THE LESSON LIBRARY / CHEMISTRY
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Average Bond Enthalpy Estimates
Average bond enthalpies provide a quick estimate of reaction enthalpy when detailed formation data are unavailable. The method counts bonds broken in gaseous reactants and bonds…
Explore lesson ChemistryLessonAverage Molar Mass of Gas Mixtures
A gas mixture has one total mass and one total mole amount, even though its molecules have different masses. Dividing the two gives a mean molar mass. This quantity links…
Explore lesson ChemistryLessonAvogadro's Gas Hypothesis
Equal volumes of two different gases do not generally have equal masses, but at the same temperature and pressure they contain equal numbers of molecules in the ideal-gas model.…
Explore lesson ChemistryLessonAvogadro's Law for Gas Volume
Adding more gas to a container with a movable boundary can make the gas occupy more volume. Under fixed pressure and temperature, the ideal-gas equation predicts volume…
Explore lesson ChemistryLessonAxial and Equatorial Positions
A cyclohexane chair has two kinds of substituent positions at every carbon. Axial bonds point roughly up or down along the ring axis; equatorial bonds project outward around the…
Explore lesson ChemistryLessonAxial Chirality in Allenes and Biphenyls
The four-different-groups carbon is a common source of chirality, not the only one. An allene can be chiral because its terminal substituents occupy perpendicular planes around a…
Explore lesson ChemistryLessonAzeotropes and Distillation Limits — Solutions and Colligative Properties
Ordinary distillation separates volatile liquids because their vapour composition differs from their liquid composition. An azeotrope is a special composition at which the…
Explore lesson ChemistryLessonAzeotropes and Distillation Limits — Statistical Thermodynamics and Phase Equilibria
Distillation relies on vapour being compositionally different from the liquid. At an azeotrope, the coexisting vapour and liquid have the same composition. Ordinary equilibrium…
Explore lesson ChemistryLessonAzo Coupling
An arenediazonium ion need not lose N₂. With an electron-rich aromatic ring, it can form a new C–N bond while keeping both nitrogens in an azo bridge, Ar–N=N–Ar′. This is azo…
Explore lesson ChemistryLessonAzo Coupling with Arylamines
Aniline and other arylamines can serve as the electron-rich aromatic partner in azo coupling. The free amino group donates electron density into the ring, favouring attack at…
Explore lesson ChemistryLessonAzo Coupling with Phenols
Arenediazonium ions can couple with electron-rich aromatic rings instead of losing N₂. Phenols are common partners because oxygen donation activates the ring. The reaction forms…
Explore lesson ChemistryLessonAzo Dyes and Conjugation
Many azo compounds contain an Ar–N=N–Ar′ framework joining two aromatic rings. The alternating p-orbital network can delocalise electron density over much of the molecule, often…
Explore lesson ChemistryLessonBack Titrations
Some analytes react too slowly, dissolve poorly or lack a convenient direct endpoint. A back titration adds a known excess of reagent, allows it to react with the sample, then…
Explore lesson ChemistryLessonBackbone Torsion Angles and Ramachandran Plots
Peptide bonds are nearly planar, so much of a protein chain's local flexibility lies in two neighbouring single bonds. The corresponding dihedral angles, phi (φ) and psi (ψ)…
Explore lesson ChemistryLessonBackground Radiation and Measurement
A radiation detector can register events even when the source being studied is absent. Those events make up a background count that must be measured if we want to estimate a weak…
Explore lesson ChemistryLessonBaeyer–Villiger Oxidation
Baeyer–Villiger oxidation inserts one oxygen into a ketone's carbon skeleton, converting a ketone to an ester. If the ketone is cyclic, the inserted oxygen becomes part of a…
Explore lesson ChemistryLessonBalance Before Calculating
Stoichiometric arithmetic can be neat and still wrong if its equation is unbalanced. A missing coefficient changes the predicted reagent need and product amount. Balancing is…
Explore lesson ChemistryLessonBalanced Equations as Amount Maps
A balanced equation does more than name reactants and products. Its coefficients map the relative numbers of particles and therefore the relative mole amounts that react or form.…
Explore lesson ChemistryLessonBalancing by Inspection: The Basic Method
Balancing by inspection is a controlled cycle of counting, adjusting and checking. It works well for many classroom equations without advanced algebra. The method succeeds when…
Explore lesson ChemistryLessonBalancing Carbonate and Acid Reactions
