THE LESSON LIBRARY / CHEMISTRY
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Statistical Entropy and the Sackur–Tetrode Equation
Boltzmann's formula S = k ln W links entropy to the number of microstates of an isolated system. In practice we work at constant temperature, not constant energy, and we need an…
Explore lesson ChemistryLessonStatistical Models of Phase Separation
Why do some liquids mix fully while others separate? Mixing creates entropy, favouring one phase, but unlike-molecule interactions can impose an energetic cost. A simple…
Explore lesson ChemistryCollectionStatistical Thermodynamics and Phase Equilibria
Study Statistical Thermodynamics and Phase Equilibria with 35 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonStatistical Thermodynamics and Phase Equilibria Review
This unit built a bridge from molecules to measurable properties. Ensembles gave the rules for counting states under different constraints; partition functions turned those…
Explore lesson ChemistryLessonStatistics Formulae for Chemical Data
Chemical measurements vary because of sampling, preparation and instrument behavior. Statistics formulae summarize that variation but do not make a result automatically correct.…
Explore lesson ChemistryLessonSteady States and Flux Balance
An intermediate can remain at nearly constant concentration while molecules continuously enter and leave its pool. This is a steady state, not chemical inactivity. Flux balance…
Explore lesson ChemistryLessonSteady-State Approximation — Advanced Electrochemistry and Kinetics
Exact solutions are available only for the simplest mechanisms. Once steps are second order or reversible, the rate equations rarely have tidy analytical answers. The…
Explore lesson ChemistryLessonSteady-State Approximation — Chemical Kinetics
An intermediate can be produced and consumed continuously while remaining at a low, nearly constant concentration. In that regime, its time derivative is approximately zero even…
Explore lesson ChemistryLessonSteam Cracking for Alkenes
Ethene and propene are starting materials for polymers and many other chemicals. A major route to them is steam cracking: a hydrocarbon feed, such as ethane or naphtha, passes…
Explore lesson ChemistryLessonSteel and Stainless Steel
Steel is a family of iron-based alloys, not one substance. Carbon helps control strength and hardness, while chromium is central to stainless steels' corrosion resistance. These…
Explore lesson ChemistryLessonStep vs Chain Growth Compared
The same final-looking long chain can arise by very different reaction histories. The clearest comparison of step and chain growth is how monomer disappears and how molar mass…
Explore lesson ChemistryLessonStep-Growth Kinetics
Carothers' equation relates conversion to average chain length, but it does not tell us how long a reactor must run. Kinetics supplies that missing time dimension.…
Explore lesson ChemistryLessonStep-Growth Polymerisation: Principles
Step-growth polymerisation starts with functional groups rather than a small set of permanently active chain ends. Any compatible ends may react, so monomers, dimers and longer…
Explore lesson ChemistryLessonStep-Growth Polymerization
Some polymers grow without one uniquely active chain end. A monomer can react with another monomer, an oligomer can react with a monomer, and two oligomers can join. This…
Explore lesson ChemistryLessonStepping Down: Removing One Carbon
Some conversion targets have one fewer carbon than the available starting material. The missing carbon must have a destination in a byproduct. Hofmann bromamide rearrangement…
Explore lesson ChemistryLessonStepping Up: Adding One Carbon
A target with one more carbon than the starting compound requires a carbon source. Cyanide ion and carbon dioxide are common one-carbon inputs, but they attach through different…
Explore lesson ChemistryLessonStereocentres and Stereogenic Units
The four-different-groups rule helps locate common stereocentres, but a careful chemist must compare complete substituent paths and also recognise stereogenic double bonds, axes…
Explore lesson ChemistryCollectionStereochemistry and Conformational Analysis
Study Stereochemistry and Conformational Analysis with 40 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonStereochemistry and Conformational Analysis: Unit Review
Stereochemistry connects molecular geometry to names, physical properties and reaction outcomes. The most reliable habit is to ask what is fixed, what can rotate and what can…
Explore lesson ChemistryLessonStereochemistry and Reaction Outcomes
Reaction mechanisms often determine product stereochemistry as strongly as they determine which bonds change. Backside attack in SN2, planar carbocation capture in SN1 and…
Explore lesson ChemistryLessonStereochemistry in Biology and Medicine
Biological molecules are three-dimensional and often handed. An enzyme or receptor can therefore distinguish two enantiomers that have the same formula and most ordinary physical…
Explore lesson ChemistryLessonStereochemistry of Addition in Conversions
Adding two atoms or groups across an alkene can convert flat trigonal carbons into tetrahedral stereocentres. The product's connectivity alone is not enough to identify it. The…
Explore lesson ChemistryLessonStereochemistry of Carbonyl Addition
