THE LESSON LIBRARY / CHEMISTRY
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Redox Versus Acid–Base Reaction
Acid–base and redox are classifications based on different chemical changes. Neutralisation may transfer a proton without changing oxidation numbers, while a metal reacting with…
Explore lesson ChemistryLessonRedox Versus Precipitation
A new solid can appear in both precipitation and redox, but the underlying chemistry may differ. In precipitation, existing ions assemble into an insoluble compound without…
Explore lesson ChemistryLessonRedox with Dichromate in Acid
Dichromate contains two chromium atoms, so its electron count requires attention to both atoms. In the stated acidic reduction, each chromium changes from +6 to +3. One…
Explore lesson ChemistryLessonRedox with Permanganate in Acid
Permanganate is a useful oxidising reagent, but its manganese product depends on conditions. In the acidic examples on this page, MnO₄⁻ becomes Mn²⁺. Manganese falls from +7 to…
Explore lesson ChemistryLessonReducing a Representation
Once a basis has been converted into a list of characters, the next question is which irreducible symmetry species it contains. The character reduction formula answers this…
Explore lesson ChemistryLessonReducing Agents
A reducing agent enables another species to be reduced. It donates electrons in simple ionic reactions and is oxidised itself. Just as “oxidising agent” names a species by its…
Explore lesson ChemistryLessonReducing Air Pollution
Earlier in this unit you met the main air pollutants from burning fuels: carbon monoxide, soot, unburnt hydrocarbons, sulfur dioxide and nitrogen oxides. Knowing where pollution…
Explore lesson ChemistryLessonReducing and Alkylating Acid Derivatives
An ester or amide can be transformed by strong hydride or carbon nucleophiles, but the final product depends on which group leaves and whether the newly formed intermediate…
Explore lesson ChemistryLessonReducing Derivatives and Protecting Groups
Protecting groups can be indispensable when a molecule contains several reactive sites. They temporarily block one group while another reacts, then are removed. Each added…
Explore lesson ChemistryLessonReducing Sugars
Why does glucose give a positive copper-reduction test while intact sucrose usually does not? The answer is found at the anomeric center. A free cyclic hemiacetal can open to a…
Explore lesson ChemistryLessonReduction as Removal of Oxygen
The historical partner of oxygen-addition oxidation is oxygen-removal reduction. A metal oxide can lose oxygen and become a metal, while another reactant takes up that oxygen.…
Explore lesson ChemistryLessonReduction of Aldehydes and Ketones
Aldehydes and ketones can be reduced to alcohols. An aldehyde normally gives a primary alcohol, and a ketone normally gives a secondary alcohol. This pattern follows directly…
Explore lesson ChemistryLessonReduction with a More Reactive Metal
One metal can reduce another metal's oxide when forming its own oxide is favorable under suitable conditions. Aluminium is a familiar reductant for selected metal oxides. In the…
Explore lesson ChemistryLessonReduction with Carbon
Carbon can help turn some metal oxides into elemental metals by taking oxygen into carbon-containing products. This is a useful extraction principle for suitable oxides, but not…
Explore lesson ChemistryLessonReduction with Carbon Monoxide
Carbon monoxide can remove oxygen from suitable metal oxides in a hot reactor. The oxide's metal ions gain electrons and form metal, while CO becomes CO₂. This gas–solid route is…
Explore lesson ChemistryLessonReductive Elimination
Oxidative addition brings two fragments onto a metal. Reductive elimination can join two metal-bound groups into a new A–B bond and release the product. In cross-coupling…
Explore lesson ChemistryLessonReference Electrodes
A voltmeter measures a difference between two electrode connections; it cannot report one isolated absolute half-cell potential. To study an electrode reaction, chemists pair the…
Explore lesson ChemistryLessonRefining Metals to High Purity
Extracted metal is rarely pure enough for every use. Residual carbon, other metals, oxygen or nitrogen can change conductivity, corrosion behaviour and mechanical properties.…
Explore lesson ChemistryLessonRegioselectivity in Diels–Alder Reactions
An unsymmetrical diene and an unsymmetrical dienophile can meet in two end-to-end orientations. Both may obey the basic [4+2] atom count and preserve stereochemistry, yet they…
Explore lesson ChemistryLessonRegression for Chemical Data
Chemical data often form curves: absorbance versus concentration, rate versus reactant amount, or capacity versus cycle number. Regression turns a proposed relationship into…
Explore lesson ChemistryLessonRegulating the Citric Acid Cycle
The citric acid cycle is a hub for both energy production and biosynthetic precursors. Its flux should rise when cells need ATP and fall when reduced carriers and ATP are…
Explore lesson ChemistryLessonReimer–Tiemann Reaction
Phenol can gain an aldehyde group on its aromatic ring when treated with chloroform and aqueous base, followed by hydrolysis and acid work-up. The main introductory product has…
Explore lesson ChemistryLessonRelative Atomic Mass and Isotopes
The atomic mass printed on a periodic table is often not a whole number. It represents an abundance-weighted average of the masses of naturally occurring isotopes, expressed…
Explore lesson ChemistryLessonRelative Atomic Mass Revisited
