix of two or more substances. The part in bigger amount is the solvent, the smaller part is the solute. We tell 'how strong' a solution is with concentration terms: mass %, volume %, ppm, mole fraction, molarity (per litre of solution) and molality (per kg of solvent). Solids usually dissolve more when hot. Gases dissolve more when their pressure is high (Henry's law, p = KH·x) and less when it is hot.
- Solutions: How Things Dissolve and How Much Can Dissolve – A solution is a uniform mixture of a solute dissolved in a solvent. In water (an aqueous solution) the solute breaks into particles too small to see, so it never settles and passes through filter paper. Concentration tells how much solute is present (mass % = solute ÷ solution × 100). Solubility is the most that can dissolve in 100 g of solvent at a given temperature; beyond it the solution is saturated. Evaporation, crystallisation and distillation separate solutions.
- Electromagnetic Waves – A changing electric field acts like a current, called the displacement current, and it makes a magnetic field. A changing magnetic field makes an electric field. Together they travel as an electromagnetic (EM) wave at c = 3 × 10⁸ m/s, even through empty space. E and B are at right angles to each other and to the direction of travel, so EM waves are transverse. Sorted by wavelength, they form the spectrum: radio, microwave, infrared, visible, ultraviolet, X-rays and gamma rays.
- Spectroscopy and the Beer-Lambert Law – Spectroscopy studies how matter absorbs or gives out light. Light is made of photons with energy E = hf = hc/λ. Atoms give line spectra because electrons jump between fixed energy levels. A coloured solution absorbs its complementary colour. A spectrophotometer measures transmittance T = I/I₀ and absorbance A = log₁₀(I₀/I). The Beer-Lambert law says A = εlc, so a calibration line of A against c lets us find an unknown concentration.
4. Chemical Reactions
Introduction for Reactions · Net Ionic Equations · Representations of Reactions · Physical and Chemical Changes · Stoichiometry · Introduction to Titration · Types of Chemical Reactions · Introduction to Acid-Base Reactions · Oxidation-Reduction (Redox) Reactions
- Chemical Reactions: Equations, Types, Prediction and Coupled Reactions – A chemical reaction rearranges atoms into new substances; atoms and mass are conserved, so equations must balance. The same reaction can be written as a word equation, a balanced formula equation with state symbols, a full ionic equation or a net ionic equation that leaves out spectator ions. Reactions are sorted into types: synthesis, decomposition, single displacement, double displacement (precipitation, neutralisation, gas-forming), combustion, and by the particle that moves: electrons (redox) or protons (acid–base). Outer (valence) electrons let us predict what forms: metals lose electrons, non-metals gain them, and the numbers lost and gained must match. A reaction that cannot happen alone (ΔG > 0) can be driven by coupling it to a strongly favourable one so that the total ΔG is negative.
- Chemical Bonding: Ionic, Covalent and Metallic Bonds – Atoms join together (bond) to become more stable. Only their outer electrons take part. Most atoms are most stable with 8 outer electrons: the octet rule. There are three main ways to reach it. In an ionic bond, a metal gives electrons to a non-metal, making oppositely charged ions that attract. In a covalent bond, two non-metals share pairs of electrons to make molecules. In a metallic bond, metal atoms release outer electrons into a shared 'sea' that holds positive ions together. The difference in electronegativity (how strongly an atom pulls shared electrons) tells us which kind of bond forms. The type of bond explains melting points, whether a substance conducts electricity, and whether it dissolves in water.
- Kossel-Lewis Approach and the Ionic Bond – Atoms join so that each gets a stable outer shell of 8 electrons (an octet), like a noble gas. Kossel said atoms can give or take electrons to make ions (ionic bond). Lewis said atoms can also share pairs of electrons (covalent bond). Lewis structures show these electrons as dots and lines. Formal charge (V − L − B/2) helps pick the best Lewis structure. Ions pack into a crystal, and the energy released is linked to the lattice enthalpy.