A planar carbonyl carbon presents two faces to an incoming reagent. The faces can look identical in a flat drawing yet lead to different three-dimensional products after the…
Explore lesson ChemistryLessonStereochemistry of Elimination in Conversions
An elimination arrow often shows only “alkyl halide → alkene.” For E2, the actual three-dimensional arrangement matters. The base removes a beta hydrogen while the leaving group…
Explore lesson ChemistryLessonStereochemistry of Substitution in Conversions
Organic conversions often change a leaving group at a stereogenic carbon. A flat formula such as R–Br → R–OH hides whether the spatial configuration survives. SN2 and SN1 routes…
Explore lesson ChemistryLessonStereocontrol in Synthesis Planning
A synthesis that makes the right molecular formula and connectivity can still fail if it gives the wrong three-dimensional arrangement. Ring junctions, double-bond geometry and…
Explore lesson ChemistryLessonStereoisomers Formed in Multi-Step Routes
A single reaction's stereochemical rule may be familiar, yet a route of several arrows can still produce a wrong final answer. A centre might be created in the first step…
Explore lesson ChemistryLessonStereoselective Synthesis
Making the right bonds is not enough if a target is one stereoisomer among several. Stereoselective synthesis favours one spatial arrangement over alternatives. The planning task…
Explore lesson ChemistryLessonStereospecific versus Stereoselective Reactions
Both words begin with “stereo,” but they answer different questions. Stereospecificity asks whether the spatial configuration of the starting material determines a particular…
Explore lesson ChemistryLessonSteric and Electrosteric Stabilisation
Charged particles are not the only stable colloids. A particle coated with solvated polymer chains can resist close approach even when electrolyte screens electrostatic forces.…
Explore lesson ChemistryLessonSteric Effects
Reactants do not react only according to electron density; atoms must also approach in a workable geometry. Bulky groups can block a nucleophile from reaching carbon or prevent a…
Explore lesson ChemistryLessonStern–Volmer Quenching
Adding a second species can dim a fluorophore. The Stern–Volmer experiment measures how emission changes with quencher concentration and can reveal whether the excited molecule…
Explore lesson ChemistryLessonStirring and Particle Size
A spoonful of fine powder often disappears sooner than a single lump of equal mass. Stirring may also shorten the waiting time. These changes usually act by exposing more solid…
Explore lesson ChemistryLessonStoichiometric Imbalance and Chain Stoppers
The Carothers equation shows that step-growth chains only become long when conversion is extremely close to complete. That result assumed a perfect 1:1 balance of the two…
Explore lesson ChemistryLessonStoichiometric Matrices
A network diagram becomes easier to calculate with when its reaction coefficients are placed in a matrix. Each row represents a species, each column a reaction and each entry…
Explore lesson ChemistryCollectionStoichiometry and Mole Calculations
Study Stoichiometry and Mole Calculations with 70 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonStoichiometry and Mole Calculations: Unit Review
The mole connects particle-scale equations with laboratory measurements. The unit's problems differ in the first or last conversion—mass, gas volume, solution concentration…
Explore lesson ChemistryLessonStoichiometry and Solutions Practice
Stoichiometry is a chain: identify species, balance the net reaction, convert measurements to moles, compare reactants by coefficients and convert the result to the requested…
Explore lesson ChemistryLessonStoichiometry as a Quantitative Reaction Map
A chemical equation tells which substances react and form, but a balanced equation does more: it predicts their relative amounts. Stoichiometry uses those fixed relationships to…
Explore lesson ChemistryLessonStoichiometry Terms
Stoichiometry translates a balanced chemical equation into measurable amounts. Its vocabulary can become confusing because mass, number of particles, amount of substance…
Explore lesson ChemistryLessonStokes and Anti-Stokes Raman Lines
A Raman spectrum is often plotted as intensity versus *shift* from a laser line, not versus the actual color of every outgoing photon. A vibrating molecule can take energy from a…
Explore lesson ChemistryLessonStopped-Flow and Flash Photolysis Techniques
Fast chemistry needs a fast start and a fast clock. If a reaction completes before a sample can be mixed and placed in a spectrometer, an ordinary concentration–time experiment…
Explore lesson ChemistryLessonStraight, Branched and Cyclic Skeletons
Before interpreting a functional group, identify the carbon skeleton. It may be an unbranched open chain, a branched open chain or a ring. These categories describe connectivity…
Explore lesson ChemistryLessonStrength of Attractions and Melting and Boiling Points
Oxygen boils at −183 °C, water boils at 100 °C and iron does not even melt until 1538 °C. Why do substances change state at such wildly different temperatures? The answer lies in…
Explore lesson ChemistryLessonStrength Versus Concentration
