THE LESSON LIBRARY / CHEMISTRY
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The s and p Subshells
For the first twenty elements, electron configurations can be built mainly with s and p subshells, followed by the beginning of 4s. An s subshell has one orbital and holds at…
Explore lesson ChemistryLessonThe s, p, d and f Blocks
The table's distinctive shape follows the capacities of electron subshells. Its s, p, d and f regions are called blocks. Block names provide a compact way to connect element…
Explore lesson ChemistryLessonThe Sabatier Principle
A reactant must often interact with a catalytic site long enough to react, but the resulting intermediate or product must also leave so the site can work again. The Sabatier…
Explore lesson ChemistryLessonThe Schrödinger Description of Hydrogen
Hydrogen is a particularly important quantum example because its one electron interacts mainly with one proton, allowing an exact nonrelativistic solution in a simplified model.…
Explore lesson ChemistryLessonThe Scientific Method in Chemistry
How do chemists know what they know? They do not simply trust their feelings or accept an idea because an important person said it. Instead, they follow a way of working called…
Explore lesson ChemistryLessonThe Self-Ionisation of Water
Even carefully purified water contains a small number of ions. Two water molecules can exchange a proton, creating hydronium and hydroxide together. This self-ionisation explains…
Explore lesson ChemistryLessonThe Semi-Empirical Mass Formula
Could the binding energy of any nucleus be predicted from just its proton and neutron numbers? In 1935 Carl Friedrich von Weizsäcker showed that a remarkably good estimate…
Explore lesson ChemistryLessonThe Shape of d Orbitals
d orbitals are commonly drawn with four lobes, though one familiar d shape has a different appearance. The drawings are probability-and-phase maps, not five varieties of electron…
Explore lesson ChemistryLessonThe Shape of p Orbitals
p orbitals introduce direction into the spatial picture of electron probability. They are often drawn as two lobes on opposite sides of a nucleus. The lobes are parts of one…
Explore lesson ChemistryLessonThe Shape of s Orbitals
An s orbital is often drawn as a sphere, but that drawing can hide important detail. Spherical symmetry means the probability density depends on distance from the nucleus rather…
Explore lesson ChemistryLessonThe Shockley–Queisser Limit
Even a flawless single-band-gap solar cell cannot turn all sunlight into electricity. Sunlight contains photons of many energies, whereas one semiconductor has one principal…
Explore lesson ChemistryLessonThe Simple Collision Theory Rate Constant
Page 3107 counted how often A and B molecules collide in a dilute gas. A chemical reaction usually occurs less often because only a subset of encounters can cross the relevant…
Explore lesson ChemistryCollectionThe Solid State
Study The Solid State with 25 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonThe Solid State: Unit Review
The solid state connects repeating atomic geometry with measurable properties. A unit cell tells how positions repeat, but correct counting, bonding and defects are needed to…
Explore lesson ChemistryLessonThe Solvent-System Definition of Acids and Bases
Water is only one possible solvent for acid-base chemistry. In water, acidifying solutes increase H₃O⁺ and basic solutes increase OH⁻. The solvent-system definition generalises…
Explore lesson ChemistryLessonThe Special Behavior of First-Row Elements
The first full period of the main-group pattern is period 2, from lithium to neon. Its elements often differ noticeably from heavier members of their groups. Small atomic and…
Explore lesson ChemistryLessonThe Spectrochemical Series Explained
The spectrochemical series is often memorised as halides below water and ammonia, with cyanide and carbon monoxide near the strong-field end. Its ordering is empirical…
Explore lesson ChemistryLessonThe Spin-Only Magnetic Moment Formula
Counting unpaired electrons predicts whether a complex is paramagnetic, but a numerical magnetic moment needs another step. For many first-row complexes, a useful first…
Explore lesson ChemistryLessonThe Steric Factor
Two molecules can collide with enough relative energy and still separate unchanged. The incoming atoms may face the wrong way, or the trajectory may not pass through the…
Explore lesson ChemistryLessonThe Sum Rule for Neutral Compounds
The oxidation numbers of all atoms in a neutral compound sum to zero. Once the usual values for some elements are known, this rule lets us solve for an unknown value. It is an…
Explore lesson ChemistryLessonThe Sum Rule for Polyatomic Ions
The oxidation numbers of atoms in a polyatomic ion add to the ion's overall charge, not to zero. This is the neutral-compound sum rule with a different target. It allows a…
Explore lesson ChemistryLessonThe Thermodynamic Limit and Ensemble Equivalence
An isolated solid has fixed energy, while the same solid in a thermostat has fluctuating energy. Why do both descriptions normally predict the same bulk temperature, pressure and…
Explore lesson ChemistryLessonThe Three States of Matter
Look around the room you are in. The desk is solid, the water in your bottle is liquid, and the air you breathe is a gas. Almost everything you meet in daily life falls into one…
Explore lesson ChemistryLessonThe Three Subatomic Particles Compared
