THE LESSON LIBRARY / CHEMISTRY
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Ester Functional Group
An ester has the pattern R–C(=O)–O–R′: a carbonyl carbon attached to an oxygen that continues to another carbon group. The nearby C=O makes it different from an ether's simple…
Explore lesson ChemistryLessonEster Hydrolysis
Water can help break an ester linkage under suitable conditions. The product written for the acid-derived portion depends on the medium: acidic hydrolysis can yield a carboxylic…
Explore lesson ChemistryLessonEster Hydrolysis and Saponification
Esterification can be run in reverse. Heating an ester with water splits it back into a carboxylic acid and an alcohol, a process called hydrolysis. Chemists can use either…
Explore lesson ChemistryLessonEsterification and Hydrolysis
A carboxylic acid and an alcohol can form an ester and water under acid catalysis. The same ester can be hydrolysed by water in acid to regenerate the starting acid and alcohol.…
Explore lesson ChemistryLessonEsterification of an Alcohol and Acid
Ethanol and ethanoic acid can combine to form ethyl ethanoate and water under suitable acid-catalysed conditions. The new molecule contains an ester linkage. Because the reaction…
Explore lesson ChemistryLessonEsterification of Carboxylic Acids
Esters give fruits, flowers and many perfumes their smells, and they form the backbone of fats, oils and polyester fibres. The simplest way to make an ester is to heat a…
Explore lesson ChemistryLessonEsters: Formation, Hydrolysis and Transesterification
An ester has the structure R–C(=O)–OR'. Its acyl carbon can exchange the OR' group with an oxygen nucleophile or be hydrolysed back toward a carboxylic acid. Whether acid or base…
Explore lesson ChemistryLessonEstimating an Answer before Calculation
An exact-looking numerical result can still be impossible. Estimating before calculation provides a rough scale and expected direction. Limiting cases test whether a formula…
Explore lesson ChemistryLessonEthane Conformations
Ethane can rotate around its carbon-carbon single bond while keeping the same atoms connected. The rotation is not energetically flat: staggered and eclipsed arrangements differ…
Explore lesson ChemistryLessonEthanoic Acid Structure and Acidity
Ethanoic acid, CH₃COOH, is the simple two-carbon carboxylic acid familiar from vinegar solutions. Its –COOH group can transfer a proton to water, yet most molecules remain…
Explore lesson ChemistryLessonEthanoic Acid with Bases
Ethanoic acid reacts with bases through its carboxyl O–H proton. Sodium hydroxide produces sodium ethanoate and water. The acid is weak in water, but its partial ionisation does…
Explore lesson ChemistryLessonEthanoic Acid with Carbonates
Carbonate and hydrogencarbonate bases release carbon dioxide when they react with ethanoic acid. The bubbles are an observable sign of gas formation. Balancing the equation…
Explore lesson ChemistryLessonEthanol Combustion
Ethanol burns in oxygen and releases energy. It is an oxygen-containing fuel, so balancing its combustion requires counting the oxygen already inside CH₃CH₂OH as well as O₂ from…
Explore lesson ChemistryLessonEthanol Oxidation to Ethanoic Acid
Ethanol can be oxidised to ethanoic acid under suitable conditions. The two-carbon skeleton stays intact while the terminal carbon gains more bonding to oxygen. This differs from…
Explore lesson ChemistryLessonEthanol Structure and Properties
Ethanol, CH₃CH₂OH, combines a small carbon portion with one hydroxyl group. That structure explains why it mixes with water, is useful as a solvent and still burns as an organic…
Explore lesson ChemistryLessonEthene and Ethyne as Lewis Examples
Methane shows carbon with four single bonds. Ethene and ethyne show how the same local carbon valence can be represented with multiple bonds. Their formulas have fewer hydrogens…
Explore lesson ChemistryLessonEthene in Hückel Theory
Ethene is the smallest conjugated pi system that displays the essential Hückel construction. Each sp² carbon contributes one p orbital, so two local functions generate one lower…
Explore lesson ChemistryLessonEther Functional Group
An ether joins two carbon-containing groups through an oxygen atom: C–O–C. This is a different arrangement from the C–O–H of an alcohol. The difference is easy to overlook in a…
Explore lesson ChemistryLessonEther Preparation by Williamson Synthesis
Williamson ether synthesis joins an alkoxide with a suitable alkyl halide or related leaving-group substrate. Oxygen forms a new bond to the alkyl carbon as the leaving group…
Explore lesson ChemistryLessonEthics and Research Integrity
Chemical research becomes useful only when others can trust what was measured and how it was interpreted. A clean-looking spectrum is not valuable if inconvenient peaks were…
Explore lesson ChemistryLessonEvaluating Competing Routes
The fewest-arrow answer is not automatically the best synthesis. A short route can produce a mixture of isomers, require dangerous reagents or discard most input atoms. A longer…
Explore lesson ChemistryLessonEvaluating Periodic Predictions
A periodic prediction is useful when it can be checked against data. “First ionisation energy always increases with atomic number” fails at well-known neighbouring pairs; “it…
Explore lesson ChemistryLessonEvaporation and Transpiration
Wet washing dries on a line, puddles vanish after a shower and a glass of water left on a windowsill slowly empties — all without boiling. The water has evaporated into the air.…