Strong, weak, concentrated and dilute describe two different aspects of an acid solution. A strong acid can be dilute, and a weak acid can be concentrated. Keeping these…
Explore lesson ChemistryLessonStrengths and Limits of Collision Theory
Collision theory has a compelling starting idea: reactant particles must encounter one another before many reactions can occur. Number density, relative speed, energy and…
Explore lesson ChemistryLessonStrong Acid and Base Calculations
Strong-acid and strong-base calculations begin with stoichiometry rather than a weak-electrolyte equilibrium expression. In dilute introductory models, a strong monoprotic acid…
Explore lesson ChemistryLessonStrong Acid-Strong Base Titrations
Strong acid-strong base titration is primarily a mole-accounting problem. Hydronium and hydroxide neutralize nearly completely, so the excess strong reagent controls pH away from…
Explore lesson ChemistryLessonStrong and Weak Acids — Acids, Bases and Salts
Hydrochloric acid and ethanoic acid (the acid in vinegar) can be made up at exactly the same concentration, yet the hydrochloric acid has a much lower pH, conducts electricity…
Explore lesson ChemistryLessonStrong and Weak Acids — pH, Salts and their Uses
The words *strong* and *weak* describe how extensively an acid ionises in water, not how much acid is in a bottle. This distinction is essential for predicting which particles…
Explore lesson ChemistryLessonStrong and Weak Alkalis
Sodium hydroxide solution and household ammonia are both alkalis: both turn red litmus blue and both neutralise acids. Yet at the same concentration, sodium hydroxide has a…
Explore lesson ChemistryLessonStrong and Weak Bases
Bases differ in how they make hydroxide available in water. Dissolved sodium hydroxide separates into ions essentially completely, while ammonia accepts protons from water only…
Explore lesson ChemistryLessonStrong and Weak Electrolytes
Strong and weak electrolytes differ in how extensively they produce ions, not simply in how many grams were poured into the beaker. A dilute strong electrolyte can have fewer…
Explore lesson ChemistryLessonStrong and Weak Jahn–Teller Effects
The Jahn–Teller theorem predicts a symmetry-lowering route for an appropriate degenerate electronic state, but not every route produces a dramatic bond-length difference. In…
Explore lesson ChemistryLessonStrong Electrolyte Conductance
Strong electrolytes such as many soluble salts provide substantial numbers of ions in water. Yet their molar conductivity is usually smaller at finite concentration than at the…
Explore lesson ChemistryLessonStrongly and Weakly Acidic Substances
Knowing that the pH scale runs from 0 to 14 is only the start. The real skill is being able to look at a substance from the kitchen, the bathroom or the garden shed and say…
Explore lesson ChemistryLessonStructural Deduction from Reaction Data
Inorganic structure questions often begin with outcomes rather than a formula: a gas is released with acid, a compound hydrolyzes, a precipitate resists acid, or a spectrum…
Explore lesson ChemistryLessonStructural Isomerism in Complexes
Two coordination compounds may have the same overall atoms but connect them differently. These are structural isomers. The difference may place an anion inside rather than…
Explore lesson ChemistryLessonStructural Isomers of Butane
The first open-chain saturated hydrocarbon formula with two carbon skeletons is C₄H₁₀. Butane has an unbranched four-carbon path; 2-methylpropane has a three-carbon path with a…
Explore lesson ChemistryLessonStructural Isomers of Pentane
Five carbon atoms can form three distinct connected, acyclic saturated skeletons. They are pentane, 2-methylbutane and 2,2-dimethylpropane. All are C₅H₁₂, but their longest paths…
Explore lesson ChemistryLessonStructural Reasoning in Inorganic Chemistry
Qualitative observations gain explanatory power when connected to structure. Why does one compound hydrolyze, another remain inert, and a third form coloured complexes? A first…
Explore lesson ChemistryLessonStructure and Bonding Summary
Four common structural categories organise this unit: ionic, simple molecular, giant covalent and metallic. A useful comparison asks the same questions of each one: what…
Explore lesson ChemistryLessonStructure and Composition of the Atmosphere
The atmosphere is a thin envelope of gas: half of its mass lies below about 5.5 km, a height less than one-thousandth of the Earth's radius. Yet within this shell the temperature…
Explore lesson ChemistryLessonStructure and Mechanism at a Metal Site
A crystal structure of a metalloenzyme is a beautiful and persuasive image. It is tempting to look at it and "see" the mechanism. But a structure is a time-averaged snapshot of…
Explore lesson ChemistryLessonStructure Determination: Worked Problem I
This page works through a complete identification from start to finish. An unknown liquid is known to be a simple carbonyl compound. You are given its high-resolution mass…
Explore lesson ChemistryLessonStructure Determination: Worked Problem II
Isomers are the ultimate test of spectral interpretation, because they share a molecular formula and molecular mass. A molecular ion alone cannot tell them apart. This page takes…
Explore lesson ChemistryCollectionStructure of Atom: Quantum Model