Acid–carbonate equations can look crowded because they have three products. The reliable method is to determine the correct salt, keep water and carbon dioxide in the account and…
Explore lesson ChemistryLessonBalancing Charge as Well as Atoms
Atoms must balance in every chemical equation. When ions appear, electric charge must also balance. A missing coefficient may leave an attractive-looking atom tally but an…
Explore lesson ChemistryLessonBalancing Combustion Equations
Combustion equations are among the most common equations you will be asked to balance, and they can look awkward: oxygen appears in both products, and the numbers often come out…
Explore lesson ChemistryLessonBalancing Combustion of Alcohols
An alcohol fuel contains oxygen as well as carbon and hydrogen. The carbon-first, hydrogen-second strategy still works, but oxygen from the fuel contributes to the products.…
Explore lesson ChemistryLessonBalancing Combustion of Hydrocarbons
Complete combustion of a hydrocarbon follows one clear product pattern: carbon dioxide and water. The fuel's carbon and hydrogen counts determine those product coefficients, and…
Explore lesson ChemistryLessonBalancing Decomposition Reactions
Decomposition equations have one chemical reactant but may have two or more product substances. Balancing them requires the same element-by-element audit as any other reaction. A…
Explore lesson ChemistryLessonBalancing Displacement Reactions
Displacement equations have a free element on each side: one enters a compound and another leaves. Balancing often involves a diatomic halogen or a new salt formula. The correct…
Explore lesson ChemistryLessonBalancing Equations Across Reaction Types
Knowing a reaction's type can help predict product formulas, but it does not automatically balance the equation. Every atom present before the reaction must appear afterward.…
Explore lesson ChemistryLessonBalancing Metal and Acid Reactions
Balancing a metal–acid equation requires more than placing hydrogen on the right. The metal's ionic charge and the acid-derived anion determine the salt formula, while elemental…
Explore lesson ChemistryLessonBalancing Metal Displacement Equations
Simple Zn/Cu²⁺ displacement is 1:1, but other metal pairs require less obvious coefficients. A reliable method writes oxidation and reduction half-equations, matches the electron…
Explore lesson ChemistryLessonBalancing Neutralisation Equations
In familiar acid–hydroxide neutralisations, acidic hydrogen and hydroxide combine to form water while the other ions give a salt. Balancing these equations requires correct…
Explore lesson ChemistryLessonBalancing Nuclear Equations
Nuclear equations use small numbers in the upper and lower left corners of symbols, and each has a different job. The upper number A counts nucleons; the lower number Z…
Explore lesson ChemistryLessonBalancing Precipitation Reactions
Mixing two aqueous salts can form an insoluble solid while other ions remain dissolved. A precipitation equation names and balances both products, not just the visible solid.…
Explore lesson ChemistryLessonBalancing Redox in Acidic Solution
Simple metal-ion half-reactions need only electrons to balance charge. Oxyanions require additional oxygen and hydrogen atoms. In an acidic aqueous equation, water can supply or…
Explore lesson ChemistryLessonBalancing Redox in Basic Solution
The acidic half-reaction method gives a convenient way to balance oxygen and hydrogen, but a final equation for basic solution should not leave H⁺ as a reactant. Add enough OH⁻…
Explore lesson ChemistryLessonBalancing Simple Metal–Ion Half-Reactions
Simple metal–ion half-reactions are an ideal place to practise the rules of chemical balancing. The metal atom count stays the same, but the ion's charge changes. Electrons…
Explore lesson ChemistryLessonBalancing Simple Synthesis Reactions
Simple synthesis equations combine reactants into one named product. They are useful early balancing exercises because there are few formulas, but a short equation can still…
Explore lesson ChemistryLessonBalancing with Polyatomic Ions as Units
When the same polyatomic ion appears intact on both sides of an equation, counting it as a block can make inspection faster. Sulfate, nitrate and hydroxide are familiar examples.…
Explore lesson ChemistryLessonBand Alignment at Solar-Cell Interfaces
Absorbing sunlight creates electrons and holes, but a solar cell only produces useful power when they reach different electrical contacts. The interfaces between absorber…
Explore lesson ChemistryLessonBand Broadening and the van Deemter Equation
Even if two compounds move at different average speeds, their peaks can overlap if each band spreads too widely. Column efficiency describes how narrow the peaks remain during…
Explore lesson ChemistryLabBand formation
Atomic energy levels spread into bands as more atoms join a chain.