- Acids, Bases, Salts and Titration – Inorganic compounds fall into four big classes: oxides, acids, bases and salts. They are linked: a metal makes a basic oxide, that makes a base, and a base plus an acid makes a salt and water. A titration uses this neutralisation to measure an unknown concentration: base of known concentration is added from a burette until all the acid is used up (the equivalence point). Then n(acid) = n(base) by the reaction ratio, so C₁V₁ = C₂V₂ for a 1 : 1 reaction.
- Stoichiometry, Limiting Reagent and Concentration Terms – Stoichiometry means measuring the amounts of substances in a reaction. A balanced equation acts like a recipe: its numbers give the mole ratio of reactants and products. With it you can change any mass into moles, use the ratio, and change back to the mass of any other substance. The reactant that runs out first is the limiting reagent; it decides how much product forms. For solutions, concentration is given as mass percent, mole fraction, molarity or molality.
- Acids and Bases: Properties, Indicators and Reactions – An acid gives H⁺ ions in water and a base gives OH⁻ ions. Indicators show which one is present by a colour or smell change, and when H⁺ meets OH⁻ they make water, leaving a salt behind.
- Redox Reactions: From Oxygen to Electron Transfer – Oxidation first meant adding oxygen or removing hydrogen. Reduction meant the opposite. Today we use a bigger idea: oxidation is losing electrons and reduction is gaining electrons. Both always happen together, so we call them redox reactions. A more active metal gives electrons to the ion of a less active metal.
5. Kinetics
Reaction Rates · Introduction to Rate Law · Concentration Changes Over Time · Elementary Reactions · Collision Model · Reaction Energy Profile · Introduction to Reaction Mechanisms · Reaction Mechanism and Rate Law · Pre-Equilibrium Approximation · Multistep Reaction Energy Profile · Catalysis
- Rate of a Chemical Reaction – The rate of a reaction tells how fast a reactant is used up or a product is made, per unit time. Rate = −Δ[R]/Δt = +Δ[P]/Δt (unit mol L⁻¹ s⁻¹). The rate law, rate = k[A]^x[B]^y, is found by experiment; x + y is the order. Molecularity is the number of particles that collide in one elementary step.
- Integrated Rate Equations: Zero and First Order – Integrated rate equations link concentration with time. Zero order: [R] = [R]₀ − kt (straight line), t½ = [R]₀/2k. First order: k = (2.303/t) log([R]₀/[R]), ln[R] falls in a straight line with slope −k, and t½ = 0.693/k, which does not depend on the starting amount.
- Temperature, Activation Energy, Catalysts and Collision Theory – Reactant molecules must climb an energy hill, the activation energy Ea, to become products. The Arrhenius equation k = A e^(−Ea/RT) shows that a small rise in temperature lets many more molecules cross, so k rises fast. A catalyst gives a lower hill without changing ΔH. Collision theory: molecules react only when they collide with enough energy and the right orientation.
6. Thermochemistry
Endothermic and Exothermic Processes · Energy Diagrams · Heat Transfer and Thermal Equilibrium · Heat Capacity and Calorimetry · Energy of Phase Changes · Introduction to Enthalpy of Reaction · Bond Enthalpies · Enthalpy of Formation · Hess's Law
- First Law of Thermodynamics: System, Heat, Work and ΔU – Thermodynamics tracks energy. The part we study is the system; the rest is the surroundings; the wall between them is the boundary. A system can be open, closed or isolated. Internal energy U is the total energy stored in the system. It changes only in two ways: by heat q or by work w. The first law says ΔU = q + w (IUPAC signs: q and w are positive when energy goes INTO the system). U is a state function; q and w are path functions. For expansion against a constant outside pressure, w = −p_ext ΔV; for a reversible isothermal expansion of an ideal gas, w = −2.303 nRT log(V₂/V₁).