Before we can weigh out moles of a substance, we need reliable masses for its atoms. You have already met relative atomic mass as a way of comparing atoms. Now we look at it…
Explore lesson ChemistryLessonRelative Atomic Mass: A First Look
Atoms are astonishingly light. A single hydrogen atom has a mass of about 1.7 × 10⁻²⁴ g — far too small to weigh directly or to use comfortably in calculations. Chemists solve…
Explore lesson ChemistryLessonRelative Atomic Mass: The Idea
If someone tells you that an elephant "weighs about as much as sixty people", you instantly get a feel for its mass, even without a number in kilograms. That is a relative…
Explore lesson ChemistryLessonRelative Formula Mass
Once you know how heavy each type of atom is on the relative scale, you can work out how heavy a whole molecule or formula unit is. Just add up the relative atomic masses of…
Explore lesson ChemistryLessonRelative Formula Mass of Hydrated Salts
Some crystalline salts contain water as part of their stated chemical formula. Ignoring it can cause a large error in a formula mass or mole calculation. Copper(II) sulfate…
Explore lesson ChemistryLessonRelative Formula Mass of Ionic Compounds
Ionic compounds such as calcium carbonate and copper sulfate have no molecules, so the phrase "relative molecular mass" does not really fit them. Instead, we use the relative…
Explore lesson ChemistryLessonRelative Formula Mass of Molecules
Relative atomic masses describe single atoms, but most substances are made of atoms joined together. To weigh out a mole of water, sugar or carbon dioxide, we first need the…
Explore lesson ChemistryLessonRelative Lowering of Vapour Pressure
Adding a nonvolatile solute to an ideal liquid solution reduces the solvent's mole fraction below one. The solvent vapour pressure falls from p° to p. Dividing this drop by p°…
Explore lesson ChemistryLessonRelative Molecular Mass
Once we know the relative masses of atoms, we can find the relative masses of molecules. A molecule is simply a group of bonded atoms, so its mass is the total of the masses of…
Explore lesson ChemistryLessonRelativistic Effects in Heavy-Element Chemistry
Nonrelativistic quantum chemistry is remarkably useful for many light-element molecules, but electrons close to a heavy nucleus experience strong electric fields. Their behavior…
Explore lesson ChemistryLessonRelaxation Methods for Fast Reactions
Some reactions finish before reactants can be mixed and sampled by ordinary methods. Relaxation experiments take a different approach: begin with a system already at equilibrium…
Explore lesson ChemistryLessonRemoving Translations and Rotations
A 3N displacement representation includes every small Cartesian motion, but spectroscopy of internal vibrations requires a smaller space. Whole-molecule translations and…
Explore lesson ChemistryLessonRenewable Feedstocks
Fossil feedstocks formed over geological timescales, while biomass can regrow within years or decades. Green chemistry encourages using renewable starting materials where…
Explore lesson ChemistryLessonRepeated Half-Life Calculations
Half-life calculations often look like subtraction problems, but they are repeated multiplication by one-half. The amount lost in each interval changes because each interval…
Explore lesson ChemistryLessonReplicates and Independent Samples
“We measured six replicates” can describe six independent reactions or six injections of one reaction mixture. Those designs answer different questions. Repeated readings reveal…
Explore lesson ChemistryLessonRepresentations and Matrices
Geometric operations become useful in quantum chemistry when we know how they act on wavefunctions, coordinates or atomic displacements. A representation assigns a matrix to each…
Explore lesson ChemistryLessonRepresenting Organic Molecules
The formula C₄H₁₀ tells you what atoms a molecule contains, but not how they are joined — and two different compounds share that formula. Organic chemists therefore use several…
Explore lesson ChemistryLessonRepresenting Organic Structures
Organic molecules can be written at several levels of detail. C₃H₈O is compact but ambiguous. CH₃CH₂CH₂OH fixes a connectivity, while a displayed drawing shows bonds more…
Explore lesson ChemistryLessonReproducible Computational Analysis
Modern chemistry can turn a raw spectrum into a concentration through dozens of computational choices: baseline subtraction, smoothing, peak finding, calibration, blank…
Explore lesson ChemistryLessonReproducible Computational Workflows
A number such as “barrier = 42 kJ mol⁻¹” is not a complete computational result. Another researcher needs to know the reactant and transition-state structures, charge…
Explore lesson ChemistryLessonReproducible Nanomaterials Research
Nanomaterial properties depend on details that a chemical formula does not capture: core-size distribution, shape, crystal phase, surface ligands, residual reagents and…
Explore lesson ChemistryLessonResearch and Data Terms
Research terms determine how strongly a chemical conclusion is supported. A colorful reaction is an observation; an explanation of its mechanism is a hypothesis; a rate equation…
Explore lesson ChemistryLessonResearch Methods and Literature: Unit Review
Research methods connect a chemical question to a defensible answer. A good experiment defines a measurable claim, uses controls to isolate effects, calibrates instruments…
Explore lesson ChemistryCollectionResearch Methods, Data Analysis and Literature