Explore lesson ChemistryLessonEvaporation Causes Cooling
Step out of a swimming pool on a breezy day and you shiver, even when the air is warm. A dab of hand sanitiser feels cold on your skin. Your body sweats when you exercise. All of…
Explore lesson ChemistryLessonEvaporation Compared with Boiling
A kettle of water on a hob and a puddle on a pavement both end up as water vapour, yet the two processes look completely different. The kettle roars and bubbles, while the puddle…
Explore lesson ChemistryLessonEvaporation to Recover a Dissolved Solid
Filtration cannot separate salt from salt water, because the dissolved salt passes straight through the paper. So how do we get the salt back? We remove the water instead. When a…
Explore lesson ChemistryLessonEveryday Chemistry: Reduce, Reuse, Recycle
Every item in your home — a drinks can, a jam jar, a phone, a T-shirt — began as raw materials dug from the ground, pumped from wells or grown in fields, and every one required…
Explore lesson ChemistryLessonEveryday Pure Versus Chemically Pure
A carton says "100% pure orange juice". A bottle says "pure mountain spring water". A jeweller sells "pure gold". Are these pure in the chemist's sense? Usually not. Advertisers…
Explore lesson ChemistryLessonEveryday Uses and Responsible Handling
Alcohols, phenols, and ethers appear in solvents, fuels, materials manufacture, and synthesis. Their functional groups influence boiling, water mixing, and chemical reactivity…
Explore lesson ChemistryLessonEveryday Uses of Carbon Compounds
Carbon compounds appear in fuels, solvents, plastics, medicines, food lipids and cleaning products. Their uses are linked to structure: hydrocarbon energy, polar groups, reactive…
Explore lesson ChemistryLessonEverything Is Made of Particles
If you could cut a drop of water in half, then in half again, over and over, would you ever reach a piece that could not be divided without stopping being water? Scientists…
Explore lesson ChemistryLessonEvidence Behind Modern Atomic-Number Order
Atomic mass usually increases as one moves through the periodic table, but it is not a reliable element address. Tellurium has a higher average atomic mass than iodine yet comes…
Explore lesson ChemistryLessonEvidence for Particles: Brownian Motion
In 1827 the Scottish botanist Robert Brown looked through a microscope at tiny particles released from pollen grains floating in water. He saw them jiggling constantly in random…
Explore lesson ChemistryLessonEvidence for Particles: Diffusion
When someone opens a bottle of perfume at the front of a classroom, the smell reaches the back a short time later, even if nobody moves and there is no draught. A drop of ink in…
Explore lesson ChemistryLessonEvidence for Particles: Dissolving
Drop a spoonful of sugar into water and stir: the crystals vanish, yet the water tastes sweet everywhere. Drop a single crystal of purple potassium manganate(VII) into a large…
Explore lesson ChemistryLessonEvidence That a Reaction Has Happened
Before writing an equation, a chemist often sees a change: bubbles, a new solid, a different colour or a temperature shift. Such evidence can suggest that new substances have…
Explore lesson ChemistryLessonEvidence That Atoms Have Parts
Scientists did not discover atomic structure by looking inside an atom with an ordinary microscope. They observed what matter did under controlled conditions and compared those…
Explore lesson ChemistryLessonExact Exchange and Hybrid DFT
Hybrid density functionals combine approximate density-functional exchange and correlation with an orbital-based exchange term of Hartree–Fock form. The latter is often called…
Explore lesson ChemistryLessonExact Numbers and Defined Quantities
Every measured number carries some uncertainty, which is why we have spent so much effort on significant figures. But not every number in a calculation is measured. If you count…
Explore lesson ChemistryLessonExam Skills: Explaining Properties Using Bonding
Bonding questions reward a connected explanation, not a long list of familiar words. A strong answer identifies the particles, describes their arrangement and interactions, then…
Explore lesson ChemistryLessonExam Skills: Synthesis Roadmaps
An exam synthesis problem usually rewards a coherent route more than a collection of plausible reagent names. The target and starting material set strict atom and…
Explore lesson ChemistryLessonExam Strategy for Organic Reasoning
Long organic questions often combine an unknown starting compound, reagent arrows, a diagnostic test and an isomer count. The fastest reliable solution is not to memorize a…
Explore lesson ChemistryLessonExam Strategy for Qualitative Analysis
In a qualitative-analysis exam, a correct ion name without its evidence often earns less than a clear reagent–observation–inference chain. The best answer distinguishes what was…
Explore lesson ChemistryLessonExceptions in Oxidation-State Assignment
“Oxygen is −2” and “hydrogen is +1” are useful starting rules, not universal laws. Peroxides contain O–O bonds and give each equivalent oxygen −1. Metal hydrides commonly give…
Explore lesson ChemistryLessonExceptions to the 18-Electron Rule
The 18-electron rule is a tendency, not a requirement. Many important catalysts are stable and active with fewer than 18 valence electrons. Understanding why prevents rejecting…
Explore lesson ChemistryLessonExceptions to the Metal and Non-metal Rules