- Enthalpy, Calorimetry and Hess's Law – Enthalpy H = U + pV. At constant pressure the heat taken in or given out equals ΔH; at constant volume it equals ΔU. We measure ΔU in a sealed bomb calorimeter and ΔH in an open cup calorimeter, using q = C ΔT or q = m c ΔT. For gases, ΔH = ΔU + Δn_g RT. The reaction enthalpy ΔrH is negative for exothermic and positive for endothermic reactions, and ΔrH° = ΣΔfH°(products) − ΣΔfH°(reactants). Hess's law: the total enthalpy change is the same whether a reaction happens in one step or many, so thermochemical equations can be added like algebra.
- Chemical Equilibrium: Kc, Kp, Q and Gibbs Energy – In a closed container a reversible reaction goes both ways. After some time the forward and backward rates become equal, so amounts stop changing, but the reaction does not stop. This is dynamic equilibrium. At equilibrium the ratio of products to reactants (each raised to its coefficient) is a fixed number, the equilibrium constant K. Kc uses concentrations, Kp uses partial pressures, and Kp = Kc(RT)^Δn. Pure solids and liquids are left out of K. The reaction quotient Q tells the direction: Q < K goes forward, Q > K goes backward, Q = K is equilibrium. K and Gibbs energy are linked: ΔG = ΔG° + RT ln Q and ΔG° = −RT ln K.
- Acids, Bases, Salts and Titration – Inorganic compounds fall into four big classes: oxides, acids, bases and salts. They are linked: a metal makes a basic oxide, that makes a base, and a base plus an acid makes a salt and water. A titration uses this neutralisation to measure an unknown concentration: base of known concentration is added from a burette until all the acid is used up (the equivalence point). Then n(acid) = n(base) by the reaction ratio, so C₁V₁ = C₂V₂ for a 1 : 1 reaction.
- Enthalpies of Different Types of Reactions – Each kind of change has its own named enthalpy, always for 1 mol. Phase changes: fusion (melting), vaporisation (boiling) and sublimation (ΔsubH = ΔfusH + ΔvapH); all are endothermic. Combustion: 1 mol burns completely in oxygen; always exothermic. Atomisation: 1 mol of a substance breaks fully into gaseous atoms. Bond dissociation enthalpy: 1 mol of a given bond is broken in the gas phase; for polyatomic molecules we use mean bond enthalpy. ΔrH ≈ Σ(bonds broken) − Σ(bonds formed). Lattice enthalpy: 1 mol of an ionic solid is split into gaseous ions (found by a Born–Haber cycle). Enthalpy of solution = lattice enthalpy + hydration enthalpy.
7. Equilibrium
Introduction to Equilibrium · Direction of Reversible Reactions · Reaction Quotient and Equilibrium Constant · Calculating the Equilibrium Constant · Magnitude of the Equilibrium Constant · Properties of the Equilibrium Constant · Calculating Equilibrium Concentrations · Representations of Equilibrium · Introduction to Le Châtelier's Principle · Reaction Quotient and Le Châtelier's Principle · Introduction to Solubility Equilibria · Common-Ion Effect
- Chemical Equilibrium: Kc, Kp, Q and Gibbs Energy – In a closed container a reversible reaction goes both ways. After some time the forward and backward rates become equal, so amounts stop changing, but the reaction does not stop. This is dynamic equilibrium. At equilibrium the ratio of products to reactants (each raised to its coefficient) is a fixed number, the equilibrium constant K. Kc uses concentrations, Kp uses partial pressures, and Kp = Kc(RT)^Δn. Pure solids and liquids are left out of K. The reaction quotient Q tells the direction: Q < K goes forward, Q > K goes backward, Q = K is equilibrium. K and Gibbs energy are linked: ΔG = ΔG° + RT ln Q and ΔG° = −RT ln K.
- Le Chatelier's Principle: Factors Affecting Equilibrium – Le Chatelier's principle says: if you disturb a system at equilibrium, it shifts in the direction that reduces the disturbance. Add a reactant or remove a product → shifts forward. Increase pressure (smaller volume) → shifts to the side with fewer gas moles. Raise temperature → shifts in the heat-absorbing (endothermic) direction, and K changes. A catalyst only helps reach equilibrium faster; it does not move it. Inert gas at constant volume does nothing; at constant pressure it acts like lowering pressure. Only temperature changes the value of K.