Protons, neutrons and electrons differ in charge, mass and location. These three properties should be learned together without being confused with each other. A particle can be…
Explore lesson ChemistryLessonThe Time-Independent Schrödinger Equation
The time-independent Schrödinger equation, Ĥψ = Eψ, is the central energy problem of quantum chemistry. Given a system's Hamiltonian and boundary conditions, solve for…
Explore lesson ChemistryLessonThe Transfer Coefficient
Applied overpotential changes the free-energy landscape for an electrode reaction, but it need not change the forward and reverse barriers by equal amounts. A transfer…
Explore lesson ChemistryLessonThe Transition Metals
Iron in bridges, copper in wiring, gold in jewellery, titanium in hip replacements: many of the metals we rely on most come from the wide central block of the periodic table.…
Explore lesson ChemistryLessonThe Translational Partition Function
A gas molecule can translate through a container in three directions. Its allowed quantum energies are discrete, as for a particle in a box, yet a macroscopic box has levels so…
Explore lesson ChemistryLessonThe Uncertainty Principle
An electron in an atom cannot be described by an exact position and an exact momentum at the same instant. This is a property of quantum states, not merely a complaint that…
Explore lesson ChemistryLessonThe Uncertainty Principle in Quantum Chemistry
In classical physics a particle has a definite position and a definite momentum at every instant. Quantum mechanics says otherwise. Werner Heisenberg showed in 1927 that the more…
Explore lesson ChemistryLessonThe Valley of Stability and Decay Modes
The chart of nuclides arranges nuclei by proton number Z and neutron number N. Stable nuclides occupy a narrow, curved region rather than a simple line where N equals Z. Nuclei…
Explore lesson ChemistryLessonThe van 't Hoff Factor
One mole of a dissolved chemical formula does not always create one mole of independent solute species. Salts can dissociate into ions, while some molecular solutes can associate…
Explore lesson ChemistryLessonThe Variation Principle
When the Schrödinger equation cannot be solved exactly, we need a method that tells us not only an approximate answer but also how to judge whether one approximation is better…
Explore lesson ChemistryLessonThe Vibrational Partition Function
Molecules vibrate, but at room temperature most of them are not vibrating any more vigorously than quantum mechanics demands. The vibrational partition function tells us exactly…
Explore lesson ChemistryLessonThe Virial Theorem for Hydrogen
The total energy of a hydrogen atom in its ground state is −13.6 eV. But this single number hides two competing contributions: a positive kinetic energy from the electron's…
Explore lesson ChemistryLessonThe Volumetric Flask and Meniscus
The neck of a volumetric flask has one line, not a full measuring scale. It is designed to contain a specified volume when the liquid surface is set correctly. A few drops too…
Explore lesson ChemistryLessonThe Water Cycle: An Overview
The glass of water you drink today may once have fallen as snow on a mountain, flowed down a river, floated in a cloud over the ocean or been breathed out by a plant. Water is…
Explore lesson ChemistryLessonThe Wavefunction and Its Meaning
In classical mechanics the state of a particle is fully described by its position and momentum at one instant; Newton's laws then predict its future exactly. Quantum mechanics…
Explore lesson ChemistryLessonThe Wittig Reaction
The Wittig reaction replaces the oxygen of an aldehyde or ketone carbonyl with a carbon fragment, producing an alkene. Its value in synthesis is precise carbon-skeleton…
Explore lesson ChemistryLessonThe Woodward–Hoffmann Rules: An Introduction
Pericyclic reactions can be predicted by asking whether occupied molecular orbitals correlate continuously with product bonding orbitals as bonds reorganise. Woodward–Hoffmann…
Explore lesson ChemistryLessonThe σ-Only Octahedral MO Diagram
The σ-only molecular-orbital diagram gives the familiar octahedral d split a bonding interpretation. Six ligand donor functions form A₁g, E_g and T₁u combinations. Their…
Explore lesson ChemistryLessonTheoretical and Actual Yield
A balanced equation predicts what a limiting supply *could* produce under its stated pathway. A laboratory reports what was actually obtained. These two quantities answer…
Explore lesson ChemistryLessonTheoretical and Percentage Yield
Stoichiometry predicts an ideal product amount, but a laboratory normally recovers a measured amount. Comparing those values shows how effectively the specified product was…
Explore lesson ChemistryLessonTheoretical Capacity and Specific Energy
Theoretical battery capacity begins with an electron count. If one formula unit reversibly transfers n electrons and has molar mass M, Faraday's constant gives the charge…
Explore lesson ChemistryLessonThermal Conductivity
On a cold morning, a metal door handle feels much colder than a wooden door, even though both are at the same temperature. The difference is thermal conductivity — how easily…
Explore lesson ChemistryLessonThermal Cracking and Free-Radical Mechanisms
Heavy hydrocarbon fractions do not become lighter products merely by distillation. Thermal cracking deliberately breaks bonds at high temperature, making smaller molecules…
Explore lesson ChemistryLessonThermal Decomposition
Heat a lump of limestone strongly and it looks almost the same afterwards, yet it has become a completely different substance. Heat green copper carbonate and it turns black. In…