Explore lesson ChemistryLessonBand Intensities and Band Widths
Two absorption peaks at similar wavelengths can have very different meanings. A weak, broad feature may be a ligand-field transition; a strong band may involve charge transfer.…
Explore lesson ChemistryLessonBand Structure Diagrams
An electronic band structure is often drawn as many curved lines over a labelled path through a Brillouin zone. It is tempting to read it like a familiar molecular-orbital…
Explore lesson ChemistryLessonBand Theory of Main-Group Solids
Carbon, silicon, germanium and tin each have four valence electrons, yet their elemental solids span wide-gap insulating, semiconducting and metallic behaviours. The difference…
Explore lesson ChemistryLessonBand Theory: Checkpoint Review
Band theory has several starting points that can look contradictory. A free-electron picture ignores the ions; nearly-free theory brings in a weak periodic potential; tight…
Explore lesson ChemistryLessonBands in Transition-Metal Compounds
Transition-metal compounds can be metallic, semiconducting, magnetic or insulating even when elementary electron counting predicts a partly filled d-derived band. Their d…
Explore lesson ChemistryLessonBarrier Protection Against Corrosion
A paint, polymer or other coating can protect metal by keeping water, oxygen and aggressive ions away from its surface. Barrier protection is straightforward in principle but…
Explore lesson ChemistryLessonBase and Water Equilibrium Data
Tables often place Ka, Kb and Kw on separate pages, but these values are linked. A base and its conjugate acid cannot be assigned arbitrary constants at the same temperature and…
Explore lesson ChemistryLessonBase Behavior in Water
Bases are commonly associated with hydroxide ions, but not every base contains OH in its formula. Sodium hydroxide supplies hydroxide when it dissolves; ammonia produces…
Explore lesson ChemistryLessonBase-Promoted Ester Hydrolysis
An ester can be hydrolysed by hydroxide in a process often called saponification. Hydroxide attacks the acyl carbon, the tetrahedral intermediate collapses and an alkoxy group…
Explore lesson ChemistryLessonBases and Alkalis Around Us
Acids are only half of the story. The soap you wash your hands with, the baking soda that makes a cake rise and the tablet you might take for indigestion all belong to a second…
Explore lesson ChemistryLessonBasis Sets and the Road to Computational Chemistry
Every idea in the variation principle — trial functions, adjustable parameters, linear combinations and secular determinants — comes together in modern computational chemistry.…
Explore lesson ChemistryLessonBasis-Set Convergence and Extrapolation
An electronic energy changes when the basis is enlarged because the calculation can represent a wider variety of orbital shapes. The *complete-basis-set* or CBS limit asks what…
Explore lesson ChemistryLessonBasis-Set Size and Systematic Improvement
Choosing an electronic-structure method is only half of a calculation. The basis defines which spatial shapes that method can use. A minimal basis can be useful for a fast…
Explore lesson ChemistryLessonBasis-Set Superposition Error
A weak complex can appear more stable than it really is because its fragments gain access to one another's basis functions. In a finite atom-centered basis, the calculation on AB…
Explore lesson ChemistryLessonBatch Planning from a Target Product Mass
Stoichiometry can plan a batch before reagents are measured. Start with the desired product mass, convert it to moles, and reverse the balanced coefficient ratio to find…
Explore lesson ChemistryLessonBatch versus Continuous Processes
Two plants can carry out the same balanced reaction in different operating modes. A batch vessel starts with a charge, reacts for a defined period and is then emptied. A…
Explore lesson ChemistryLessonBatteries and Cell Chemistry
A battery uses one or more electrochemical cells to supply useful current. Its output depends on specific redox couples, electrolyte, separator, and electrode design. Primary…
Explore lesson ChemistryLessonBattery Capacity and Energy Metrics
Battery performance numbers change meaning when the denominator changes. A cathode may report high mAh g⁻¹, an electrode may deliver several mAh cm⁻², and a packaged cell may be…
Explore lesson ChemistryLessonBattery Degradation and Safety
A rechargeable battery changes slowly even when every intended discharge reaction is nominally reversible. Side reactions consume lithium, electrodes lose usable structure, and…
Explore lesson ChemistryLessonBattery Degradation Diagnosis
An aging battery often stores less charge, delivers less power or both. The same observed capacity fade can have different causes. Lithium can be consumed in interphase products…
Explore lesson ChemistryLessonBattery Fundamentals and Performance Metrics
A battery can be described as high-voltage, high-capacity or high-power, but those claims refer to different physical quantities. Capacity counts stored charge, energy accounts…
Explore lesson ChemistryLessonBattery Power and Rate Performance
A battery can store substantial energy but release it too slowly for a particular task. Power concerns how fast electrical energy can be delivered, and its instantaneous value is…
Explore lesson ChemistryLessonBattery Safety and Thermal Stability
Battery safety is a system outcome. Heat can arise from high current, an internal short or an external hot environment; rising temperature can then accelerate chemical reactions…
Explore lesson ChemistryLessonBattery Voltage and Capacity