Study Research Methods, Data Analysis and Literature with 30 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonResiduals and Model Misspecification
A fitted equation compresses chemical observations into a small set of parameters. Its residuals—the parts the equation does not explain—can show where that compression fails. A…
Explore lesson ChemistryLessonResidue and Filtrate
Filtration always produces two products, and chemists give each a name. The solid left behind on the filter paper is the residue; the liquid that drips through into the flask is…
Explore lesson ChemistryLessonResolution of Racemic Mixtures
Chemical reactions that make a new stereocentre from achiral materials normally give a racemate. Yet a medicine, flavour or agrochemical may need only one enantiomer. Separating…
Explore lesson ChemistryLessonResolution, Plate Number and Plate Height
Chromatograms display two linked but different qualities: how far apart peak centres are and how broad each peak is. Resolution combines both. Plate number and plate height…
Explore lesson ChemistryLessonResonance and Delocalised Electrons
A single Lewis diagram sometimes has to choose one place for a double bond even though measurements show that several bonds are equivalent. Resonance is the language for using…
Explore lesson ChemistryLessonResonance Effects
Some molecules cannot be described adequately by one localised Lewis structure. Resonance contributors distribute π electrons and lone pairs across a connected set of atoms while…
Explore lesson ChemistryLessonResonance Effects of Substituents
A group attached to a conjugated framework may influence distant positions by resonance. Lone-pair-bearing groups can donate electron density into a pi system, while groups with…
Explore lesson ChemistryLessonResonance in Nitrate and Carbonate
Nitrate NO₃⁻ and carbonate CO₃²⁻ each have three equivalent oxygen positions around a central atom in their usual bonding models. A single Lewis drawing places one double bond at…
Explore lesson ChemistryLessonResonance in Organic Structures
A single Lewis drawing can force a double bond or charge into one place even when electrons are spread across several atoms. Resonance uses multiple valid contributors to…
Explore lesson ChemistryLessonResonance Is Not Molecular Switching
Several kinds of chemistry diagrams show alternatives. Two sketches may be resonance contributors, structural isomers or reactants and products in an equilibrium. They can look…
Explore lesson ChemistryLessonResonance Raman Spectroscopy
Ordinary Raman scattering is weak because only a small fraction of incident photons exchange vibrational energy with molecules. If the laser is tuned near an electronic…
Explore lesson ChemistryLessonResonance: How an NMR Spectrometer Works
Placing nuclei in a magnetic field creates two spin states separated by a tiny energy gap. On its own, that does nothing observable. To obtain a spectrum, the nuclei must be made…
Explore lesson ChemistryLessonResponse of a Buffer to Strong Acid
A buffer earns its name when something is added to it. Pour a small amount of hydrochloric acid into pure water and the pH can crash by several units; pour the same acid into a…
Explore lesson ChemistryLessonResponse of a Buffer to Strong Base
A buffer must defend against change in both directions. When strong base such as sodium hydroxide is added, it is the weak-acid member of the pair that does the work, donating…
Explore lesson ChemistryLessonResponsible Interpretation of Computed Results
Computational chemistry can make otherwise invisible molecular mechanisms testable and quantitative. Its results are strongest when reported as predictions from a defined model…
Explore lesson ChemistryLessonResponsible Photochemical Measurement
A claim that a reaction ran “under blue light” leaves many unanswered questions. Different blue lamps emit different spectra and powers; geometry changes exposure; and a colored…
Explore lesson ChemistryLessonResting States and Turnover-Limiting Steps
When a catalyst turns over, it passes through several intermediates, but it does not spend equal time in each. One species usually dominates: the resting state. Separately, one…
Explore lesson ChemistryLessonRestricted and Unrestricted Hartree–Fock
A closed-shell molecule can pair α and β electrons in the same spatial orbitals, but a radical has unpaired electrons and needs a different treatment. Hartree–Fock variants…
Explore lesson ChemistryLessonRetention Factors and Identification
Chromatography needs a way to describe where or when a component appears. A planar Rf value compares spot distance with solvent-front distance, while column chromatography…
Explore lesson ChemistryLessonRetrosynthesis: Problem Solving
An unfamiliar target can make memorized named reactions feel disconnected. A systematic solution begins with a complete target drawing, then searches for recognizable…
Explore lesson ChemistryLessonRetrosynthetic Analysis: Working Backwards
When a target molecule has several rings and functional groups, guessing reagents from the starting-material side can become a maze. Retrosynthetic analysis reverses the…
Explore lesson ChemistryLessonRetrosynthetic Thinking
Forward conversion asks what a reagent does to a given molecule. Retrosynthesis asks the complementary planning question: what precursor could become the target through a known…
Explore lesson ChemistryLessonReverse Osmosis and Solution Separation
Ordinary osmosis draws solvent toward a solution across a membrane that retains solute. If sufficient external pressure is applied to the solution side, the net solvent direction…