- Buffer Solutions and Solubility Product – A buffer is a solution that keeps its pH nearly the same when a little acid or base is added. An acidic buffer is a weak acid with its salt (CH₃COOH + CH₃COONa); a basic buffer is a weak base with its salt (NH₄OH + NH₄Cl). Its pH is given by the Henderson equation: pH = pKa + log([salt]/[acid]). A sparingly soluble salt in its saturated solution sets up an equilibrium with its ions; the product of ion concentrations (each raised to its coefficient) is the solubility product Ksp. For AB, Ksp = s²; for AB₂ or A₂B, Ksp = 4s³. If the ionic product Q exceeds Ksp, a precipitate forms. A common ion lowers solubility.
8. Acids and Bases
Introduction to Acids and Bases · pH and pOH of Strong Acids and Bases · Weak Acid and Base Equilibria · Acid-Base Reactions and Buffers · Acid-Base Titrations · Molecular Structure of Acids and Bases · pH and pKa · Properties of Buffers · Henderson-Hasselbalch Equation · Buffer Capacity · pH and Solubility
- Ionic Equilibrium: Acids, Bases, Ionisation and pH – Acids and bases can be defined in three ways: Arrhenius (give H⁺ or OH⁻ in water), Brønsted–Lowry (proton donor or acceptor) and Lewis (electron-pair acceptor or donor). Strong acids and bases ionise fully; weak ones ionise only a little and set up an equilibrium with constant Ka or Kb. Water itself ionises: Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. pH = −log[H⁺] and pH + pOH = 14. For a weak electrolyte, α ≈ √(K/C), so dilution increases α (Ostwald's dilution law). For a conjugate pair, Ka × Kb = Kw. Salts of weak acids or weak bases react with water (hydrolysis) and give non-neutral solutions.
- Buffer Solutions and Solubility Product – A buffer is a solution that keeps its pH nearly the same when a little acid or base is added. An acidic buffer is a weak acid with its salt (CH₃COOH + CH₃COONa); a basic buffer is a weak base with its salt (NH₄OH + NH₄Cl). Its pH is given by the Henderson equation: pH = pKa + log([salt]/[acid]). A sparingly soluble salt in its saturated solution sets up an equilibrium with its ions; the product of ion concentrations (each raised to its coefficient) is the solubility product Ksp. For AB, Ksp = s²; for AB₂ or A₂B, Ksp = 4s³. If the ionic product Q exceeds Ksp, a precipitate forms. A common ion lowers solubility.
- Acids, Bases, Salts and Titration – Inorganic compounds fall into four big classes: oxides, acids, bases and salts. They are linked: a metal makes a basic oxide, that makes a base, and a base plus an acid makes a salt and water. A titration uses this neutralisation to measure an unknown concentration: base of known concentration is added from a burette until all the acid is used up (the equivalence point). Then n(acid) = n(base) by the reaction ratio, so C₁V₁ = C₂V₂ for a 1 : 1 reaction.
- Atoms and Molecules – In a chemical reaction mass is neither created nor destroyed (conservation of mass), and a compound always has its elements in the same ratio by mass (constant proportions). Dalton explained both: matter is made of tiny atoms that join in small whole numbers. Atoms join to form molecules; charged atoms or groups are ions. Formulae are written by crossing valencies. Molecular mass (or formula unit mass for ionic compounds) is the sum of the atomic masses in the formula, in u.
- Mole Concept, Molar Mass and Chemical Formulas – Atoms are far too small to count one by one, so chemists count them by weighing. Atomic masses are given in u, where 1 u is one-twelfth the mass of a carbon-12 atom. One mole is 6.022 × 10²³ particles, and its mass in grams equals the formula mass in u. With moles we can find the percentage of each element in a compound, and work back from percentages to the empirical and molecular formulas.