Study Structure of Atom: Quantum Model with 50 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonStructure of Atom: Quantum Model Review
Atomic structure is learned through a chain of evidence and models. Scattering reveals a nucleus; spectra show discrete energies; photon experiments and electron diffraction…
Explore lesson ChemistryCollectionStructure of the Atom
Study Structure of the Atom with 60 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonStructure of the Atom: Unit Review
Atomic structure connects evidence at several scales. Scattering locates the nucleus, isotope notation counts nuclear particles, spectra reveal energy differences, and…
Explore lesson ChemistryLessonStructures of Metal Oxides and Halides
Across a period, an oxide or chloride formula can conceal a major structural change. Sodium and magnesium oxides are often described as ionic lattices; silica is a covalent…
Explore lesson ChemistryLessonStructures of the Noble Gas Compounds
Noble gases are often introduced as unreactive because their valence shells are filled. Xenon fluorides and oxides show that “unreactive” is a trend, not an absolute prohibition.…
Explore lesson ChemistryLessonStudent's t-Test: Comparing Means
An analyst may want to know whether a measured mean differs more from a reference than expected from random variation. Student's t test compares the difference with the…
Explore lesson ChemistryLessonSubatomic Particles in Ions
Ion formation changes the balance of charge in an atom without normally changing its nucleus. The particle counts therefore provide a precise way to describe the transformation.…
Explore lesson ChemistryLessonSublimation and Deposition
Most substances go from solid to liquid to gas as they are heated. A few take a shortcut. Solid carbon dioxide, known as dry ice, never forms a puddle: it turns straight into…
Explore lesson ChemistryLessonSubscripts in Chemical Formulae
The small numbers tucked below the line in formulae such as H₂O and CO₂ are called subscripts. They look minor, but they carry some of the most important information in…
Explore lesson ChemistryLessonSubscripts Versus Coefficients
The difference between a small subscript and a large coefficient is the central rule of equation balancing. A subscript defines a species, while a coefficient tells us how many…
Explore lesson ChemistryLessonSubstances Without Discrete Molecules
Water is made of separate molecules, each with exactly two hydrogen atoms and one oxygen atom. But what is "one molecule" of table salt, of a diamond or of a copper coin? The…
Explore lesson ChemistryLabSubstituent effects in aromatic substitution
Substituents on benzene decide whether a new group goes ortho/para or meta, and how fast.
Explore lesson ChemistryLessonSubstituent Effects on Carboxylic Acid Acidity
Not all carboxylic acids have the same acidity. Replacing a nearby H with an electron-withdrawing group can stabilise the conjugate-base carboxylate and lower pKa. Placing that…
Explore lesson ChemistryLessonSubstituent Effects on Phenol Acidity
Adding a group to phenol's ring can make its O–H proton easier or harder to remove. The direction depends on how the group changes the stability of phenoxide relative to phenol.…
Explore lesson ChemistryLessonSubstituents on Aromatic Amine Basicity
Aniline is a baseline, not a single basicity value for every aromatic amine. A substituent on the benzene ring can pull electron density away from or push it toward the…
Explore lesson ChemistryLessonSubstitution and Elimination Networks
A haloalkane and reagent do not arrive with a label saying "substitution" or "elimination." The same substrate can form an alcohol, ether, nitrile or alkene depending on the…
Explore lesson ChemistryLessonSubstitution on Aromatic Halides
Aryl halides resist ordinary alkyl SN1 and SN2, but some can undergo nucleophilic aromatic substitution. A common activated route requires a strong electron-withdrawing…
Explore lesson ChemistryLessonSubstitution versus Elimination
A haloalkane can produce a substitution product, an alkene, or both. Nucleophiles and bases are often the same electron-pair-donating reagents, but they use their electron pair…
Explore lesson ChemistryLessonSubstitution versus Elimination: Choosing the Pathway
The same alkyl halide may form a substitution product, an alkene, or both. Choosing a pathway requires more than remembering a single slogan about strong reagents. A nucleophile…
Explore lesson ChemistryLessonSuccessive Ionisation Energies
Magnesium commonly forms Mg²⁺, but a third electron removal is far harder than the first two. Once its two outer 3s electrons are gone, the next electron would come from the…
Explore lesson ChemistryLessonSuccessive Ionisation Enthalpies
First ionisation enthalpy removes one electron from a neutral atom. A second removes one from the resulting positive ion, and so on. The sequence generally increases. A…
Explore lesson ChemistryLessonSulfonation and Friedel-Crafts Reactions
Aromatic substitution can introduce more than halogen or nitro groups. Sulfonation attaches a sulfonic-acid group; Friedel-Crafts alkylation attaches an alkyl carbon fragment…
Explore lesson ChemistryLessonSulfur Allotropes and Ring Structures
Elemental sulfur can be yellow even though its atoms form several different solid arrangements. The common rhombic and monoclinic crystalline forms both involve S₈ rings, but the…