Explore lesson ChemistryLessonThermal Decomposition of Carbonates
Limestone is mainly calcium carbonate, CaCO₃. On strong heating under suitable conditions, it decomposes into calcium oxide, known as quicklime, and carbon dioxide gas. This…
Explore lesson ChemistryLessonThermal Decomposition of Hydroxides and Nitrates
Heating some metal hydroxides and nitrates breaks them into simpler substances. The products vary with the metal and compound, so patterns must be used with care. Copper(II)…
Explore lesson ChemistryLessonThermal Runaway and Battery Safety
Most lithium-ion cells operate safely within their designed limits, but stored energy and reactive components make failure analysis essential. Thermal runaway is a feedback…
Explore lesson ChemistryLessonThermal Stability of Carbonates and Nitrates
Group 2 carbonates and nitrates become harder to decompose as the metal changes from magnesium toward barium. Their products differ: carbonates give metal oxide and carbon…
Explore lesson ChemistryLessonThermal Stability of Group 1 and Group 2 Salts
Heating a carbonate or nitrate may release gases and leave a metal oxide or nitrite. Lithium compounds often behave differently from heavier Group 1 salts, while Group 2…
Explore lesson ChemistryLessonThermochemical Cycle Problem-Solving Review
A measured heat and a tabulated reaction enthalpy may appear inconsistent even when both calculations are correct. They may refer to different reaction amounts, water phases…
Explore lesson ChemistryLessonThermochemical Cycles
A thermochemical cycle presents Hess's law as a closed network of states. One path may be measured directly; another may be assembled from known steps. Since a full return to the…
Explore lesson ChemistryLessonThermochemical Equations
A thermochemical equation states both what reacts and the enthalpy change for that balanced event. Its ΔH belongs to the stoichiometric equation as written, with specified…
Explore lesson ChemistryLessonThermochemical Formation Data
Formation enthalpies provide a reusable reference system for reaction-energy calculations. Instead of measuring every reaction directly, combine tabulated values for reactants…
Explore lesson ChemistryLessonThermochemistry and Equilibrium Challenge
Thermochemistry tells you how much heat a reaction releases or absorbs; equilibrium tells you how far it goes. The bridge between them is the Gibbs energy. A single problem can…
Explore lesson ChemistryLessonThermochemistry Formulae
Thermochemistry formulae translate temperature measurements into heat flows and combine known reaction enthalpies into unknown ones. The central equations are q = mcΔT for a…
Explore lesson ChemistryLessonThermodynamic Consistency of a Network
A kinetic model can assign a forward and reverse rate to every arrow yet still imply an impossible perpetual circulation. Thermodynamic consistency prevents this. When a set of…
Explore lesson ChemistryLessonThermodynamic Cycles for Acid Strength
Why does highly polar HF remain a weak acid in water while HI is strong? A single factor cannot answer the question. A thermodynamic cycle separates the cost of generating ions…
Explore lesson ChemistryLessonThermodynamic Ensembles: Choosing the Constraints
Statistical thermodynamics predicts macroscopic properties by averaging over microscopic states. The first decision is not which equation to memorise but what the system can…
Explore lesson ChemistryCollectionThermodynamics
Study Thermodynamics with 50 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonThermodynamics and Kinetics Map
Thermodynamics asks which direction a system tends to move and where equilibrium lies. Kinetics asks how rapidly it moves and by which pathway. These questions are related but…
Explore lesson ChemistryLessonThermodynamics and Kinetics of Catalytic Steps
A catalyst speeds up a reaction without changing its overall thermodynamics. Yet within a catalytic cycle, every elementary step has its own free-energy change and barrier. Some…
Explore lesson ChemistryLessonThermodynamics of Gas Adsorption
Gas molecules can attach to a porous solid and later leave it when conditions change. The balance depends on both energy and disorder. Attractive surface interactions often…
Explore lesson ChemistryLessonThermodynamics of Intercalation Electrodes
An intercalation electrode stores lithium in a host rather than depositing all lithium as a separate metal phase. As lithium content changes, the host's chemical potential…
Explore lesson ChemistryLessonThermodynamics of Micellisation
Surfactant molecules at low concentration can exist mainly as individual monomers and adsorb at interfaces. As concentration rises, many species begin to form micelles, with…
Explore lesson ChemistryLessonThermodynamics of Mixing Ideal Gases
Two different ideal gases placed in separate compartments can spread through one another when the partition is removed. No chemical bond has to form, and at fixed temperature the…
Explore lesson ChemistryLessonThermodynamics of Point Defects
A crystal diagram usually fills every regular site, but an equilibrium specimen at any nonzero temperature generally contains a finite concentration of defects. Creating a…
Explore lesson ChemistryLessonThermodynamics of Protein Folding
Why does a long polypeptide adopt a specific functional shape instead of remaining a shapeless coil? Folding is a thermodynamic competition between ensembles of conformations in…
Explore lesson ChemistryLessonThermodynamics Practice