A phone battery label might read "3.85 V, 4500 mA h, 17.3 W h". Each of those three numbers answers a different question. The voltage tells you how much energy each unit of…
Explore lesson ChemistryLessonBattery Voltage from Chemical Potentials
A battery voltage is not a fixed label printed by chemistry alone. It represents the reversible electrical work available per unit charge for a specified reaction and…
Explore lesson ChemistryLessonBeckmann Rearrangement
An oxime made from a ketone can rearrange into an amide under strongly activating acidic conditions. In the Beckmann rearrangement, one carbon substituent migrates from the oxime…
Explore lesson ChemistryLessonBeer–Lambert Calculations
The Beer–Lambert law is simple to write but appears in examinations and laboratories inside longer calculations. You may be given a percentage transmittance rather than an…
Explore lesson ChemistryLessonBeetroot, Tea and Berry Indicators
A kitchen is full of hidden indicators. Squeeze lemon into a cup of black tea and it turns lighter. Bake blueberry muffins with too much baking soda and the berries can turn…
Explore lesson ChemistryLessonBenchmarking Against Experiment
“The calculation agrees with experiment” is meaningful only if both numbers describe the same property. An electronic energy at 0 K is not automatically a 298-K solution Gibbs…
Explore lesson ChemistryLessonBenefits and Drawbacks of Hard Water
Hard water is often described as a nuisance: it wastes soap, leaves scum and furs up kettles. Yet many people prefer the taste of hard water, and it brings some real benefits for…
Explore lesson ChemistryLessonBenzene and Aromatic Rings: An Introduction
In 1825 Michael Faraday isolated a liquid from the oily residue of gas lighting. Its formula, C₆H₆, puzzled chemists for decades: six carbon atoms but only six hydrogens suggests…
Explore lesson ChemistryLessonBenzene as a Distinct Carbon Ring
Benzene C₆H₆ is often drawn as a hexagon with alternating single and double lines. That drawing is a useful valence representation, but the real molecule has delocalized pi…
Explore lesson ChemistryLessonBenzene Pi Molecular Orbitals
Closing a six-site conjugated chain into a ring changes the Hückel matrix because carbon 6 now couples directly to carbon 1. This cyclic connection creates characteristic…
Explore lesson ChemistryLessonBenzene Structure and Aromaticity
Benzene, C₆H₆, is often drawn as a hexagon with alternating single and double bonds. That drawing is useful for electron bookkeeping but should not be read as three fixed…
Explore lesson ChemistryLessonBenzyne Pathway Introduction
An unactivated aryl halide usually resists the addition–elimination SNAr route because no strong electron-withdrawing group stabilises a Meisenheimer intermediate. Under much…
Explore lesson ChemistryLessonBeryllium's Anomalous Chemistry
Beryllium sits above magnesium in group 2 and has two valence electrons, yet its compounds do not always follow the simplest alkaline-earth pattern. Its very small atom and…
Explore lesson ChemistryLessonBeta Decay, Neutrinos and Energy Spectra
An alpha emitter can produce a relatively sharp particle-energy line for a given daughter state, but beta electrons or positrons from one nuclear transition leave with a spread…
Explore lesson ChemistryLessonBeta-Minus Emission
Alpha decay removes a four-nucleon cluster, but beta-minus decay changes one kind of nucleon into another. A neutron becomes a proton, and an electron and an electron…
Explore lesson ChemistryLessonBeta-Plus Emission
Some proton-rich nuclides can change a proton into a neutron and emit a positron. This is beta-plus decay. It is related to beta-minus decay but moves atomic number in the…
Explore lesson ChemistryLessonBeyond Bohr: A Preview of Orbitals
The words orbit and orbital look similar but mean different things. A classical orbit is a path followed through space. An atomic orbital belongs to a quantum description that…
Explore lesson ChemistryLessonBeyond Lithium-Ion: Solid-State, Sodium and Lithium–Sulfur
“Beyond lithium-ion” describes several different research directions, not one replacement chemistry. Solid-state designs change the electrolyte and often consider lithium metal…
Explore lesson ChemistryLessonBeyond Qualitative Crystal Field Theory
A diagram that merely puts three d orbitals below two others explains why a complex might absorb light. Advanced coordination chemistry asks harder questions: how large is the…
Explore lesson ChemistryLessonBidentate and Polydentate Ligands
Some ligands hold a metal through two or more donor atoms at once. Ethylenediamine, abbreviated en, is a classic bidentate ligand; EDTA can use several donors. These ligands form…
Explore lesson ChemistryLessonBinary Liquid–Liquid Equilibrium
Two liquids do not always mix into one phase at every composition. At a particular temperature, an intermediate overall composition may separate into an A-rich liquid and a…
Explore lesson ChemistryLessonBinary Solid–Liquid Equilibrium
Cooling a mixture of two substances can produce a pure or nearly pure solid of one component before the remaining liquid reaches a special eutectic composition. At the eutectic…
Explore lesson ChemistryLessonBinary Vapour–Liquid Equilibrium
A binary liquid generally evaporates into a vapour with a different composition. This difference makes distillation possible. A phase diagram displays both the liquid composition…
Explore lesson ChemistryLabBinding energy curve
The binding energy per nucleon curve: why fusion and fission both release energy.