Explore lesson ChemistryLessonSulfur and Its Oxoacids
Sulfur forms rings, chains, oxides and oxoacids. At ordinary temperature, a common stable elemental form contains S₈ rings rather than isolated S atoms. Burning sulfur gives SO₂…
Explore lesson ChemistryLessonSulfur Chemistry and Acid Deposition
Unpolluted rain is already slightly acidic because it dissolves carbon dioxide, giving a pH of about 5.6. In the second half of the twentieth century, rain in parts of Europe and…
Explore lesson ChemistryLessonSulfur Dioxide Chemistry
Sulfur dioxide is a pungent gas with sulfur at formal oxidation state +4. It can form acidic aqueous species, react with bases and participate in redox reactions. Because +4 lies…
Explore lesson ChemistryLessonSulfur Dioxide, Nitrogen Oxides and Acid Rain
Clean rain is naturally slightly acidic, but in the twentieth century rain over industrial regions of Europe and North America became far more acidic than it should have been.…
Explore lesson ChemistryLessonSulfur Oxyanion Lewis Models
Sulfate, SO₄²⁻, exposes a limit of simple rules. Some diagrams draw four S–O single bonds and many formal charges; others draw two S=O double bonds and two singles, reducing…
Explore lesson ChemistryLessonSulfur Trioxide and Sulfuric Acid
Sulfur trioxide is the +6 oxide of sulfur and the immediate chemical precursor to sulfuric acid. Its hydration is strongly exothermic, which shapes industrial handling. The…
Explore lesson ChemistryLessonSuperacids and Non-Aqueous Acidity
Ordinary aqueous pH is a useful measure for many dilute solutions, but it cannot by itself describe the protonating power of a nearly water-free acid mixture. Some media can…
Explore lesson ChemistryLessonSupercapacitors and Pseudocapacitance
Electrochemical capacitors, often called supercapacitors, can deliver high power and withstand many cycles because much of their charge storage occurs near surfaces. A porous…
Explore lesson ChemistryLessonSuperconductors
Cooling some materials below a critical temperature produces a phase with no measurable dc electrical resistance and a distinctive response to magnetic fields. The magnetic…
Explore lesson ChemistryLessonSupercritical Carbon Dioxide
Carbon dioxide above its critical point is neither an ordinary liquid nor an ordinary gas. Its density and dissolving ability can be adjusted with pressure and temperature, while…
Explore lesson ChemistryLessonSuperexchange and Copper(II) Acetate
Hydrated copper(II) acetate is a classic demonstration that two locally paramagnetic metal ions can form a nearly nonmagnetic molecular ground state. Its two Cu²⁺ centres are…
Explore lesson ChemistryLessonSupersaturation and Crystallisation
Cooling a hot saturated solution does not always cause crystals to appear immediately. If dissolved material temporarily stays in the liquid above the new equilibrium limit, the…
Explore lesson ChemistryLessonSupported Molecular Catalysts
Homogeneous catalysts offer precise, tunable active sites, but separating them from products is costly. Supported molecular catalysts try to solve this by anchoring a…
Explore lesson ChemistryLessonSurface and Adsorption Formulae
Surface formulae are compact only when their interface and assumptions are named. Surface tension can be expressed as force per length or energy per area; a Langmuir isotherm…
Explore lesson ChemistryCollectionSurface Chemistry
Study Surface Chemistry with 20 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryCollectionSurface Chemistry, Colloids and Nanochemistry
Study Surface Chemistry, Colloids and Nanochemistry with 40 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonSurface Chemistry, Colloids and Nanochemistry: Unit Review
This unit started with the energetic cost of making interfaces and ended with nanomaterials whose useful properties depend on their size and surfaces. Adsorption, micelles…
Explore lesson ChemistryLessonSurface Chemistry: Unit Review
Surface chemistry links events at interfaces to large-scale observations: gas capture, catalytic conversion, stable milk, clear water and persistent foams. The common thread is…
Explore lesson ChemistryLessonSurface Hopping Models
Photochemical and other multistate reactions need both moving nuclei and changing electronic populations. Fully quantum dynamics across all nuclear coordinates can be…
Explore lesson ChemistryLessonSurface Slabs and Adsorption Energies
A clean infinite crystal does not expose a surface, but catalysts, electrodes and sensors act at surfaces. Periodic electronic-structure calculations represent a surface with a…
Explore lesson ChemistryLessonSurface Tension and Viscosity
A liquid droplet tends to minimise its surface area, while syrup resists flowing more than water. These observations involve two different properties. Surface tension concerns…
Explore lesson ChemistryLessonSurface-Area-to-Volume Scaling
One of the clearest size effects in nanoscience is geometric. Cutting the same amount of solid into many smaller pieces increases its total surface area. The increase exposes…
Explore lesson ChemistryLessonSurface-Enhanced Raman Scattering
A molecule can have a very weak ordinary Raman signal yet produce a strong spectrum when placed close to a rough metal surface or engineered nanostructure. Surface-enhanced Raman…