Thermodynamics practice requires disciplined signs and reference states. Reversing a reaction reverses its enthalpy change; doubling every coefficient doubles the per-equation…
Explore lesson ChemistryLessonThermodynamics Terms
Thermodynamic terms answer “what direction is favored?” and “how much energy is transferred?” under stated conditions. They do not tell us whether a change happens quickly.…
Explore lesson ChemistryLessonThermodynamics versus Kinetics
An organic reaction can make several products. The product that forms fastest need not be the most stable one. Kinetic control reflects differences in transition-state barriers…
Explore lesson ChemistryLessonThermodynamics: Unit Review
Thermodynamics organizes chemical change through carefully defined states, boundaries and constraints. The first law accounts for energy entering and leaving; enthalpy and Hess's…
Explore lesson ChemistryLessonThin-Film Photovoltaic Absorbers
Thin-film solar cells deposit an absorber directly onto a supporting substrate instead of relying on a thick, free-standing crystalline-silicon wafer. Cadmium telluride (CdTe)…
Explore lesson ChemistryLessonThinking Like a Chemist
You have reached the end of the first unit of ChemVerse. You have learned what chemistry is, where it appears in daily life, how chemistry grew as a science, how chemists work…
Explore lesson ChemistryLessonThomson Discovers the Electron
The electron's discovery changed the meaning of the word atom. Matter that seemed to consist of indivisible building blocks could release much smaller charged particles.…
Explore lesson ChemistryLessonThomson's Model and Its Prediction
Once electrons were known, a neutral atom needed positive charge somewhere to balance them. Thomson pictured negative electrons embedded within a spread-out region of positive…
Explore lesson ChemistryLessonThree Kinds of Strong Chemical Bond
Salt, oxygen and iron all involve strong chemical bonding, yet their particles are organised differently. Three introductory models explain much of this variation: ionic…
Explore lesson ChemistryLessonThree-Component Systems: Triangular Diagrams
Three-component mixtures require two independent mole fractions because the third is fixed by their sum. A triangular diagram uses its plane to display all possible compositions…
Explore lesson ChemistryLessonThree-Dimensional Carbon Geometry
Carbon skeleton drawings are usually flat, but molecules occupy three-dimensional space. A carbon with four single bonds is approximately tetrahedral; one with a double bond has…
Explore lesson ChemistryLessonThree-Reactant Limiting Problems
Adding a third reactant does not require a new limiting-reagent rule. Convert every starting supply to moles, divide each by its own balanced coefficient, and choose the smallest…
Explore lesson ChemistryLessonTight-Binding Model: Bands from Orbitals
The nearly-free-electron model starts with waves spread through space and adds a weak periodic potential. Tight binding starts from the other end: electrons reside mainly in…
Explore lesson ChemistryLessonTime-Domain NMR and the Fourier Transform
Modern pulsed NMR instruments do not directly draw a row of frequency peaks as a sample sits in a magnetic field. A radio-frequency pulse creates transverse nuclear…
Explore lesson ChemistryLessonTime-Resolved Spectroscopy
Steady-state spectra tell us what a sample absorbs or emits after many molecules and times have been averaged together. Time-resolved spectroscopy asks what happens after…
Explore lesson ChemistryLessonTime: The Second
For most of history, time was measured by the sky: a day was one turn of the Earth, and a second was a tiny fraction of that day. But the Earth's spin is not perfectly steady…
Explore lesson ChemistryLessonTimed Problem-Solving Strategy
Most marks lost in timed physical-chemistry papers are not lost through ignorance. They disappear through misread units, a skipped conversion from cm³ to m³, a forgotten…
Explore lesson ChemistryLessonTimescale Separation
Large reaction networks often contain events that occur in milliseconds alongside changes that take minutes. This separation can simplify modelling: a fast reversible step may…
Explore lesson ChemistryLessonTin and Lead Oxidation States
Tin and lead lie toward the metallic end of group 14. Both make compounds in +2 and +4 oxidation states, but the balance changes down the group: lead(II) is generally more stable…
Explore lesson ChemistryLessonTitrating Weak and Polyprotic Acids
Weak acids create buffer regions during titration, and polyprotic acids can create more than one. The curve records both stoichiometry and equilibrium. A half-equivalence pH can…
Explore lesson ChemistryLessonTitration Amount Calculations
In a titration, a known solution is added to a measured portion of an unknown until an observable endpoint signals that the reaction is near a chosen stoichiometric condition.…
Explore lesson ChemistryLessonTitration as a Measurement of Amount
A titration converts a measured volume into a chemical amount. A standard solution of known concentration reacts with an analyte until an endpoint indicates proximity to…
Explore lesson ChemistryLessonTitration Calculations: Concentration
A titration gives you two volumes: the fixed volume pipetted into the flask and the mean titre from the burette. On their own, these are just numbers. Combined with a balanced…
Explore lesson ChemistryLabTitration curve
A virtual titration. Add base from the burette and watch the pH curve and the species in the flask.