Explore lesson ChemistryLessonReversible and Irreversible Changes
Ice can melt and freeze again as many times as you like. A burnt piece of toast can never become bread again. The difference is reversibility: whether you can get the starting…
Explore lesson ChemistryLessonReversible Chemical Reactions
Most chemical reactions go one way. You cannot "unburn" a match or "uncook" an egg. But some reactions can run forwards and backwards: the products can react together to form the…
Explore lesson ChemistryLessonReversible Isothermal Gas Work
For a reversible isothermal expansion, an ideal gas pushes against an external pressure kept infinitesimally below its own pressure. The pressure falls as volume rises, so…
Explore lesson ChemistryLessonReversible Reaction Kinetics
Simple integrated rate laws assume a reaction runs to completion. Many reactions do not: as products accumulate, the reverse reaction becomes significant, and the composition…
Explore lesson ChemistryLessonReversible Reaction Networks
Many network arrows are reversible. A product may convert back to reactant, a surface species may adsorb and desorb, and an intermediate can exchange among several forms. Net…
Explore lesson ChemistryLessonReversible Reaction Rates
Many reactions are reversible. Reactant becomes product while product can become reactant, and the measured concentration change is the difference between these fluxes. At…
Explore lesson ChemistryLessonReversible Reactions and Equilibrium State
An equilibrium state is not defined by which side was present at the beginning. A reversible reaction can approach the same equilibrium composition from a reactant-rich start or…
Explore lesson ChemistryLessonReversing and Scaling Thermochemical Equations
Most Hess-law errors arise before the final addition: a step is reversed but its sign is not, or coefficients are halved while enthalpy stays unchanged. Manipulating…
Explore lesson ChemistryLessonReversing Physical Changes
Salt dissolves in seawater and seems to vanish. Water boils away from a pan and disappears into the air. Yet in both cases nothing has really been lost: the salt and the water…
Explore lesson ChemistryCollectionRevision and Practice Sets
Study Revision and Practice Sets with 15 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonRing Currents and Anisotropy
Electronegativity explains many chemical shifts, but it cannot explain the most striking ones. Benzene contains only carbon and hydrogen, yet its protons appear at about δ 7.3…
Explore lesson ChemistryLessonRing Flipping and Other Cyclohexane Conformers
A cyclohexane chair is flexible rather than fixed. Its ring can flip to another chair without breaking a bond. Following the motion explains why axial substituents can become…
Explore lesson ChemistryLessonRing Strain in Cycloalkanes
A carbon ring restricts bond angles and rotation. The simplest cycloalkanes therefore do not all have the same stability per carbon. Their shapes balance angle strain and…
Explore lesson ChemistryLessonRing-Opening Polymerisation
A cyclic monomer can become a long chain when its ring opens and the newly created end reacts with another ring. Lactones, lactams and cyclic ethers illustrate ring-opening…
Explore lesson ChemistryLessonRings and the Hydrogen Count
A saturated cycloalkane contains a carbon ring but no C=C or C≡C bond. Its simplest one-ring formula is CₙH₂ₙ. That matches a simple open-chain monoalkene, because both a ring…
Explore lesson ChemistryLessonRNA Structure and Roles
RNA is often summarized as a single-stranded copy of DNA, but that picture is too narrow. Its ribose sugar and uracil base distinguish it chemically, and one RNA chain can fold…
Explore lesson ChemistryLessonRoasting and Calcination
Many ores are not initially in the form chosen for metal production. A zinc sulfide concentrate may be roasted to zinc oxide, while zinc carbonate can be calcined to the same…
Explore lesson ChemistryLessonRoasting of Sulfide Ores
Many sulfide minerals are processed by heating in air so sulfur-containing material is oxidized. In simple examples, metal sulfide becomes metal oxide and sulfur dioxide gas.…
Explore lesson ChemistryLessonRobinson Annulation
Robinson annulation assembles a six-membered carbon ring by linking two familiar reactions. A stabilised carbon nucleophile first makes a Michael addition to an enone, forming a…
Explore lesson ChemistryLessonRoothaan–Hall Equations
The Fock operator acts on continuous orbital functions, but most practical calculations expand those orbitals in a finite set of atom-centred basis functions. This converts the…
Explore lesson ChemistryLessonRotational Heat Capacity of Molecules
Classical equipartition gives k of rotational heat capacity per linear molecule, but this is a high-temperature limit. A light molecule can have sufficiently separated rotational…
Explore lesson ChemistryLessonRounding to Significant Figures
A calculator shows 0.043 857 142 9 for the concentration of a solution, but your measurements justify only three significant figures. You need to shorten the number without…
Explore lesson ChemistryLessonRoutes to Amines
An amine target can be reached from several starting groups, but the routes are not interchangeable. Reducing a nitrile makes an amine with a CH₂ between the original R group and…
Explore lesson ChemistryLessonRRK and RRKM Theory in Outline
The simple Lindemann-Hinshelwood model treats every energised A* molecule as if it were the same. Real molecules carry a distribution of internal energies, and a molecule only a…