9. Thermodynamics and Electrochemistry
Introduction to Entropy · Absolute Entropy and Entropy Change · Gibbs Free Energy and Thermodynamic Favorability · Thermodynamic and Kinetic Control · Free Energy and Equilibrium · Free Energy of Dissolution · Coupled Reactions · Galvanic (Voltaic) and Electrolytic Cells · Cell Potential and Free Energy · Cell Potential Under Nonstandard Conditions · Electrolysis and Faraday's Law
- Spontaneity, Entropy and Gibbs Energy – A spontaneous process happens by itself, without outside help (it may be fast or slow). ΔH alone cannot predict it: ice melts on its own although it takes in heat. Entropy S measures how spread out energy and matter are; ΔS = q_rev/T. Second law: for any spontaneous change, ΔS_total = ΔS_system + ΔS_surroundings > 0; at equilibrium it is zero. Third law: a perfect crystal at 0 K has zero entropy. Gibbs energy G = H − TS combines both: at constant T and p, ΔG = ΔH − TΔS, and ΔG < 0 means spontaneous, ΔG = 0 means equilibrium. It links to the equilibrium constant by ΔG° = −RT ln K = −2.303 RT log K.
- First Law of Thermodynamics – Internal energy U is the total energy of the molecules inside a system. It changes in only two ways: by heat Q (energy that flows because of a temperature difference) and by work W (energy moved by a force, like a moving piston). First law: ΔQ = ΔU + ΔW. Heat given to a gas partly raises its internal energy and partly lets it do work. Work by a gas at constant pressure is PΔV. For an ideal gas Cp − Cv = R.
- Solutions: How Things Dissolve and How Much Can Dissolve – A solution is a uniform mixture of a solute dissolved in a solvent. In water (an aqueous solution) the solute breaks into particles too small to see, so it never settles and passes through filter paper. Concentration tells how much solute is present (mass % = solute ÷ solution × 100). Solubility is the most that can dissolve in 100 g of solvent at a given temperature; beyond it the solution is saturated. Evaporation, crystallisation and distillation separate solutions.
- Chemical Reactions: Equations, Types, Prediction and Coupled Reactions – A chemical reaction rearranges atoms into new substances; atoms and mass are conserved, so equations must balance. The same reaction can be written as a word equation, a balanced formula equation with state symbols, a full ionic equation or a net ionic equation that leaves out spectator ions. Reactions are sorted into types: synthesis, decomposition, single displacement, double displacement (precipitation, neutralisation, gas-forming), combustion, and by the particle that moves: electrons (redox) or protons (acid–base). Outer (valence) electrons let us predict what forms: metals lose electrons, non-metals gain them, and the numbers lost and gained must match. A reaction that cannot happen alone (ΔG > 0) can be driven by coupling it to a strongly favourable one so that the total ΔG is negative.
- Galvanic Cells and the Nernst Equation – A galvanic cell turns the energy of a redox reaction into electricity. Oxidation happens at the anode (−) and reduction at the cathode (+). Each electrode has a potential measured against the standard hydrogen electrode (0 V). E°cell = E°cathode − E°anode. The Nernst equation, E = E° − (0.059/n) log Q at 298 K, gives the cell voltage at any concentration, and ΔG = −nFE links voltage to energy.
- Electrolysis, Batteries, Fuel Cells and Corrosion – In an electrolytic cell an outside source of electricity forces a non-spontaneous reaction: cations are reduced at the cathode (−) and anions oxidised at the anode (+). Faraday's laws link the mass changed to the charge: m = (M/nF) × I × t. Which product forms depends on electrode potentials and overpotential. Batteries are galvanic cells: primary (dry cell, mercury cell) cannot be recharged; secondary (lead storage, Ni–Cd) can. Fuel cells burn H₂ with O₂ to give electricity directly. Corrosion (rusting) is an unwanted galvanic cell on the metal surface.