Explore lesson ChemistryLessonTitration Curves at an Introductory Level
A titration curve records how pH changes as a known solution is added to an analyte. Its shape tells more than one pH reading: it reveals a starting condition, regions of gradual…
Explore lesson ChemistryLessonTitration: The Idea
Suppose you have a bottle of hydrochloric acid and you want to know exactly how much sodium hydroxide solution is needed to neutralise 25.0 cm³ of it — not roughly, but to the…
Explore lesson ChemistryLessonTitrimetry Problem Solving
Multi-step titration problems are difficult mainly because they contain several vessels and reactions, not because their arithmetic is advanced. A measured titre may describe…
Explore lesson ChemistryLessonTMS as the Reference Standard
A chemical shift is always measured relative to something. For ¹H and ¹³C NMR, that something is tetramethylsilane, TMS, which defines the zero of the δ scale. The choice is not…
Explore lesson ChemistryLessonTOCSY: Whole Spin-System Mapping
COSY links a proton only to its direct coupling partners, so identifying a long chain means walking step by step, and one overlapped signal can halt the walk. TOCSY takes a…
Explore lesson ChemistryLessonTooth Decay and Toothpaste
Tooth enamel is the hardest substance in the human body, harder than bone. Yet it can be worn away by something as ordinary as a sugary drink. The culprit is acid, made by…
Explore lesson ChemistryLessonTorsional Strain and the Energy Profile of Ethane
Ethane rotates around its C–C single bond, but the motion is not energetically flat. A graph of energy against H–C–C–H dihedral angle displays alternating high eclipsed and low…
Explore lesson ChemistryLessonTotal Vapour Pressure of an Ideal Binary Solution
For a binary mixture of volatile liquids A and B, the pressure above the liquid includes contributions from both vapours. If the liquid mixture is ideal, Raoult's law gives each…
Explore lesson ChemistryLessonTrade-Offs and Limits of Green Chemistry
The twelve principles of green chemistry guide design, but they do not produce twelve green ticks for every real process. A solvent may be less toxic but require hotter…
Explore lesson ChemistryLessonTraining and Testing Chemical Predictors
A predictor can perform well on a random test split yet fail on a new reaction family or laboratory. The split defines what “generalization” means. Honest evaluation begins by…
Explore lesson ChemistryLessonTrajectories and Energy Disposal
A potential-energy surface tells us which molecular geometries are energetically accessible, but molecules also have momentum. Two collisions with the same total energy can…
Explore lesson ChemistryLessonTransient Kinetics
A steady outlet rate can hide a long chain of adsorption, bond making and product release. Transient kinetics deliberately changes a condition and follows the response in time. A…
Explore lesson ChemistryLessonTransition and Inner-Transition Placement
The center and detached bottom rows of the common periodic table are not afterthoughts. The central d-block occupies parts of periods 4–7, while the f-block belongs within…
Explore lesson ChemistryLessonTransition Elements and Their Definition
“Transition metal” is often used loosely for the central metals of the periodic table, but the formal transition-element definition asks an electronic question. Does the…
Explore lesson ChemistryLessonTransition Elements in Periodic Classification
The central block of the periodic table includes iron, copper and many other metals with chemistry more varied than the simple group-one or group-two charge patterns. Their d…
Explore lesson ChemistryLessonTransition Metals as Catalysts
Some of the most important reactions in the modern world would be far too slow to be useful without help. Making fertiliser, turning vegetable oils into spreads and cleaning car…
Explore lesson ChemistryLessonTransition Metals in Catalysis
Iron, nickel, palladium and many other transition metals accelerate reactions. Their ability to bind substrates and access multiple electronic states can create paths with lower…
Explore lesson ChemistryLessonTransition Metals: General Characteristics
Transition-metal compounds often display multiple oxidation states, vivid colours, catalytic activity and magnetic behaviour. These features arise because d electrons participate…
Explore lesson ChemistryLessonTransition-Metal Alloys and Interstitial Compounds
Pure-element trends are only a starting point for engineering materials. Mixing transition metals with other metals or placing small atoms in lattice gaps can change hardness…
Explore lesson ChemistryLessonTransition-Metal Colours
Many transition-metal compounds are coloured, but the presence of a d-block element is not a guarantee. Colour depends on which light is absorbed by a particular compound, with…
Explore lesson ChemistryLessonTransition-Metal Oxides and Halides
Transition metals form many oxides and halides because they can adopt several oxidation states. A low-state oxide may behave as a base, an intermediate oxide can be amphoteric…