Explore lesson ChemistryLessonBioaccumulation and Biomagnification
An extremely low dissolved concentration can coexist with a much higher concentration in fish tissue. This need not violate conservation of mass: an organism processes large…
Explore lesson ChemistryLessonBiocatalysis: Enzymes as Green Catalysts
Enzymes are catalysts evolved to recognize molecules and promote specific transformations. Their active sites can distinguish functional groups or mirror-image substrates with…
Explore lesson ChemistryLessonBiochemical Network Models
Living cells run many coupled reactions at once. Enzymes shape rates, metabolites form pools, and regulation redistributes flux when nutrient supply or demand changes. A…
Explore lesson ChemistryCollectionBiochemistry
Study Biochemistry with 50 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonBiochemistry and Environmental Practice
Biochemistry and environmental chemistry both follow molecules through networks. A metabolite's concentration is not the same as its rate of transformation, and a pollutant's…
Explore lesson ChemistryLessonBiochemistry and Materials Map
Biochemistry and materials chemistry seem far apart in scale, yet both ask how structure gives rise to function. An enzyme's amino-acid sequence influences folding, active-site…
Explore lesson ChemistryLessonBiochemistry as Molecular Chemistry
Biochemistry applies the same chemical principles used for laboratory reactions to living systems, but with an added layer of organisation. Molecules are compartmentalised…
Explore lesson ChemistryLessonBiochemistry Terms
Biochemistry uses ordinary chemical ideas inside organized living systems. The vocabulary spans small building blocks, large polymers, catalysts and networks of reactions. An…
Explore lesson ChemistryLessonBiochemistry, Environmental and Materials Chemistry
Some of the most exciting chemistry today happens where chemistry meets other subjects. Biochemistry connects chemistry with biology and medicine. Environmental chemistry…
Explore lesson ChemistryLessonBiochemistry: Unit Review
Biochemistry connects chemistry at several scales. Amino-acid side chains and peptide bonds constrain protein shapes; those shapes create enzyme active sites; enzyme kinetics and…
Explore lesson ChemistryLessonBiodegradable and Sustainable Polymers
The words “biobased,” “biodegradable” and “compostable” often appear together, but they answer different questions. One describes feedstock origin, another a possible biological…
Explore lesson ChemistryCollectionBioinorganic Chemistry
Study Bioinorganic Chemistry with 30 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonBioinorganic Chemistry: Unit Review
Metal ions give proteins chemical capabilities that ordinary carbon, hydrogen, nitrogen and oxygen frameworks often cannot supply alone: accessible oxidation states, strong Lewis…
Explore lesson ChemistryLessonBioinorganic Problem-Solving Workshop
Bioinorganic chemistry problems rarely ask only for a metal's oxidation state. An oxygen carrier combines coordination, ligand binding and protein conformation. A redox enzyme…
Explore lesson ChemistryLessonBiological Ligands and Coordination Sites
A metal ion's biological role depends strongly on the atoms immediately around it. Protein side chains provide nitrogen, oxygen or sulfur donors; water and small-molecule…
Explore lesson ChemistryLessonBiological Redox and Reduction Potentials
Cells harvest free energy by moving electrons from nutrient-derived donors toward acceptors with more favourable reduction potentials. The language of oxidation and reduction can…
Explore lesson ChemistryLabBiomolecule builder
Build a peptide from amino acids and watch it fold into an α-helix — or unfold when heated.
Explore lesson ChemistryLessonBiomolecules and Macromolecules
Living systems use the same atoms and chemical bonds studied elsewhere in chemistry, but arrange them into molecules with remarkable functional specificity. A small change in a…
Explore lesson ChemistryCollectionBiomolecules and Polymers
Study Biomolecules and Polymers with 30 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonBiomolecules and Polymers: Unit Review
Biomolecules and synthetic polymers reveal the same central lesson: atom counts alone do not determine function. Connectivity, stereochemistry, sequence, chain length, folding…
Explore lesson ChemistryLessonBisulfite Addition Compounds
Some aldehydes and ketones form addition compounds with hydrogen sulfite ions, HSO₃⁻. The carbonyl C=O becomes a tetrahedral carbon bearing an OH group and a sulfur-containing…
Explore lesson ChemistryLessonBlackbody Radiation and Quantization
A heated object emits a broad range of electromagnetic radiation. The pattern of intensity across wavelengths changes with temperature, and classical predictions failed badly at…
Explore lesson ChemistryLessonBlast-Furnace Reduction Equations
Blast-furnace chemistry is commonly taught through several linked equations. Carbon burns, hot carbon-containing gas can form CO, and CO reduces iron oxide. The equations should…
Explore lesson ChemistryLessonBleaching and Disinfection Chemistry
Chlorine-derived oxidants can remove color from some dyes and inactivate microorganisms, but the chemistry is more specific than “chlorine turns everything white.” Hypochlorous…
Explore lesson ChemistryLessonBleaching Powder and Chlorine-Based Products
Bleaching powder is often introduced with a single school formula, yet commercial chlorinated-lime products can be mixtures whose composition varies. Their useful action comes…
Explore lesson ChemistryLessonBloch's Theorem
The free-electron model ignores the crystal's periodic ionic potential. An actual electron sees a landscape repeated from cell to cell. Solving Schrödinger's equation…
Explore lesson ChemistryLessonBlocks and the Filling of Subshells
The familiar periodic table has a narrow left region, a broad right region, a middle rectangle and two rows displayed below. These are called the s, p, d and f blocks. The labels…
Explore lesson ChemistryLessonBlocks of the Periodic Table
Look at the shape of the periodic table: a tall pair of columns on the left, a wide section on the right, a low central area and two long rows floating underneath. That odd shape…
Explore lesson ChemistryLessonBody-Centered Cubic Packing
Body-centered cubic packing adds a particle at the centre of a cube to the corner array. In a monatomic BCC crystal, the central and corner points are equivalent under lattice…
Explore lesson ChemistryLabBohr atom builder
Build any atom or ion from protons, neutrons and electrons, and see what it is.