Explore lesson ChemistryLessonSurfactant Monolayers at Interfaces
An amphiphile can reach a water surface in two quite different ways. A soluble surfactant can adsorb from the water below, while an almost insoluble lipid can be spread directly…
Explore lesson ChemistryLessonSurfactant Structure and Classification
One end of a surfactant interacts favourably with water, while another part prefers oil or air. This molecular contrast explains why surfactants collect at interfaces, reduce…
Explore lesson ChemistryLessonSuspensions and Colloids
Salt water is clear, muddy water is cloudy and settles, and milk is cloudy but never settles no matter how long you leave it. These three liquids show that there is more than one…
Explore lesson ChemistryLessonSustainability of Energy Materials
Energy technologies can reduce emissions in use while still demanding mining, processing, manufacturing and end-of-life management. A chemistry with abundant elements may need…
Explore lesson ChemistryLessonSuzuki–Miyaura Coupling
The Suzuki–Miyaura coupling joins an aryl or vinyl halide with an organoboron compound, usually a boronic acid, using a palladium catalyst and a base. It is the most widely used…
Explore lesson ChemistryLessonSymbols for Atoms
Writing "one atom of sodium joined to one atom of chlorine" every time would be slow and clumsy. Chemists use a shorthand understood all over the world: chemical symbols. The…
Explore lesson ChemistryLessonSymbols from Latin Names
Some symbols seem to make no sense at first: why is iron Fe, gold Au and lead Pb? The answer is history. When Berzelius created letter symbols, Latin was the shared language of…
Explore lesson ChemistryLessonSymmetry as a Quantum-Chemistry Tool
Quantum chemistry can become algebraically demanding even for small molecules. Symmetry provides a disciplined way to remove combinations that cannot interact, identify…
Explore lesson ChemistryLessonSymmetry Elements and Achirality
Finding a stereocentre is useful, but the ultimate chirality test concerns the whole molecule and its mirror image. A molecular mirror plane can make a structure achiral even…
Explore lesson ChemistryLessonSymmetry Elements and Chirality in Complexes
To decide whether a coordination arrangement has optical isomers, ask whether its mirror image can be superimposed by rotation. Symmetry provides quick tests. A mirror plane or…
Explore lesson ChemistryLessonSymmetry in Computational Chemistry
Group theory has a practical role in computational chemistry beyond assigning labels after a calculation. A symmetry-adapted basis makes many matrix elements exactly zero…
Explore lesson ChemistryLessonSymmetry Numbers and Nuclear Spin
The high-temperature rotational partition function of a linear molecule, q_R = kT/(hcB̃), counts every rotational level J as if each one were available. For HCl that is correct.…
Explore lesson ChemistryLessonSymmetry of Normal Vibrations
An N-atom molecule has three Cartesian displacement coordinates per atom, giving a 3N-dimensional space of small motions. Not every motion is a vibration: some move the whole…
Explore lesson ChemistryLabSymmetry operations
Apply symmetry operations to a molecule and work out its point group.
Explore lesson ChemistryLessonSymmetry Operations and Elements
Point-group analysis begins with precise transformations. A drawing may look balanced, but a valid symmetry operation must move every nucleus to a position occupied by an…
Explore lesson ChemistryLessonSymmetry-Adapted Linear Combinations
When several ligands surround a central atom, testing every ligand orbital against every central orbital hides the symmetry of the whole arrangement. A symmetry-adapted linear…
Explore lesson ChemistryLessonSynthesis of Solid-State Materials
A target formula does not specify how to make a useful solid. The same average composition can appear as a dense ceramic, nanocrystalline powder, porous film or epitaxial layer…
Explore lesson ChemistryLessonSynthetic Equivalents
Retrosynthesis may produce fragments such as a methyl anion or acyl cation on paper. Many such species are not practical to isolate and combine. Synthetic equivalents are real…
Explore lesson ChemistryLessonSynthetic Indicators: Methyl Orange
Phenolphthalein detects alkalis. For detecting acids, chemists often reach for a different synthetic indicator: methyl orange. It is red in acids and yellow in alkalis, with an…
Explore lesson ChemistryLessonSynthetic Indicators: Phenolphthalein
Natural indicators from plants are cheap and fun, but their colours vary and they spoil quickly. Chemists therefore use synthetic indicators, made in factories with a fixed, pure…
Explore lesson ChemistryLessonSynthetic Strategy: Choosing the Best Route
Retrosynthesis often produces several chemically plausible routes. Choosing among them is a separate skill. The best route is not simply the shortest tree or the one using the…
Explore lesson ChemistryLessonSynthons and Synthetic Equivalents
Retrosynthesis often breaks a target bond into idealized pieces called synthons. A drawn synthon may carry a formal positive or negative charge to show the reactivity needed in…
Explore lesson ChemistryLessonSystem, Surroundings and Boundary