Explore lesson ChemistryLessonTransition-State Stabilisation in Enzyme Catalysis
Enzymes increase rate by lowering activation free energy for a reaction pathway. A useful molecular picture is that the active site favours the transition-state geometry and…
Explore lesson ChemistryLessonTransition-State Theory
The Arrhenius equation describes how rate constants vary with temperature, but its pre-exponential factor is only an empirical number. Transition-state theory, developed by…
Explore lesson ChemistryLessonTransition-State Theory from Flux
Transition-state theory (TST) connects an energy landscape to a rate constant. Its central idea is a surface through a reaction bottleneck: count reactant systems crossing it…
Explore lesson ChemistryLessonTransition-State Theory: Core Assumptions
Collision theory counts encounters and asks how many have enough energy and a suitable orientation. Transition-state theory (TST) takes a different starting point: imagine a…
Explore lesson ChemistryLessonTransmetallation
In a cross-coupling reaction, palladium must hold two different organic groups before it can join them. The first arrives by oxidative addition of an organic halide. The second…
Explore lesson ChemistryLessonTransmission Coefficients and Quantum Tunnelling
Ideal transition-state theory counts thermal trajectories that cross a barrier surface and assumes they continue to products. Real trajectories may turn back, and quantum…
Explore lesson ChemistryLessonTransmission Electron Microscopy
Transmission electron microscopy, or TEM, can reveal the size, shape, lattice fringes and arrangements of nanomaterials at scales inaccessible to ordinary light microscopy. It is…
Explore lesson ChemistryLessonTransmittance and Absorbance
A spectrometer cannot measure "how much light a molecule absorbs" directly. What it actually measures is the brightness of the beam before it reaches the sample and after it has…
Explore lesson ChemistryLessonTransparent Conducting Oxides
Displays, solar cells and light-emitting devices need electrodes that carry current while letting light pass. Metals conduct well but usually reflect or absorb much visible light…
Explore lesson ChemistryLessonTransport Numbers
Both cations and anions move in an electrolyte, but they need not carry equal shares of the current. Transport numbers quantify those unequal shares. They matter when…
Explore lesson ChemistryLessonTreating Factory Waste and Acid Rain
Factories that make metals, paper, dyes and fertilisers often produce waste water that is strongly acidic or strongly alkaline. If this waste flowed straight into a river, it…
Explore lesson ChemistryLessonTrends Across the 3d Series
From scandium to zinc, protons are added to the nucleus while electrons mainly enter the 3d subshell. Atomic sizes change much less dramatically than across a typical main-group…
Explore lesson ChemistryLessonTrends in Binary Hydride Acidity
Hydrogen bonded to another nonmetal is not automatically an acid of predictable strength. In water, HF is weaker than HCl, HBr and HI even though fluorine is the most…
Explore lesson ChemistryLessonTrends in Oxide Acid-Base Character
Oxides change acid-base behaviour across the periodic table. Strongly electropositive metals tend to form basic oxides; borderline metals can form amphoteric oxides; nonmetal…
Explore lesson ChemistryLessonTrends in the Halogens
The halogens are one of the best places to see how physical properties change steadily down a group. At the top, fluorine is a pale gas; at the bottom of the everyday halogens…
Explore lesson ChemistryLessonTrends in the Noble Gases
The noble gases are all colourless, unreactive and monatomic, so at first sight they look almost identical. Look at their data, though, and clear patterns appear. Boiling points…
Explore lesson ChemistryLessonTrends Within the p-Block
The p-block contains a broad gradient from more metallic elements at its lower left to nonmetals near its upper right. Atomic radius, electron binding and electronegativity help…
Explore lesson ChemistryLessonTrial Wavefunctions and Variational Parameters
Exact Schrödinger solutions exist for only a few ideal systems. The variational method turns a plausible wavefunction into a controlled estimate of the ground-state energy. By…
Explore lesson ChemistryLessonTriglycerides and Phospholipids
Glycerol can anchor fatty-acid chains in more than one type of lipid. A triglyceride has three acyl chains and is suited to dense energy storage. A common glycerophospholipid has…
Explore lesson ChemistryLessonTrigonal Bipyramidal Geometry
Five electron domains around one centre adopt a trigonal bipyramidal reference arrangement in basic VSEPR. Three positions lie around an equatorial plane and two lie above and…
Explore lesson ChemistryLessonTriple Bonds: The Nitrogen Molecule
Nitrogen makes up much of the atmosphere, yet it does not rapidly react with every substance around it. Its strong N≡N bond contributes to that behaviour. The dot-and-cross…
Explore lesson ChemistryLessonTriprotic Acid Speciation
A triprotic acid can exist in four protonation states. Citric acid, phosphoric acid and arsenic acid are common examples, and many biological molecules behave similarly. The same…