Explore lesson ChemistryLessonRules for Counting Significant Figures
Knowing that significant figures show precision is only half the job; you also need to count them reliably. Non-zero digits cause no trouble, but zeros are tricky. Sometimes a…
Explore lesson ChemistryLessonRun-off, Infiltration and Groundwater
When rain falls on a hillside, where does it go? Some of it runs straight over the surface and into the nearest stream. Some soaks into the soil and is taken up by plant roots.…
Explore lesson ChemistryLessonRusting of Iron
Iron rusts when it is exposed to suitable moisture and oxygen. The reddish-brown material is often summarized as hydrated iron oxide, but real rust can contain several iron…
Explore lesson ChemistryLessonRusting of Iron Needs Water and Oxygen
An iron object can remain relatively unchanged in very dry air yet develop brown rust when damp air reaches it. Water alone, if oxygen is rigorously excluded, also gives much…
Explore lesson ChemistryLabRutherford scattering
Alpha particles are fired at gold foil. A few bounce back — evidence for a tiny, dense nucleus.
Explore lesson ChemistryLessonRutherford's Gold Foil Experiment
If atoms are too small to inspect directly, their internal structure can still be tested by how they deflect a probe. Alpha-particle scattering from thin metal foil supplied just…
Explore lesson ChemistryLessonRutherford's Nuclear Atom
Rutherford's nuclear model reorganised the atom. Positive charge and most mass were concentrated in a minute centre, with electrons associated with the much larger surrounding…
Explore lesson ChemistryLessonSacrificial Anodes
A steel structure exposed to water can be protected by attaching a metal that oxidizes more readily. That attached piece is a sacrificial anode. It supplies electrons through the…
Explore lesson ChemistryLessonSacrificial Protection and Galvanising
Paint and grease protect iron only while they are intact. But what if the protection could keep working even after a scratch? Sacrificial protection does exactly this. By…
Explore lesson ChemistryLessonSacrificial Protection of Iron
Iron can be protected by electrically connecting it to a metal that oxidises more readily under the service conditions, commonly zinc or magnesium. The attached metal is consumed…
Explore lesson ChemistryLessonSaddle Points and the Minimum-Energy Path
A one-dimensional reaction diagram shows a peak between reactants and products. On a full potential-energy surface, that peak is usually a saddle point: energy falls if the…
Explore lesson ChemistryLessonSafe Virtual Laboratories
In the ChemVerse Reaction Lab you can combine sodium with chlorine, spark a hydrogen–oxygen mixture or heat limestone — reactions that would be dangerous, expensive or impossible…
Explore lesson ChemistryLessonSafety Thinking in Inorganic Analysis
Classical inorganic analysis includes elegant reactions with materials that require care: sulfide acidification can release H₂S, sulfite can release SO₂, halogen tests can…
Explore lesson ChemistryLessonSafety with Acids, Bases and Salts
Acids and alkalis are among the most useful substances in a laboratory and in the home, but they can also cause serious injuries. A splash of concentrated alkali in the eye can…
Explore lesson ChemistryLessonSalt Bridge and Charge Balance
A wire can connect the electrodes of a galvanic cell, yet sustained electron flow still fails if charge cannot move through the electrolyte. A salt bridge or suitable separator…
Explore lesson ChemistryLessonSalt Hydrolysis
Dissolving a salt can produce a solution that is acidic, basic, or approximately neutral. The salt's ions may react with water after dissociation. Predicting pH therefore…
Explore lesson ChemistryLessonSalt Hydrolysis: The Central Idea
A neutral salt formula can produce an acidic or basic aqueous solution. The reason is not a failure of charge balance: after the salt dissolves, one of its ions may exchange a…
Explore lesson ChemistryLessonSalts in Food and Medicine
Salts are not just laboratory curiosities. You sprinkle one on your chips, bake with another, swallow a third when you have indigestion, and a fourth may help a doctor see inside…
Explore lesson ChemistryLessonSalts of Strong Acid and Strong Base
Some familiar salts give approximately neutral aqueous solutions. Sodium chloride is a useful example because its ions come from a strong acid and a strong hydroxide base and…
Explore lesson ChemistryLessonSalts of Strong Acid and Weak Base
A weak base can accept a proton from a strong acid and form a salt whose cation retains acid character. Ammonium salts are the clearest introductory examples. When dissolved…
Explore lesson ChemistryLessonSalts of Weak Acid and Strong Base
When a weak acid reacts with a strong hydroxide base, the salt often contains the weak acid's conjugate base. That anion may accept a proton from water and generate hydroxide.…
Explore lesson ChemistryLessonSampling and Sample Preparation
The first chemical operation in an analysis may happen before the instrument or laboratory ever sees the material: selecting a sample. A highly precise method can give a…
Explore lesson ChemistryLessonSampling, Equilibration and Autocorrelation
A molecular-dynamics file may contain millions of frames, but its statistical information can be far smaller. A water molecule's orientation at one picosecond is related to its…
Explore lesson ChemistryLessonSandmeyer and Diazonium Replacements