Explore lesson ChemistryLessonBohr Energies and Spectral Transitions
The Bohr energy formula turns integer hydrogen levels into numerical photon predictions. Its sign convention and the distinction between atom energy change and photon energy are…
Explore lesson ChemistryLessonBohr Model of Hydrogen
Bohr proposed an early solution to the hydrogen spectrum: the electron could occupy only certain allowed states and would emit or absorb light when changing between them. The…
Explore lesson ChemistryLessonBohr's Energy-Level Model
The nuclear atom explained scattering but not stable electrons or hydrogen's separated spectral lines. Bohr added a restriction: a hydrogen electron can occupy only certain…
Explore lesson ChemistryLessonBohr's Model of the Atom
Bohr's model kept the small positive nucleus but changed the rules used for electrons. Only selected states were allowed, and radiation was associated with transitions between…
Explore lesson ChemistryLessonBoiling
Put a pan of water on a hot stove and watch. At first nothing much seems to happen. Then small bubbles cling to the bottom of the pan, a few rise and vanish, and finally the…
Explore lesson ChemistryLessonBoiling and External Pressure
A liquid can evaporate from its surface at many temperatures, but boiling involves vapour bubbles forming and surviving within the liquid. The boiling temperature is reached when…
Explore lesson ChemistryLessonBoiling and Solubility from Force Patterns
Boiling and dissolving are whole-molecule phenomena. A hydrogen-bond donor can raise a boiling point, but a long hydrocarbon chain adds dispersion and can reduce water…
Explore lesson ChemistryLessonBoiling Point — Matter and its Properties
When water is heated in a kettle, small bubbles appear, then large bubbles rise and burst, and steam pours from the spout. The water is boiling. The boiling point is another…
Explore lesson ChemistryLessonBoiling Point — States of Matter: Particle Model
Ask anyone at what temperature water boils and they will probably say 100 °C. That number is so reliable that it was once used to define the Celsius scale itself. Every pure…
Explore lesson ChemistryLessonBoiling Point and Air Pressure
Climbers making tea near the summit of Mount Everest find that their water boils at only about 70 °C. The tea tastes weak and eggs take far longer to cook. Nothing is wrong with…
Explore lesson ChemistryLessonBoiling Trends in Carbon Compounds
Organic boiling points depend on forces between molecules, not only on formula mass. Larger molecules often have stronger dispersion attractions, branching can change how…
Explore lesson ChemistryLessonBoiling-Point Elevation
A liquid boils when its equilibrium vapour pressure reaches the external pressure. Adding a nonvolatile solute lowers the solvent's vapour pressure at a given temperature, so a…
Explore lesson ChemistryLabBoltzmann distribution
Energy quanta are swapped at random between oscillators, and the Boltzmann distribution appears by itself.