Before assigning a sign to heat or work, decide what counts as the system. The same experiment can be described with the reacting chemicals as the system or with the calorimeter…
Explore lesson ChemistryLessonSystematic and Random Errors
When analytical results disagree with expectation, the pattern of disagreement provides clues. Some errors shift almost every result in one direction. Others make results scatter…
Explore lesson ChemistryLessonSystematic Errors
A balance that shows 0.20 g with nothing on the pan will add 0.20 g to every mass you record. You can weigh a sample ten times, get beautifully consistent results, and still be…
Explore lesson ChemistryLessonSystematic Isomer Counting: The Method
Isomer counting is easiest to get wrong by drawing many pictures and treating every different-looking projection as a new compound. A systematic method fixes a reference…
Explore lesson ChemistryLessonTafel Analysis
At enough overpotential in one direction, one Butler–Volmer exponential can dominate the other. Taking a logarithm then turns an exponential current relation into a straight-line…
Explore lesson ChemistryLessonTafel Behavior
At sufficiently large overpotential, one direction of electrode electron transfer can dominate the other. The Butler–Volmer equation then simplifies to a logarithmic current…
Explore lesson ChemistryLessonTanabe–Sugano Diagrams for d³ and d⁸
Chromium(III) and nickel(II) offer practical examples of multi-band coordination spectra. Cr³⁺ is d³ and Ni²⁺ is d⁸; both have an octahedral A₂g ground state derived from an F…
Explore lesson ChemistryLabTanabe–Sugano explorer
Fit a Tanabe–Sugano diagram to a real complex’s spectrum to find Δo and the Racah B.
Explore lesson ChemistryLessonTandem Solar Cells
A single band gap wastes low-energy photons by transmission and much of high-energy photon energy by thermalization. A tandem places absorbers with different gaps in the path of…
Explore lesson ChemistryLessonTemperature and pH Effects on Enzyme Rates
Enzyme rates depend on temperature and pH, but their response cannot be reduced to one universal optimum. Warming can accelerate elementary chemistry while also destabilising…
Explore lesson ChemistryLessonTemperature and pH Effects on Enzymes
Enzymes do not have one universal “best” temperature or pH. A measured optimum reflects competing physical processes: molecular motion and catalytic rate may rise with…
Explore lesson ChemistryLessonTemperature and Pressure Control in MD
An MD trajectory does not automatically represent the laboratory conditions of an experiment. A sealed fixed-volume system with no heat exchange approximates one ensemble; a…
Explore lesson ChemistryLessonTemperature and Pressure Dependence of Chemical Potential
Phase stability can change when temperature or pressure changes because each phase's chemical potential responds differently. A pure phase has a particularly useful differential…
Explore lesson ChemistryLessonTemperature and Rate Constants
Heating many reactions makes them faster, but a temperature change can also alter equilibrium composition. These are different effects. Kinetics asks how the forward and reverse…
Explore lesson ChemistryLessonTemperature and Solid Solubility
Heating helps many solids dissolve faster, and many solids have higher equilibrium solubility in hotter water. The second statement is a trend with important exceptions, not a…
Explore lesson ChemistryLessonTemperature and the Rate of Diffusion
Drop a tea bag into a cup of cold water and the colour creeps out slowly. Drop one into hot water and brown swirls spread almost at once. Food smells drift further from a hot…
Explore lesson ChemistryLessonTemperature Changes and Equilibrium
Temperature is special among common equilibrium disturbances because it can change the equilibrium constant itself. Heating favors the endothermic direction in the standard…
Explore lesson ChemistryLessonTemperature Dependence of Cell Voltage
Cell voltage changes with temperature because the chemical free-energy difference changes. Measuring reversible EMF at nearby temperatures can reveal reaction entropy and…
Explore lesson ChemistryLessonTemperature Dependence of Equilibrium Constants
An equilibrium constant can change strongly with temperature, even when no material is added. The van 't Hoff equation links its slope to standard reaction enthalpy. Exothermic…
Explore lesson ChemistryLessonTemperature Dependence of Kw and pH
The familiar statement “neutral pH is 7” is tied to water near 25 °C and common concentration approximations. Water's autoionisation equilibrium changes with temperature.…
Explore lesson ChemistryLessonTemperature Scales for Gas Problems
Gas-law formulas use absolute temperature. A temperature of 20 °C is not “twice as hot” in the gas-law sense as 10 °C, because the Celsius zero is a chosen reference near water's…
Explore lesson ChemistryLessonTemperature Thresholds for ΔG
When ΔH and ΔS have the same sign, increasing temperature can change which term controls ΔG. Setting ΔG = 0 gives a simple threshold T* = ΔH/ΔS if both values are treated as…
Explore lesson ChemistryLessonTemperature: The Kelvin
On a cold winter night the temperature might drop to −10 °C. But what does a negative temperature really mean? The Celsius scale puts zero at the freezing point of water, which…
Explore lesson ChemistryLessonTemporary Hardness