An arenediazonium salt turns an arylamine into a practical starting point for aromatic substitution. In the Sandmeyer reaction, a copper(I) halide helps replace Ar–N₂⁺ with Cl or…
Explore lesson ChemistryLessonSaponification of Fats
Saponification turns ester-rich fats or oils into glycerol and fatty-acid salts using a base such as sodium hydroxide. Each ester linkage reacts in basic hydrolysis. The…
Explore lesson ChemistryLessonSaturated Solutions
Keep adding sugar to a glass of water, stirring after each spoonful, and eventually the sugar stops disappearing and collects at the bottom. The water has taken all the sugar it…
Explore lesson ChemistryLessonSaturated versus Unsaturated
Ethane and ethene are both colourless gases, and hexane and hex-1-ene are both colourless liquids. You cannot tell them apart by looking. Yet one of each pair is saturated and…
Explore lesson ChemistryLessonSaturation Tests and Their Limits
Bromine-water decolourisation is often taught as an alkene test, but a single color change does not reveal a complete molecular structure. Other unsaturated species and…
Explore lesson ChemistryLessonScaling Laboratory Equations
A balanced equation works for a milligram experiment and a kilogram batch because its mole ratios are independent of size. Scaling the input by a factor scales theoretical…
Explore lesson ChemistryLessonScaling Relations Between Adsorbates
It would be convenient to tune each catalytic intermediate independently: stabilise the difficult one, destabilise the site-blocking one, and preserve everything else. Materials…
Explore lesson ChemistryLessonScanning Probe Microscopy
Scanning probe microscopes map surfaces by moving a sharp tip across them. Atomic force microscopy, AFM, uses mechanical interactions and can measure topography on many…
Explore lesson ChemistryLessonScattering and Diffraction at the Nanoscale
Microscopy shows selected objects directly; scattering measures how a large illuminated population redirects X-rays or neutrons. The resulting pattern is recorded in reciprocal…
Explore lesson ChemistryLessonSchottky Defects
An ionic crystal cannot normally develop a large net charge by removing only one ion type without compensation. A Schottky defect is a charge-balanced set of vacancies, typically…
Explore lesson ChemistryLessonScientific Models
Atoms are far too small to see directly, even with the best ordinary microscope. So how can chemists talk confidently about atoms bonding, electrons moving and molecules changing…
Explore lesson ChemistryLessonScientific Notation
Chemistry deals with numbers that are ridiculously large and ridiculously small. A single drop of water contains about 1 700 000 000 000 000 000 000 molecules, while one water…
Explore lesson ChemistryLessonScientific Writing for Chemistry
Good chemistry writing lets another researcher understand what was done, what was observed and why the conclusion follows. A polished narrative can still be scientifically weak…
Explore lesson ChemistryLessonScope and Language of Organic Chemistry
Organic chemistry studies a vast range of carbon compounds, from methane to medicines and polymers. The breadth is manageable when every structure is read in layers: a carbon…
Explore lesson ChemistryLessonSearching Chemical Literature
Chemical literature is large and terminology varies. The same compound may appear under a systematic name, a common name, a formula, an abbreviation or a structural identifier. A…
Explore lesson ChemistryLessonSecond Dissociation and Its Contribution
When we calculate the pH of a diprotic acid from Ka1 alone, we quietly throw away the second dissociation. Good chemistry does not leave such decisions unexamined. This page…
Explore lesson ChemistryLessonSecond Law and Total Entropy
The second law says that the entropy of an isolated total system does not decrease in a spontaneous process. The “total” includes the part we call the system and its…
Explore lesson ChemistryLessonSecond- and Third-Period Lengths
Period two runs from lithium to neon, and period three from sodium to argon. Each contains eight elements. The repeated length comes from filling two outer s positions followed…
Explore lesson ChemistryLessonSecond-Order Integrated Rate Law
For the specific second-order law −d[A]/dt = k[A]², the reciprocal of concentration rises linearly with time. Its half-life depends inversely on starting concentration, unlike…
Explore lesson ChemistryLessonSecond-Period MO Energy Ordering
The standard 2p orbital ordering in introductory MO diagrams changes across the second-period homonuclear diatomics. B₂, C₂ and N₂ commonly use π2p below σ2p, while O₂ and F₂ use…
Explore lesson ChemistryLessonSecondary Structure Geometry
Once peptide units and backbone torsions are understood, recurring local shapes become easier to explain. Secondary structure describes repeated backbone arrangements, especially…
Explore lesson ChemistryLessonSecular and Transient Equilibrium
A parent radionuclide can continuously create a radioactive daughter. If the daughter decays much faster than it is supplied, its inventory may remain small yet its activity can…
Explore lesson ChemistryLessonSecular Equations and Secular Determinants
The linear variation method reduces a quantum problem to a determinant that must equal zero. For two basis functions the determinant is only 2 × 2, yet its solution already…
Explore lesson ChemistryLessonSedimentation
Scoop a jar of water from a muddy river and leave it on a shelf. At first it is brown and cloudy; an hour later the bottom holds a layer of mud and the water above is much…