Explore lesson ChemistryLessonBoltzmann's Entropy Formula
Classical thermodynamics defines entropy through heat: dS = dq_rev/T. This definition works perfectly but gives little insight into what entropy *is*. Ludwig Boltzmann provided…
Explore lesson ChemistryLessonBomb Calorimetry
A bomb calorimeter burns a measured fuel sample in a sealed rigid vessel surrounded by a calibrated water bath or apparatus. The reaction warms the surroundings. Because the bomb…
Explore lesson ChemistryLessonBond Dipole Direction
The labels δ+ and δ− show which end of a polar bond is electron-poorer or electron-richer. A bond-dipole arrow adds direction: in a common chemistry convention, the crossed or…
Explore lesson ChemistryLessonBond Dipoles and Electronegativity
Atoms in a covalent bond can attract shared electrons unequally. The more electronegative end becomes partially negative, and the other partially positive. A bond dipole records…
Explore lesson ChemistryLessonBond Dissociation Enthalpy
Breaking a chemical bond requires energy, but the energy depends on the particular bond and molecular environment. Bond dissociation enthalpy refers to a specified gas-phase…
Explore lesson ChemistryLessonBond Enthalpy and Bond Breaking
Bond diagrams show which links are broken and formed in a reaction, but energy signs must be handled carefully. Breaking a specified covalent bond requires energy. Forming the…
Explore lesson ChemistryLessonBond Enthalpy and Reaction Energy Estimates
Bond energies provide an energetic bookkeeping method for reactions. Pulling bonded atoms apart requires energy; allowing new bonds to form releases energy. Their difference can…
Explore lesson ChemistryLessonBond Length and Bond Energy Tables
Tables of bond lengths and energies summarize many molecules, not one universal stick length or strength for each element pair. A C–O bond in an alcohol is not identical to a C=O…
Explore lesson ChemistryLessonBond Length and Bond Strength
Single, double and triple bonds differ in more than the number of lines drawn. Within a comparable set of bonds between the same elements, increasing bond order generally…
Explore lesson ChemistryLessonBond Length, Strength and Potential Energy
A bonded pair of atoms has a preferred separation, not a fixed hard-sphere contact. A potential-energy curve shows energy falling as attraction develops and rising sharply when…
Explore lesson ChemistryLessonBond Order from MO Occupancy
Molecular-orbital bond order counts the net occupation of stabilising versus destabilising orbitals. In a simple diatomic diagram, subtract antibonding electrons from bonding…
Explore lesson ChemistryLessonBond Order, Bond Length and Strength
Single, double and triple lines in Lewis structures often correspond to systematic changes in distance and energy. For the same pair of elements in comparable settings, more bond…
Explore lesson ChemistryLessonBond Polarity and Reaction Centres
Organic reactions often begin where electron density is uneven. Oxygen and common halogens draw shared electron density toward themselves in many bonds to carbon, leaving the…
Explore lesson ChemistryLessonBond-Enthalpy Estimates and Their Limits
When formation enthalpies are unavailable, bond enthalpies can estimate a reaction's energy change. Breaking bonds requires energy; making bonds releases energy. The estimate is…
Explore lesson ChemistryLessonBond-Length and Bond-Order Comparisons
Students often learn that triple bonds are shorter than double bonds, which are shorter than single bonds. This is a valuable trend for comparable atoms and environments. It…
Explore lesson ChemistryLessonBonding and Antibonding Orbitals
Two suitable atomic orbitals can combine in two mathematically distinct ways. One combination increases electron density between nuclei and is bonding; the other introduces a…
Explore lesson ChemistryCollectionBonding and Lewis Structures
Study Bonding and Lewis Structures with 60 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonBonding and Lewis Structures: Unit Review
Bonding questions often move across scales. A compound formula tells composition; a Lewis drawing tracks selected valence electrons; a spatial model gives shape; a lattice or…
Explore lesson ChemistryLessonBonding and Molecular Shape Map
Bonding explains how atoms assemble; shape explains how that assembly acts in three dimensions. A map from valence electrons through Lewis structures and electron domains to…
Explore lesson ChemistryLessonBonding and Structure Practice
Bonding problems often mix three distinct questions: how atoms are connected, what shape the resulting species adopts and how molecules interact in a bulk sample. A Lewis…
Explore lesson ChemistryLessonBonding and Structure Terms
Bonding words describe models of interactions and structures, not rigid boxes into which every material fits perfectly. Sodium chloride is a familiar ionic solid, methane has…
Explore lesson ChemistryLessonBonding Evidence from Properties
A sample's behaviour can reveal its internal arrangement. Whether it conducts as a solid or liquid, whether it melts readily, and whether it dissolves in water are useful clues.…
Explore lesson ChemistryLessonBonding in Everyday Materials
A kitchen, classroom or workshop contains examples of every major bonding idea in this unit. Salt, water, plastic, sand and pencil cores behave differently because their…
Explore lesson ChemistryLessonBonding in Mixed Ionic–Covalent Substances
Many familiar salts cannot be explained by saying that every neighboring atom is linked in the same way. Calcium carbonate contains Ca²⁺ units and carbonate groups, while…
Explore lesson ChemistryLessonBonding in Polyatomic Ionic Compounds
The phrase ionic compound can hide a second kind of bonding. Ammonium nitrate is composed of NH₄⁺ and NO₃⁻, but the atoms inside each polyatomic ion are joined by covalent bonds.…
Explore lesson ChemistryLessonBonding Model Error Clinic