The lists of typical metal and non-metal properties are useful, but nature does not always follow them. A metal that is liquid at room temperature, a non-metal that conducts…
Explore lesson ChemistryLessonExceptions to the Rules
The metal/non-metal contrast is a useful starting point, not a set of absolute definitions. Mercury is a liquid metal, sodium a soft metal, graphite a conducting form of…
Explore lesson ChemistryLessonExcess Reagent and Final Composition
Identifying a limiting reagent is only the first half of a mixture problem. A chemist often needs to know what remains after reaction: unreacted reagent, products, and sometimes…
Explore lesson ChemistryLessonExcess Reagent Remaining
Once the limiting reagent is identified, the other reactant may remain. Product calculations use the limiting supply, but leftover calculations ask a different question: how much…
Explore lesson ChemistryLessonExchange Current Density — Advanced Electrochemistry and Kinetics
A zero-current electrode can still be chemically busy. Equal oxidation and reduction events exchange electrons in opposite directions, and their common current magnitude is…
Explore lesson ChemistryLessonExchange Current Density — Electrochemistry
At an electrode's equilibrium potential, the net current is zero. That observation alone does not tell whether electron exchange is slow or fast: both oxidation and reduction may…
Explore lesson ChemistryLessonExchange–Correlation Functionals
The Kohn–Sham equations would be exact for their specified ground-state problem with the exact exchange–correlation functional, but its general form is unknown. Practical DFT…
Explore lesson ChemistryLessonExchangeable Protons and D₂O Shake
Signals from hydrogen atoms bonded to oxygen or nitrogen are the troublemakers of ¹H NMR. Their positions wander from sample to sample, they are often broad, and they usually…
Explore lesson ChemistryLessonExcitation and Emission
An atom can gain energy without losing its electron. It may enter an excited state and later return toward a lower state, sometimes emitting light. These transitions link energy…
Explore lesson ChemistryLessonExcited States and Electron Transitions
An electron configuration usually means a ground-state arrangement unless the question says otherwise. Energy input can produce an excited state with an electron in a higher…
Explore lesson ChemistryLessonExcited States with TDDFT
Color, photochemistry and fluorescence involve electronic states above the ground state. Time-dependent density-functional theory, usually abbreviated TDDFT, offers a practical…
Explore lesson ChemistryLessonExcited States: Singlets and Triplets
Absorbing a photon changes a molecule's electronic state, but electron promotion alone does not tell the full story. Electron spins can remain paired in an excited singlet or…
Explore lesson ChemistryLessonExcited-State Acid–Base Chemistry
Electronic excitation changes a molecule's charge distribution and can change its willingness to give or accept a proton. A photoacid may be modestly acidic in the ground state…
Explore lesson ChemistryLessonExcited-State Lifetimes
An excited state does not have a timer that rings at one exact moment. Its population decays statistically through several competing pathways. The lifetime measures a…
Explore lesson ChemistryLessonExfoliation and Thin-Layer Preparation
Many two-dimensional materials begin as bulk layered crystals. Strong bonds hold atoms together within each layer, while weaker forces connect neighboring layers. Exfoliation…
Explore lesson ChemistryLessonExothermic and Endothermic Changes
Some changes warm up their surroundings; others cool them down. Chemists give these two groups names: exothermic and endothermic. The words come from Greek: "exo" means outwards…
Explore lesson ChemistryLessonExothermic and Endothermic Profiles
An energy profile sketches how energy changes along a reaction coordinate. Products below reactants correspond to a negative enthalpy change in a suitable enthalpy diagram…
Explore lesson ChemistryLessonExothermic Processes as Energy Sources
Heat released by a reaction is sometimes a problem and a resource at once. Too much temperature rise can harm selectivity, catalyst life or equipment, yet controlled recovery can…
Explore lesson ChemistryLessonExpanded-Valence Lewis Drawings
Some familiar formulas cannot be shown with all their ordinary connections while keeping eight electrons around the central atom in a conventional Lewis drawing. PCl₅ and SF₆ are…
Explore lesson ChemistryLessonExpansion When Heated
On a hot summer day, railway lines can buckle, bridges grow slightly longer and power lines sag lower between pylons. A tight metal lid on a glass jar loosens when you run it…
Explore lesson ChemistryLessonExpectation Values
Quantum mechanics rarely predicts the result of a single measurement with certainty. If you measure the position of an electron in a molecule, you might find it here on one…
Explore lesson ChemistryLessonExpectation Values for the Particle in a Box
A single measurement of the position of a particle in a box can give any value between the walls. What quantum mechanics predicts precisely is the *average* of a large number of…
Explore lesson ChemistryLessonExperimental Design for Mechanism Testing
An experiment can be beautifully precise yet answer the wrong mechanistic question. If two pathways predict the same final yield, repeated final-yield measurements mostly improve…
Explore lesson ChemistryLessonExperimental Kinetics Design