Explore lesson ChemistryLessonTurmeric as an Indicator
Anyone who has cooked with turmeric knows its bright golden-yellow colour and how easily it stains. Fewer people know that this spice is also a chemical indicator. If a yellow…
Explore lesson ChemistryLessonTurning a Chemical Question into an Experiment
“Does this catalyst work better?” is a useful motivation but not yet an experiment. Better could mean higher rate, selectivity, lifetime, lower cost or less energy input, and the…
Explore lesson ChemistryLessonTurnover Number and Turnover Frequency
Catalysts are valuable because one active site can transform many molecules. Turnover number (TON) counts accumulated product per site; turnover frequency (TOF) measures how…
Explore lesson ChemistryLessonTwo Mechanisms of Polymerisation
Long chains can be assembled by two fundamentally different growth patterns. In step growth, small and large molecules react with one another through functional groups. In chain…
Explore lesson ChemistryLessonTwo-Component Vapour–Liquid Diagrams
A binary liquid mixture does not generally boil at one fixed temperature over its whole composition range. Its liquid and vapour usually have different compositions, so both…
Explore lesson ChemistryLessonTwo-Dimensional Energy Landscapes
A two-dimensional energy map offers a major improvement over a single reaction-profile curve. It can show that bond formation and bond breaking happen in a coupled, curved…
Explore lesson ChemistryLessonTwo-Dimensional Materials Beyond Graphene
Graphene is only one member of a wider family of layered solids. Molybdenum disulfide, tungsten diselenide and hexagonal boron nitride can also be prepared as very thin sheets…
Explore lesson ChemistryLessonTwo-Dimensional NMR: Axes and Cross-Peaks
A one-dimensional NMR spectrum lists frequencies, but it does not directly say which signals belong to neighbouring nuclei. Two-dimensional NMR spreads information over a plane…
Explore lesson ChemistryLessonTwo-Group Disconnections: 1,3-Dioxygenated Patterns
Two oxygen-containing functions separated by one carbon often reveal how a carbon–carbon bond was formed. A β-hydroxy aldehyde or ketone suggests an aldol reaction, whereas a…
Explore lesson ChemistryLessonTwo-Letter Symbols and Capital Letters
With 118 elements but only 26 letters, most elements need two-letter symbols. That creates a risk of confusion: is "CO" one element or two? The answer depends entirely on whether…
Explore lesson ChemistryLessonTwo-Level Systems
The simplest possible quantum system has just two states. Despite its simplicity, the two-level system models real and important situations: nuclear or electron spins in a…
Explore lesson ChemistryLessonTwo-Temperature Arrhenius Calculations
When rate constants are known at two temperatures, the Arrhenius pre-exponential factor can be eliminated. The resulting equation calculates a k ratio from Ea or estimates Ea…
Explore lesson ChemistryLessonTyndall Effect and Brownian Motion
A beam appears as a bright path through fog, and small particles in water jitter under a microscope. The first observation is optical; the second is mechanical. Both help reveal…
Explore lesson ChemistryCollectionTypes of Chemical Reactions
Study Types of Chemical Reactions with 50 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonTypes of Chemical Reactions: Unit Review
This unit has used four structural patterns to organise chemical equations: combination, decomposition, single displacement and double displacement. A useful final review goes…
Explore lesson ChemistryLessonUltrafast Dynamics
The first motions after photon absorption can occur in tens or hundreds of femtoseconds. On these timescales, a molecule may still carry directed nuclear motion created by the…
Explore lesson ChemistryLessonUncertainty and Error Budgets in Computation
A calculation can report many decimal places while still being uncertain about its central chemical conclusion. A reaction energy may depend on electronic method, basis…
Explore lesson ChemistryLessonUncertainty and Sensitivity in Derived Results
A numerical chemistry result is only as reliable as its measurements and model. Significant figures give a reporting convention, but uncertainty and sensitivity explain *why* a…
Explore lesson ChemistryLessonUncertainty in Composition Data
Empirical formulas use whole-number subscripts, while real measurements produce decimals with uncertainty. A normalized ratio of 1.49 may support 1.50 when the data are…
Explore lesson ChemistryLessonUncertainty in Computed Reaction Paths
A reaction path can be numerically converged and still predict the wrong chemistry. Its energy values depend on an approximate electronic method, its channel ranking depends on…
Explore lesson ChemistryLessonUncertainty in Kinetic Parameters
A fitted kinetic constant is an estimate, not an exact property delivered by a curve-fitting program. Sampling noise, calibration, uncertain starting amounts and model…
Explore lesson ChemistryLessonUncertainty in Measurement