Bonding errors often come from extending a good shortcut beyond its scope. The octet rule, VSEPR, hybridisation and MO diagrams solve related but different problems. An answer is…
Explore lesson ChemistryLessonBonding Models at Higher Secondary Level
Chemical bonding is described with several models because no single simple drawing answers every question. A Lewis structure counts valence electrons and bonds, a valence-bond…
Explore lesson ChemistryLessonBonding Models for Coordination Compounds
A single bonding picture cannot answer every question about a coordination compound. Lewis acid-base language identifies the electron-pair donor and acceptor. Valence-bond…
Explore lesson ChemistryLessonBonding Pairs and Lone Pairs — Bonding and Lewis Structures
The same Lewis drawing can be read two ways. For an electron ledger, every shared pair and lone pair counts two electrons. For a basic shape prediction, nearby electron density…
Explore lesson ChemistryLessonBonding Pairs and Lone Pairs — Chemical Bonding: Ionic and Covalent
Once a molecule's bonds are drawn, the remaining electrons still need somewhere to go. Lone pairs complete many familiar structures and influence shape and reactivity. Counting…
Explore lesson ChemistryLessonBoranes and Electron-Deficient Bonds
Boranes challenge the idea that every bond is an isolated pair of electrons between exactly two atoms. Diborane, B₂H₆, has two boron atoms and six hydrogens, but the available…
Explore lesson ChemistryLessonBorax and Boron Chemistry
Borax is a familiar example of a borate salt. The common crystalline material is sodium tetraborate decahydrate, Na₂B₄O₇·10H₂O. Its formula links a complex boron-oxygen anion…
Explore lesson ChemistryLessonBoric Acid and Borates
Boric acid, commonly written B(OH)₃ or H₃BO₃, illustrates why counting hydrogen atoms in a formula does not tell the entire acid-base story. In dilute water it acts mainly by…
Explore lesson ChemistryLessonBorn-Haber Cycle Steps
A Born–Haber cycle breaks formation of an ionic solid from reference elements into hypothetical gas-phase steps. Metal atoms are separated and ionized, nonmetal molecules are…
Explore lesson ChemistryLessonBorn–Haber Cycle for Sodium Chloride
A Born–Haber cycle breaks the formation of an ionic crystal into imagined thermochemical steps. It does not claim sodium chloride forms in the laboratory by first making free…
Explore lesson ChemistryLessonBorn–Oppenheimer Approximation
A molecule contains moving electrons and nuclei, so the complete Schrödinger equation is a coupled many-particle problem. Nuclei are much heavier than electrons, suggesting a…
Explore lesson ChemistryLessonBorn–Oppenheimer Surfaces and Their Limits
Potential energy surfaces are commonly constructed by treating nuclei as fixed while solving for electrons. This Born–Oppenheimer approach works well for many ground-state…
Explore lesson ChemistryLessonBoron and Its Electron-Deficient Compounds
The familiar two-atom, two-electron bond model works well for methane, but boron hydrides reveal its limits. BH₃ has only six valence electrons around boron in a simple Lewis…
Explore lesson ChemistryLessonBoron to Neon Configurations
Beryllium ends with a filled 2s subshell. The next six elements, boron through neon, add electrons to 2p. Watching the superscript grow from 1 to 6 reveals both a periodic-table…
Explore lesson ChemistryLessonBoundary Conditions and Quantisation
Inside a one-dimensional box, the Schrödinger equation has the same solutions as for a free particle, and on its own it allows any energy. Yet a confined particle turns out to…
Explore lesson ChemistryLessonBoyle's Law at Fixed Temperature
Compress a gas slowly while keeping its temperature and amount fixed, and its pressure rises. For a gas close to ideal behavior, pressure is inversely proportional to volume…
Explore lesson ChemistryLessonBrackets in Chemical Formulae
Some formulae contain brackets, such as Ca(OH)₂, Mg(NO₃)₂ and (NH₄)₂SO₄. Brackets appear when a formula contains more than one copy of a particular group of atoms that behaves as…
Explore lesson ChemistryLessonBragg's Law and the Laue Condition
An X-ray diffraction peak appears only when waves scattered from many repeats of a crystal reinforce one another. Bragg's law expresses this as an extra path length between waves…
Explore lesson ChemistryLessonBranched Alkanes and Their Names
When alkanes branch, simple names like "hexane" are no longer enough: C₆H₁₄ alone has five different structures. Chemists around the world use one agreed system, set by IUPAC, so…
Explore lesson ChemistryLessonBranching Chains and Explosion Limits
Ordinary propagation replaces one reactive carrier with another, allowing a chain to continue. Branching can turn one carrier into two or more, multiplying the population that…
Explore lesson ChemistryLessonBrass and Bronze
Brass and bronze are copper-based alloys used where pure copper's combination of properties is not ideal. Brass commonly combines copper and zinc; bronze commonly combines copper…
Explore lesson ChemistryLessonBravais Lattices and Space Groups
A photograph of a crystal may reveal repeating atoms, but repeating pattern and chemical identity are different pieces of information. Crystallographers separate the abstract…
Explore lesson ChemistryLessonBreaking Compounds Down
If elements can join to make compounds, can compounds be taken apart again? Yes, but not by filtering, sieving or using a magnet. Because the atoms in a compound are held by…
Explore lesson ChemistryLessonBreaking Scaling Relations
A scaling relation can make catalyst optimisation look like sliding along a line: improve binding of one intermediate and another changes with it. Breaking the relation means…
Explore lesson ChemistryLessonBrine Electrolysis Overview
Brine electrolysis is an industrial example of water changing the products expected from a salt. A suitable chlor-alkali cell produces chlorine at the anode, hydrogen at the…
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