A kinetic law is only as good as the measurements supporting it. Experiments must isolate variables, calibrate signals and account for timing and uncertainty. A neat…
Explore lesson ChemistryLessonExperimental Randomization
Chemical instruments drift, reagents age, temperatures change and operators become more practiced. If every control is measured first and every new material later, treatment is…
Explore lesson ChemistryLessonExplaining a Trend with Evidence
An exam answer that says “radius increases down a group because it does” has no explanation. A stronger response names the species and property, cites a comparable observation…
Explore lesson ChemistryLessonExplaining Colours in Qualitative Tests
In a qualitative test, a colour change may report precipitation, ligand exchange, oxidation-state change or a mixture of these. Aqueous copper turning deep blue with ammonia is…
Explore lesson ChemistryLessonExplaining Density with the Particle Model
Density was introduced as mass divided by volume. The particle model now lets us understand why substances have the densities they do. Only two particle-level factors matter: how…
Explore lesson ChemistryLessonExplaining Ionic Substance Properties
Many ionic solids are hard, have relatively high melting temperatures, break when struck and fail to conduct as solids. The same substances may conduct when molten or dissolved.…
Explore lesson ChemistryLessonExplaining Ionisation Exceptions
A broad trend arrow is an overview, not a substitute for reading electron configurations. In period two, boron's first ionisation energy is below beryllium's and oxygen's is…
Explore lesson ChemistryLessonExplaining Properties with the Particle Model
A model is only useful if it explains what we observe. This page tests the particle model against the everyday properties of solids, liquids and gases: why a stone keeps its…
Explore lesson ChemistryLessonExplicit Solvent and Hydrogen-Bond Networks
A continuum solvent can screen charges on average, but it cannot place one water molecule between a proton donor and acceptor. When such local geometry changes a reaction…
Explore lesson ChemistryLessonExploring Atoms in 3D
The ChemVerse atom builder lets you change protons, neutrons and electrons independently and see the resulting labels and electronic display. Used as a prediction tool, it can…
Explore lesson ChemistryLessonExploring Molecules in 3D
A flat drawing of a molecule on paper can mislead you. Methane drawn as a cross looks flat with 90° angles, but in reality it is a three-dimensional tetrahedron. Computer 3D…
Explore lesson ChemistryLessonExploring Moles with the Mole Simulator
The course's Mole visualiser gives a movable mass setting and a choice of substances. It calculates amount in moles and the count of the selected entities, then shows a scaled…
Explore lesson ChemistryLessonExponential Decay and Decay Constant
Repeated halving is convenient when time is an exact multiple of a half-life. Radioactive decay occurs continuously, however, so a formula is useful for times such as 1.5…
Explore lesson ChemistryLessonExposure and Environmental Behavior
A nanoparticle released from a product does not necessarily remain identical to the fresh particle made in the laboratory. It may aggregate, dissolve, acquire natural organic…
Explore lesson ChemistryLessonExtended Debye–Hückel and Davies Equations
The limiting law treats ions as point charges and is best near infinite dilution. Real ions have finite size and hydration shells, so activity coefficients at higher ionic…
Explore lesson ChemistryLessonExtraction of Titanium and Refractory Metals
Titanium combines low density with useful strength and corrosion resistance, yet its extraction is more involved than iron's. The issue is not merely whether an oxide can be…
Explore lesson ChemistryLessonExtrinsic Defects and Aliovalent Doping
Pure crystals have thermal vacancies and interstitials, but adding a small amount of another element can dominate their defect chemistry. An impurity may replace a host atom…
Explore lesson ChemistryLessonEyring Plots and Activation Parameters
A rate constant measured at only one temperature gives limited information about a reaction barrier. Repeating the measurement across temperatures tests whether a…
Explore lesson ChemistryLessonFace-Centered Cubic Packing
Face-centered cubic packing places equivalent particles at eight corners and six face centres of a conventional cube. It has four effective atoms per cell and twelve nearest…
Explore lesson ChemistryLessonFactorial Experimental Design
Chemical performance often depends on combinations of conditions. A catalyst may benefit from a high temperature only at low pressure; a battery coating may improve lifetime only…
Explore lesson ChemistryLessonFactorising the Molecular Partition Function
Each mode of molecular motion now has its own partition function. The obvious next question is how to combine them. The answer is remarkably simple: when the energy of a molecule…
Explore lesson ChemistryLessonFactors Affecting Micelle Formation
One CMC value is not an immutable label attached to a surfactant bottle. Change the hydrophobic tail, head group, salt concentration or temperature, and micelle formation can…
Explore lesson ChemistryLessonFactors Affecting Rate
Changing concentration, temperature, exposed surface or catalyst can change an observed reaction rate. These factors operate through different mechanisms, and not every reaction…
Explore lesson ChemistryLessonFactors Affecting Rusting Rate