Explore lesson ChemistryLessonSeeing Atoms Indirectly
Atoms are far too small to be seen with light, so how can scientists be so sure they exist? For most of history the answer was "by their effects". Just as you can know the wind…
Explore lesson ChemistryLessonSEI and Cathode Interphase Design
Electrolyte and electrodes often react where they touch. A useful battery does not necessarily eliminate all reaction: it can form a thin interphase that allows the working ion…
Explore lesson ChemistryLessonSelecting a Buffer Pair
Designing a buffer starts with a choice: which weak acid and conjugate base should be used? The obvious rule is to match pKa to the target pH, but that is only the first filter.…
Explore lesson ChemistryLessonSelecting and Converting Gas Constants
The gas constant is universal, but its number changes when its units change. A calculator cannot tell whether 8.314 belongs with pascals and cubic metres, kilopascals and litres…
Explore lesson ChemistryLessonSelection Rules for Electronic Transitions
An energy-level diagram shows candidate transitions, but not whether light can drive them strongly. The probability of absorption depends on the transition electric-dipole…
Explore lesson ChemistryLessonSelection Rules for Hydrogen Transitions
The energy-level formula for hydrogen tells us where spectral lines *could* appear: any pair of levels gives a photon of energy ΔE = hν. Yet a high-resolution spectrum shows that…
Explore lesson ChemistryLessonSelective Hydroxide Precipitation
Raising pH raises hydroxide concentration, allowing metal hydroxides to precipitate. Different metals can reach their precipitation thresholds at different pH values, making…
Explore lesson ChemistryLessonSelective Precipitation — Equilibrium: Chemical and Ionic
When two dissolved ions form different sparingly soluble salts with a shared reagent ion, one solid may begin to precipitate before the other. Controlled reagent addition can…
Explore lesson ChemistryLessonSelective Precipitation — Inorganic Reasoning and Qualitative Analysis
Selective precipitation uses a reagent ion that forms solids of different solubilities with two dissolved ions. As the reagent ion concentration rises, one solid can reach Ksp…
Explore lesson ChemistryLessonSelective Precipitation of Two Cations
Many mixtures contain two metal ions that react with the same reagent. If both form sparingly soluble salts, adding that reagent slowly can remove one ion first while the other…
Explore lesson ChemistryLessonSelective Sulfide Precipitation
Metal sulfides include some of the least soluble compounds known, yet their Ksp values range over more than twenty powers of ten. That enormous spread makes sulfide an ideal…
Explore lesson ChemistryLessonSelf-Assembly and Nanostructured Surfaces
Nanostructures need not always be carved from a larger solid. Molecules can organise themselves on a surface because binding to the substrate and interactions among neighbours…
Explore lesson ChemistryLessonSelf-Consistent Field Iteration
Hartree–Fock orbitals create the average electron field in which those same orbitals move. The equation is therefore nonlinear even though solving a Fock matrix at one iteration…
Explore lesson ChemistryLessonSelf-Interaction and Delocalization Errors
An electron repels other electrons, but it should not repel itself. In Kohn–Sham DFT, the classical Coulomb term treats the total density as a continuously charged cloud and…
Explore lesson ChemistryLessonSemiconductor Electrodes and Photocatalysis
A solar cell extracts photocarriers through a wire. A photoelectrode instead delivers them to chemical reactants in a liquid. Splitting water into hydrogen and oxygen is a…
Explore lesson ChemistryLessonSemiconductor Photocatalysts
A semiconductor photocatalyst converts absorbed light into mobile or partly localized electrons and holes. A useful band gap allows absorption of a chosen spectrum, while…
Explore lesson ChemistryLessonSemiconductor Quantum Dots
A semiconductor quantum dot is more than a tiny piece of bulk semiconductor. Its core size can set the energy of an optical transition, while surface atoms and an optional shell…
Explore lesson ChemistryLessonSemiconductors and p–n Types
Semiconductors become especially useful when their mobile-carrier populations can be deliberately changed. Group-15 dopants in silicon commonly make n-type regions with electrons…
Explore lesson ChemistryLessonSensitivity Analysis
A network model can contain dozens of rate constants and starting concentrations. Not all influence a chosen prediction equally. Sensitivity analysis asks how an output—such as…
Explore lesson ChemistryLessonSeparating Gases from Liquid Air
Every breath you take is a mixture: roughly 78% nitrogen, 21% oxygen and about 0.9% argon, with small amounts of carbon dioxide, water vapour and other gases. Hospitals need pure…
Explore lesson ChemistryLessonSeparating Immiscible Liquids
Shake a bottle of salad dressing and the oil and vinegar seem to mix, but leave it on the table for a few minutes and two layers appear again. Liquids that behave like this are…
Explore lesson ChemistryLessonSeparation of Variables in Spherical Coordinates
The hydrogen Schrödinger equation involves three coordinates at once, which looks daunting. The key idea that makes it solvable is separation of variables: guessing that the…
Explore lesson ChemistryLabSeparation techniques
Separate mixtures by extraction, distillation or TLC and see how well each works.