Some hard water becomes soft simply by being boiled. If you boil hard water from a limestone area and let it cool, soap will lather in it much more easily — but the kettle gains…
Explore lesson ChemistryLessonTerm Symbols: Orbital and Spin Angular Momentum
Orbital labels such as 2p and π describe one-electron functions, but spectra often involve entire many-electron states. Atomic term symbols summarise total electronic orbital…
Explore lesson ChemistryLessonTermolecular and Pressure-Dependent Reactions
Two reactive fragments can join, but the newly formed molecule may contain enough excess internal energy to separate again. A collision with a third particle can remove energy…
Explore lesson ChemistryLessonTernary Phase Diagrams and Tie Lines
A binary composition needs one independent fraction; a ternary composition needs two. An equilateral triangle provides a compact map because every point can represent three…
Explore lesson ChemistryLessonTesting Cations with Aqueous Ammonia
Aqueous ammonia can cause a metal hydroxide precipitate and, in excess, dissolve selected precipitates by forming soluble ammine complexes. These are two different chemical…
Explore lesson ChemistryLessonTesting Cations with Sodium Hydroxide
Sodium hydroxide supplies OH⁻, which can precipitate many metal ions as hydroxides. The precipitate's colour and response to further OH⁻ narrow cation candidates. Fe²⁺ can give…
Explore lesson ChemistryLessonTesting for Hydrogen Gas
Metal reactions with water or dilute acid can release a colourless gas, but bubbling alone cannot tell whether it is hydrogen. A standard school test brings a lighted splint to a…
Explore lesson ChemistryLessonTesting for Ions in Salts
A white powder labelled simply "salt" could be sodium chloride, sodium carbonate, sodium sulfate or many other compounds. Chemists identify it by testing for the ions it…
Explore lesson ChemistryLessonTesting for Oxygen and Carbon Dioxide
Oxygen and carbon dioxide are both colourless, odourless gases. A test tube full of one looks exactly like a test tube full of the other, or like a tube of ordinary air. So how…
Explore lesson ChemistryLessonTesting Langmuir Behaviour with Linear Plots
A curved uptake plot can resemble a Langmuir isotherm even when the microscopic surface is heterogeneous. A linear transformation offers a diagnostic and a quick way to extract…
Explore lesson ChemistryLessonTesting Purity with Boiling Points
Melting points test the purity of solids; boiling points do the same job for liquids. Pure water boils at 100 °C at sea level, and the temperature stays exactly there until all…
Explore lesson ChemistryLessonTesting Purity with Melting Points
How can a chemist tell whether a newly made white powder is pure? You cannot see impurities with the naked eye, but you can measure them indirectly. One of the quickest and most…
Explore lesson ChemistryLessonTesting the Purity of Water
Food labels often call orange juice or spring water "pure", meaning nothing has been added. A chemist means something much stricter: a pure substance contains only one element or…
Explore lesson ChemistryLessonTetrahedral and Octahedral Voids
Even the most efficient equal-sphere packing leaves spaces between spheres. Some spaces have four surrounding spheres in a tetrahedral arrangement; others have six in an…
Explore lesson ChemistryLessonTetrahedral Carbon: Shape in Three Dimensions
On paper we often draw methane as a flat cross with four hydrogens at 90° to one another. Real molecules are not flat. The four hydrogens in methane point to the corners of a…
Explore lesson ChemistryLessonTetrahedral d-Orbital Splitting
Four ligands at the corners of a tetrahedron approach between the Cartesian axes, unlike six octahedral ligands that approach along them. The direction change reverses which…
Explore lesson ChemistryLessonTetrahedral Electron Arrangements
When a central atom has four electron domains, spreading them equally in three dimensions gives a tetrahedral pattern. Methane and ammonium show the simplest case: all four…
Explore lesson ChemistryLessonTetrahedral Splitting and the 4/9 Relationship
Four ligands at the corners of a tetrahedron approach the central metal along directions between the Cartesian axes. That changes which d orbitals experience the greatest…
Explore lesson ChemistryLessonTetrahedral, Pyramidal and Bent Shapes
Methane, ammonia and water all have four electron domains at their central atoms in the basic VSEPR model. Yet their atom shapes differ: tetrahedral, trigonal pyramidal and bent.…
Explore lesson ChemistryLessonTg and Melting Compared
Glass transition and melting can both soften a polymer, but they involve different structures and different thermal signals. T_g concerns mobility in amorphous regions; T_m…
Explore lesson ChemistryLessonThe 12 Principles of Green Chemistry: An Overview
The twelve principles of green chemistry are a set of questions to ask while designing molecules and processes. They cover waste, atom use, toxicity, solvents, energy…
Explore lesson ChemistryLessonThe 18-Electron Rule
The 18-electron rule is a useful first check for many transition-metal complexes. It reflects filling a set of metal-centred valence orbitals through metal and ligand electrons.…
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