Rusting rate depends on the environment, not just on the presence of iron. Moisture permits ionic transport, oxygen accepts electrons, and dissolved salts can make a thin water…
Explore lesson ChemistryLessonFactors Affecting the Rate of Evaporation
Washing dries fastest on a warm, breezy day and slowest on a cold, damp, still day. A spilled drink on a table dries more quickly than the same drink left in a cup. These…
Explore lesson ChemistryLessonFactors Affecting the Size of Δo
Δₒ is not a universal property of a ligand. It is the energy difference between t₂g and e_g levels in a particular octahedral metal–ligand environment. Ligand identity, metal…
Explore lesson ChemistryLessonFactors Controlling SN2 Rates
The SN2 mechanism is fixed in broad outline, but its speed can vary enormously. A small change from methyl to tertiary electrophile may nearly shut off the pathway; a better…
Explore lesson ChemistryLessonFactors That Control Tg
T_g is not a fixed number determined only by a repeat-unit formula. Molecular architecture and sample composition control how easily chain segments move. Backbone rigidity, side…
Explore lesson ChemistryLessonFactors That Speed Up Rusting
A steel car in a dry desert may last decades with little rust, while the same car driven on salted winter roads or parked by the sea can rust through within a few years. Water…
Explore lesson ChemistryLessonFailures of Classical Physics
By 1900 physics seemed nearly complete. Newton's mechanics and Maxwell's electromagnetism explained motion, heat, light and electricity. Yet three stubborn experimental results…
Explore lesson ChemistryLessonFair Catalyst Benchmarking
New catalysts are often announced as “better” after tests run under different conditions or reported with different denominators. A fair benchmark uses a defined reaction, common…
Explore lesson ChemistryLessonFamilies and Similar Chemical Properties
Group 17 elements commonly form −1 halide ions, while group 1 metals commonly form +1 ions. These family patterns let a chemist make a first prediction for an unfamiliar member.…
Explore lesson ChemistryLessonFaradaic and Non-Faradaic Processes
An ammeter reports total current, not its chemical cause. Some current corresponds to oxidation or reduction of species at an electrode; another part rearranges charge in the…
Explore lesson ChemistryLessonFaraday Efficiency
Passing charge through an electrolyzer does not guarantee every electron makes the desired product. Water splitting, metal deposition or another side reaction may share the…
Explore lesson ChemistryLessonFaraday-Law Deposition Calculations
Electroplating a watch, refining copper for wiring and extracting aluminium from its oxide are all governed by one idea: electrons are a reagent. Each ion that is discharged at…
Explore lesson ChemistryLessonFaraday's Laws of Electrolysis
Electrolysis converts a measured electrical charge into chemical change. Faraday's laws express the stoichiometric connection: product amount is proportional to charge passed…
Explore lesson ChemistryLessonFates of Pyruvate and Fermentation
Glycolysis makes pyruvate and NADH, but it cannot continue unless NADH is reoxidised to NAD⁺. Pyruvate can be oxidised to acetyl-CoA for respiratory metabolism, reduced to…
Explore lesson ChemistryLessonFats, Oils and Ester Links
Many fats and oils are mixtures rich in triacylglycerols. Each triacylglycerol joins a glycerol backbone to three fatty-acid-derived chains through ester linkages. The structure…
Explore lesson ChemistryLessonFatty Acid Beta-Oxidation
Fatty acids provide a concentrated fuel reserve because their carbon chains are highly reduced. During fuel demand, cells can convert fatty acyl chains into acetyl-CoA while…
Explore lesson ChemistryLessonFatty Acid Synthesis
Cells convert excess carbon and energy into fatty acids for membrane lipids and energy stores. Although a growing fatty acid and a degrading fatty acid both involve two-carbon…
Explore lesson ChemistryLessonFeedstocks, Products and the Chemical Industry Map
Chemical plants do not stand alone. One plant's product may be another plant's feedstock, and a process can draw on several resource streams before it makes a saleable material.…
Explore lesson ChemistryLessonFermi–Dirac Statistics in Solids
The density of states counts allowed electron states, but actual electrons occupy only some of them. Electrons are fermions, and the Pauli exclusion principle prevents two…
Explore lesson ChemistryLessonFertilisers and Eutrophication
Fertilisers are one of chemistry's great gifts to humanity. By supplying nitrogen, phosphorus and potassium, they have roughly doubled crop yields and help to feed billions of…
Explore lesson ChemistryLessonFertilisers as Salts
A field of wheat removes large amounts of nutrients from the soil every harvest. To keep yields high, farmers replace them with fertilisers. Most of these are simply salts: ionic…
Explore lesson ChemistryLessonFiltering, Drying and Ignition
Once a precipitate forms, the gravimetric analysis is not finished. The solid must be recovered without losing fine particles, washed without dissolving appreciable analyte, and…
Explore lesson ChemistryLessonFiltration in Water Treatment
The water in your tap probably began in a river, a reservoir or underground rock. That raw water contains leaves, mud, fine clay and microorganisms. Before it reaches you, it…
Explore lesson ChemistryLessonFiltration: How It Works
Every time you make coffee with a paper filter, you carry out one of the most important separations in chemistry. Hot water and dissolved coffee flavour pass through; the gritty…