Explore lesson ChemistryLessonSequential Reaction Calculations
Many preparations have more than one reaction. An intermediate is produced in one step and consumed in the next. Solve each balanced step in order: convert the first input to…
Explore lesson ChemistryLessonSequential-Reaction Mole Accounting
Many chemistry problems join two equations: a first reaction makes a substance that a second reaction consumes. The shared substance is an intermediate. Its available amount in…
Explore lesson ChemistryLessonSerial Dilution
Very dilute solutions are often made in stages when direct measurement is impractical. Each stage transfers a measured aliquot and brings it to a new final volume. The…
Explore lesson ChemistryLessonSerine Proteases: A Mechanism in Detail
Serine proteases show several catalytic strategies working in one coherent cycle. Chymotrypsin, trypsin and related enzymes hydrolyse peptide bonds, but differ in the substrate…
Explore lesson ChemistryLessonSetting Up the Particle in a One-Dimensional Box
The free particle showed that an unconfined particle can have any energy. What happens when we trap it? The particle in a one-dimensional box is the simplest model of confinement…
Explore lesson ChemistryLessonShapes of s, p and d Orbitals
The familiar pictures of orbitals — a sphere for s, a dumbbell for p and a four-leaf clover for most d orbitals — are among the most used images in chemistry. Yet an orbital has…
Explore lesson ChemistryLessonShell Capacity and the 2n² Rule
The rule 2n² gives the maximum number of electrons a shell can hold. It is useful, but it answers a capacity question rather than a filling-order question. Confusing those…
Explore lesson ChemistryLessonShell Notation and Subshell Notation
Sodium can be written as 2,8,1 or as 1s² 2s² 2p⁶ 3s¹. Both descriptions count eleven electrons, but the second says which subshells hold them. Translating between notations helps…
Explore lesson ChemistryLessonShells, Subshells and Orbitals
Electron-configuration notation uses three nested levels: shells, subshells, and orbitals. Their names are sometimes used casually as though interchangeable, but they have…
Explore lesson ChemistryLessonShielding and Deshielding
If NMR simply detected hydrogen nuclei, every proton would appear at the same frequency and the technique would be useless for structure determination. The reason signals spread…
Explore lesson ChemistryLessonShielding and Penetration
Two atoms with similar proton numbers can bind particular electrons differently. One reason is shielding by other electrons; another is penetration of an orbital into regions…
Explore lesson ChemistryLessonSI Prefixes: Scaling Units Up and Down
The diameter of a hydrogen atom is about 0.000 000 000 1 m. The distance from Earth to the Sun is about 150 000 000 000 m. Numbers like these are hard to read and easy to…
Explore lesson ChemistryLessonSI Units and Prefixes
Chemistry moves between atomic sizes, laboratory volumes and industrial quantities. SI units give a coherent language for that range, while prefixes compress powers of ten. The…
Explore lesson ChemistryLessonSieving and Hand Separation
The simplest separation methods need no heat, no chemicals and no special equipment. If one part of a mixture is made of large pieces and another is made of small grains, you can…
Explore lesson ChemistryLessonSigma and Pi Bonding
A single covalent bond is usually described as one sigma bond. A double bond contains one sigma and one pi component; a triple bond contains one sigma and two pi components in…
Explore lesson ChemistryLessonSigma and Pi Orbitals in Diatomics
A diatomic molecule is special because rotation about the bond axis leaves its nuclear framework unchanged. Molecular orbitals can therefore be classified by their behaviour…
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