If you measure the length of a pencil as 14.3 cm, is it exactly 14.3 cm? Almost certainly not. It might be 14.28 cm or 14.33 cm; your ruler simply cannot tell the difference.…
Explore lesson ChemistryLessonUncertainty Propagation
Chemists often calculate a final quantity from measured masses, volumes, concentrations and signals. The arithmetic gives a central value, but the uncertainty of each input also…
Explore lesson ChemistryLessonUncertainty-Aware Reaction Prediction
A reaction model may suggest a product, yield or rate with a confidence score. That score helps only if it corresponds to actual reliability for the chemistry at hand. A 90%…
Explore lesson ChemistryLessonUncompetitive and Mixed Inhibition — Biochemistry
Competitive inhibition is only one way a molecule can reduce an enzyme's rate. Some inhibitors bind only after substrate has bound; others bind both free enzyme and the…
Explore lesson ChemistryLessonUncompetitive and Mixed Inhibition — Kinetics and Reaction Dynamics
Not all inhibitors compete only with free substrate for empty enzyme. An uncompetitive inhibitor binds the enzyme–substrate complex, while a mixed inhibitor can bind both free…
Explore lesson ChemistryLessonUnimolecular RRKM Theory
A hot molecule created by a collision or light absorption does not necessarily have a single thermal temperature. Its total internal energy may be approximately known, and it may…
Explore lesson ChemistryLabUnit cell builder
Build unit cells in 3D: count atoms, see voids, and calculate packing and density.
Explore lesson ChemistryLessonUnit Cell Geometry
A unit cell repeats to fill a crystal, so objects drawn on its boundary are shared with neighboring cells. Counting every visible corner or face atom as fully inside produces…
Explore lesson ChemistryLessonUnit Conversions for Area and Volume
One metre is 100 centimetres, so it is tempting to think that one cubic metre is 100 cubic centimetres. In fact it is one million. This page explains why, and gives a method that…
Explore lesson ChemistryLessonUnit-Cell Density Calculations
Density links a microscopic crystal structure to a bulk measurement. Count formula units in one cell, convert their molar mass to cell mass with Avogadro's constant and divide by…
Explore lesson ChemistryLessonUnits as Algebraic Evidence
Units are more than labels added after arithmetic. They behave like algebraic factors and can expose a wrong formula, missing conversion or swapped denominator before a final…
Explore lesson ChemistryLessonUniversal Indicator and Its Colour Chart
Litmus can tell you whether a solution is acidic or alkaline, but not *how* acidic or alkaline it is. Lemon juice and battery acid both turn blue litmus red. To go further…
Explore lesson ChemistryLessonUniversal Indicator and pH Paper
Universal indicator and pH paper make acid–base behavior visible across much of the usual aqueous pH range. They are good for quick estimates and comparisons. Their results are…
Explore lesson ChemistryLessonUnknown Solute from Multiple Properties
Suppose a laboratory receives a clear, colourless solution with only a label giving the mass of solute dissolved. No single measurement will reveal what the solute is, but…
Explore lesson ChemistryLessonUnsaturated and Saturated Solutions
An unsaturated solution can take up more of a particular solute under the same conditions. A saturated solution is at its equilibrium capacity. These labels require a solute…
Explore lesson ChemistryLessonUses of Isotopes
An isotope is useful when it provides a detectable difference while retaining a relevant connection with the material being studied. That difference may be mass, nuclear magnetic…
Explore lesson ChemistryLessonUses of the Gases from Air
Once air has been cooled, liquefied and separated into its parts, industry is left with huge amounts of pure oxygen, nitrogen and argon. These gases are not just laboratory…
Explore lesson ChemistryLessonUsing a Chemistry Formula Sheet
A formula sheet is a map of possible models, not a menu of answers. The correct equation follows from what is being measured, which physical assumptions hold and which quantity…
Explore lesson ChemistryLessonUsing a pH Meter
A pH meter provides a numerical reading that is usually more precise than matching indicator colors. The instrument does not simply count hydronium ions, however. Its electrode…
Explore lesson ChemistryLessonUsing Blue and Red Litmus Paper
Litmus paper is simple, but it is also easy to use badly. Dipping a whole strip into a bottle wastes the sample and can contaminate it; testing with dirty equipment can give a…
Explore lesson ChemistryLessonUsing Conservation of Mass in Calculations
Conservation of mass can turn several measured masses into one missing value. The arithmetic is straightforward once all reactants and products are included. The harder skill is…
Explore lesson ChemistryLessonUsing Evidence to Infer Bonding
Bonding models are explanations of observations, not labels imposed by a formula alone. An unknown solid's conductivity, melting behavior, solubility and crystal pattern can…
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