Explore lesson ChemistryLessonFinal Chemistry Revision Challenge
This final challenge brings the course together. Chemistry is most useful when the solver can identify the kind of question before choosing an equation: composition, structure…
Explore lesson ChemistryLessonFinding Abundances from Relative Atomic Mass
An isotope average can sometimes be used in reverse. If an element has exactly two relevant isotopes and their masses are known, the mean mass determines their fractions. The…
Explore lesson ChemistryLessonFinding an Unknown Element from Clues
An unknown element may be described by proton count, shell arrangement, common ion charge or a position between known neighbours. The strongest clue is often Z, because it…
Explore lesson ChemistryLessonFinding an Unknown Isotope Abundance
Sometimes the isotope masses and average atomic mass are known but the proportions are missing. With exactly two isotopes, one unknown fraction is enough: if one isotope's…
Explore lesson ChemistryLessonFinding Carbon Oxidation Number
Carbon can have quite different oxidation numbers in methane, carbon monoxide and carbon dioxide. Calculating them with the sum rule helps explain why combustion and fuel…
Explore lesson ChemistryLessonFinding Hydronium Concentration from pH
A pH reading is a compact description of hydronium behavior. To recover an approximate concentration in a dilute solution, reverse the logarithm: raise ten to the negative pH.…
Explore lesson ChemistryLessonFinding Molar Mass from Colligative Data
If a known mass of an unknown solute is dissolved in a known amount of solvent, a colligative effect can reveal how many effective particles the sample supplied. For a…
Explore lesson ChemistryLessonFinding Molar Mass from Mass and Moles
When mass and amount are known, the same relationship used for routine mole calculations can be reversed to find molar mass. The result helps test an unknown substance's…
Explore lesson ChemistryLessonFinding Nitrogen Oxidation Number
Nitrogen spans a wide formal oxidation-number range in common substances. It is −3 in ammonia, zero in nitrogen gas and +5 in nitrate under usual assignments. Comparing these…
Explore lesson ChemistryLessonFinding Oxygen by Mass Difference
In combustion analysis, CO₂ reveals sample carbon and H₂O reveals sample hydrogen. If the original pure compound is known to contain only C, H and O, its oxygen mass is the part…
Explore lesson ChemistryLessonFinding Redox Change in Equations
A redox equation can be recognised without seeing free electrons. Assign oxidation numbers to the elements in reactants and products, then find which values rise and which fall.…
Explore lesson ChemistryLessonFinding Solute Amount from Molarity
Molarity by itself is a ratio; a measured solution volume turns it into an actual amount of solute. The product n = cV is the bridge between pipette readings and balanced…
Explore lesson ChemistryLessonFinding Sulfur Oxidation Number
Sulfur occurs in forms with widely separated formal oxidation numbers. Sulfide sulfur is commonly −2, elemental sulfur is zero, sulfur in SO₂ is +4 and sulfate sulfur is +6. The…
Explore lesson ChemistryLessonFinding the Limiting Reagent from Moles
When a reaction has several reactants, repeated pairwise ratio checks can become awkward. Dividing each starting mole amount by its balanced coefficient gives a common progress…
Explore lesson ChemistryLessonFinding the Proportion of Oxygen in Air
How do we know that air is about 21% oxygen? You cannot see the oxygen or pick it out of the air directly. The trick, used since the eighteenth century, is to remove the oxygen…
Explore lesson ChemistryLessonFinding Valency from Hydrogen Compounds
Four simple molecules — hydrogen chloride, water, ammonia and methane — form a neat pattern. Each contains one atom of another element joined to one, two, three or four hydrogen…
Explore lesson ChemistryLessonFinite Wells and Quantum Tunnelling
The infinite box is an elegant first model, but its perfectly impenetrable walls are idealisations. A real electron often sees a potential that rises by a finite amount. Its…
Explore lesson ChemistryLessonFire Safety and Extinguishers
Every school, office and kitchen has fire extinguishers, yet many people do not know that using the wrong one can make a fire worse. Pouring water on a burning chip pan can cause…
Explore lesson ChemistryLessonFire Safety and the Fire Triangle
Combustion is one of the most useful reactions we know, but an uncontrolled fire can destroy homes and cost lives within minutes. The same chemistry that explains how fuels burn…
Explore lesson ChemistryLessonFire Safety in the Laboratory
Fire is a chemical reaction. In the laboratory we use it on purpose in Bunsen burners and in controlled experiments, but an uncontrolled fire is one of the most serious dangers.…
Explore lesson ChemistryLessonFirst Ionisation Energy Defined
It takes energy to remove an electron from a neutral atom because the electron is attracted to the nucleus. First ionisation energy gives a defined way to compare how strongly…
Explore lesson ChemistryLessonFirst Ionisation Enthalpy
First ionisation enthalpy measures how much energy is required to remove an electron from neutral gaseous atoms. It is a precise way to compare electron binding across elements.…
Explore lesson ChemistryLabFirst law: heat, work and internal energy
A gas in a piston is compressed or expanded. Track heat q, work w and internal energy ΔU.
Explore lesson ChemistryLessonFirst-Dissociation Approximation for Diprotic Acids
The complete description of a diprotic acid needs five equations, but in most real problems we do not need to solve them all. For a solution of H₂A on its own, the first…
Explore lesson ChemistryLessonFirst-Order and Continuous Phase Transitions
Not all phase changes resemble boiling. Some have a coexistence interval and latent heat; others change their structure continuously while heat capacity or susceptibility becomes…
Explore lesson ChemistryLessonFirst-Order Decay Kinetics
Earlier courses introduced half-life as the time for half of a radioactive sample to decay. At this level we derive the decay law from a single physical assumption: every nucleus…
Explore lesson ChemistryLessonFirst-Order Integrated Rate Law
For a first-order disappearance, rate = k[A]. As [A] falls, the absolute rate slows in direct proportion, but the same fraction of remaining A disappears during equal time…
Explore lesson ChemistryLessonFirst-Order Saddle Points
A first-order saddle point is a central candidate for an elementary reaction's transition structure. It is stationary because the force vanishes exactly there, but it is unstable…
Explore lesson ChemistryLessonFirst-Row d-Block Electron Configurations
The first d-block row runs from scandium to zinc. A rough construction fills 4s and then adds 3d electrons, but ground-state atoms are not forced to retain two 4s electrons.…
Explore lesson ChemistryLessonFischer Projections
A Fischer projection looks like a flat cross, but it encodes a three-dimensional tetrahedral arrangement. It is especially convenient for chains with several stereocentres, such…
Explore lesson ChemistryLessonFischer Projections: Drawing and Reading
Wedge-and-dash drawings show one stereocentre clearly, but they become cluttered for molecules with four or five stereocentres in a row, such as glucose. In 1891 Emil Fischer…
Explore lesson ChemistryLessonFission: Energetics and Product Distribution
Fission releases energy because a very heavy nucleus can form lighter products that are, in aggregate, more tightly bound per nucleon. A split is not one fixed equation with one…
Explore lesson ChemistryLessonFitting Kinetic Models
Kinetic data never lie perfectly on a curve. Instruments have noise, temperatures drift and concentrations are known only approximately. Fitting is the process of choosing model…
Explore lesson ChemistryLessonFive-Domain Lone-Pair Shapes
Replacing equatorial bonded atoms of a trigonal bipyramid with lone pairs changes the visible shape while retaining five electron domains. SF₄ becomes seesaw, ClF₃ becomes…
Explore lesson ChemistryLessonFlame Colours and s-Block Identification
A small amount of certain metal salts in a hot flame can tint it a recognisable colour. Lithium gives red or pink-red, sodium yellow, potassium lilac, calcium orange-red…
Explore lesson ChemistryLessonFlame Tests and Electronic Transitions
Some metal-containing samples colour a flame. The colour comes from light emitted when energetic particles produced in the hot region return from excited electronic states to…
Explore lesson ChemistryLessonFlame Tests and Energy Levels
Some metal-containing compounds give characteristic visible colours when studied by flame emission. The underlying explanation is electronic excitation followed by relaxation.…
Explore lesson ChemistryLessonFloating and Sinking
Why does a coin sink while a huge wooden log floats? Why can a steel ship weighing thousands of tonnes carry cargo across oceans? The answer to all these questions is density. By…
Explore lesson ChemistryLessonFluctuation Formula for Heat Capacity
Heat capacity is often introduced as the slope of mean internal energy against temperature. In a canonical ensemble it can also be found from the spread of energies at one…
Explore lesson ChemistryLessonFluorescence and Phosphorescence
Some molecules return from excited states by emitting light. Prompt fluorescence and often longer-lived phosphorescence can both report on molecular structure and surroundings.…
Explore lesson ChemistryLessonFluorescence Spectra and Stokes Shift
A fluorescent molecule usually emits at a longer wavelength than the light it absorbs most strongly. This separation is called a Stokes shift. It often reflects energy lost…
Explore lesson ChemistryLessonFluorine: The Anomalous Halogen
Fluorine is the most electronegative element and a very strong oxidant, yet the F–F bond is not unusually strong. At the same time, HF is weaker in water than HCl, HBr and HI.…
Explore lesson ChemistryLessonFolding Energy Landscapes and Chaperones
A chain with many backbone torsions has an enormous number of imaginable conformations. If it sampled them one by one at random until it found a unique correct structure, folding…
Explore lesson ChemistryLessonFollowing Neutralisation with pH Curves
When alkali is added to an acid, you might expect the pH to rise smoothly and steadily, a little for each drop. In fact it does something much more dramatic. For a long time the…
Explore lesson ChemistryLessonForces Between Particles — Matter and its Properties
If particles are constantly moving, why does a solid not simply fly apart? Why do water droplets form round beads, and why can some insects walk on water? The answer is that…
Explore lesson ChemistryLessonForces Between Particles — States of Matter: Particle Model
Why does a block of iron hold together, while the particles of air drift apart? Particles are not simply heaped up by chance. They attract one another, and these attractions act…
Explore lesson ChemistryLessonForces Stabilising Tertiary Structure
Helices and sheets describe recurring local geometry, but a protein must also arrange distant parts of its chain into a working three-dimensional fold. A buried pocket may bring…
Explore lesson ChemistryLessonFormal and Conditional Potentials
Standard reduction potentials are useful reference values, but analytical measurements often occur in concentrated electrolyte, buffers and complexing media. Under those…
Explore lesson ChemistryLessonFormal Charge and Preferred Structures
Several Lewis diagrams can use the same electron budget. Formal-charge patterns help compare them: avoid unnecessary large or separated charges, and when negative charge is…
Explore lesson ChemistryLessonFormal Charge and Resonance Problem Set
Formal charge problems test both arithmetic and chemical interpretation. A correct electron total can still produce a poor Lewis drawing, and a pleasing drawing can hide the…
Explore lesson ChemistryLessonFormal Charge Calculations
Formal charge helps evaluate a Lewis structure and check its electron accounting. It assigns each bond's electrons equally to its two atoms, then compares the assigned total with…
Explore lesson ChemistryLessonFormal Charge in Lewis Diagrams
Two Lewis drawings can use the right number of electrons and still assign those electrons differently. Formal charge provides a consistent way to compare them. It asks what…
Explore lesson ChemistryLessonFormal Charge in Mechanisms
Mechanism drawings often fail because an arrow changes bond count but the new formal charge is not updated. Formal charge is a bookkeeping tool that helps reveal such errors. A…
Explore lesson ChemistryLessonFormation and Chemistry of the SEI
The low potential needed for a high-voltage lithium-ion cell often lies outside the practical reductive stability of its carbonate electrolyte. During early charging, electrolyte…
Explore lesson ChemistryLessonFormation of a Precipitate
Pour one clear, colourless solution into another clear, colourless solution, and suddenly the mixture turns cloudy white. A solid has appeared out of two liquids. This sudden…
Explore lesson ChemistryLessonForming Compounds from Elements
Every compound on Earth was once made from elements. Water forms when hydrogen and oxygen join; rust forms when iron combines with oxygen; table salt can be made from a soft…
Explore lesson ChemistryLessonForming Enolates: Choosing the Base
Enolate chemistry often begins with choosing a base, but “base present” does not say how much enolate is available. A ketone with an alkoxide may form only a small equilibrium…
Explore lesson ChemistryLessonForming Transition-Metal Cations
Forming a transition-metal cation is an electron-counting task with a common trap. Neutral first-row metal configurations often show 4s electrons as well as 3d electrons. On…
Explore lesson ChemistryLessonFormula Mass and Molar Mass for Stoichiometry
An equation gives mole ratios, but experiments often begin with masses in grams. The bridge is molar mass. Before adding numbers from a periodic table, identify the substance's…
Explore lesson ChemistryLessonFormula Mass of Ionic Compounds
Sodium chloride, common salt, is not made of molecules. It is a giant lattice of sodium ions and chloride ions, with no separate little groups of atoms. So it makes no sense to…
Explore lesson ChemistryCollectionFormula Sheets
Study Formula Sheets with 25 free lessons, worked examples, and answered practice questions.
Explore lesson ChemistryLessonFormula Sheets: Mixed Worked Review
A formula sheet is most useful as a set of conditional tools, not a page of incantations. A question about how much substance is present may need *n = m/M*; a question about a…
Explore lesson ChemistryLessonFormula, Lewis Diagram and Real Structure
Chemistry uses several representations of the same substance because no one drawing carries every fact. CO₂ says what atoms occur in a molecule; O=C=O adds a Lewis bond-order…
Explore lesson ChemistryLessonFormulas Containing Polyatomic Ions
Some charged particles contain more than one atom. Nitrate, NO₃⁻, is an anion even though nitrogen and oxygen are covalently connected within it. When nitrate combines with a…
Explore lesson ChemistryLessonFormulations: Mixtures Designed for a Purpose
Paint, toothpaste, cough medicine, shampoo and garden fertiliser are all mixtures — but not random ones. Each is made by carefully combining specific ingredients in carefully…
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