What does the Maxwell–Boltzmann distribution show?

It shows how the energies of the molecules in a sample of gas are spread out at a particular temperature.

Why does the Maxwell–Boltzmann curve begin at the origin?

No molecule in the sample is completely without energy, so the number of molecules having zero energy is zero.

Describe the shape of the Maxwell–Boltzmann curve.

The curve rises steeply from the origin to a peak and then falls away more gradually, with a long tail that approaches the energy axis without ever touching it.

What does the peak of the curve represent?

The peak lies at the most probable energy, the energy possessed by more molecules than any other single value.

Why does the tail of the curve never meet the energy axis?

There is no upper limit to the energy a molecule may have, although very high energies become vanishingly rare.

What does the total area under the curve represent?

The total area represents the total number of molecules in the sample.

CCEA A-Level Chemistry 1110

Formulae, Equations and Amounts of Substance

Topic overview Ionic charges and the formulae of compound ions Writing and balancing full and ionic equations The mole, molar mass and Avogadro's constant Reacting masses and reactants in excess Hydrated salts and water of crystallisation

Atomic Structure

Topic overview Protons, neutrons and electrons Atomic number, mass number and the composition of ions Isotopes and relative isotopic mass Relative atomic, molecular and formula mass Mass spectra and relative atomic mass calculations Mass spectra of diatomic elements Electronic configuration and the building up principle Orbitals, electron spin and orbital shapes The s-, p-, d- and f-blocks of the Periodic Table Ionisation energies and their equations Trends in ionisation energy as evidence for shells and subshells

Bonding

Topic overview Ionic bonding and electron transfer Dot and cross diagrams for ionic compounds Covalent bonding and the shared pair Lone pairs and co-ordinate bonding Dot and cross diagrams for covalent molecules and ions The octet rule and its limitations Electronegativity and bond polarity Metallic bonding

Intermolecular Forces and Structure

Topic overview Van der Waals' forces and permanent dipole-dipole attractions Hydrogen bonding, boiling points and solubility Giant ionic, metallic and giant covalent structures Molecular covalent structures and melting points across Period 3

Shapes of Molecules and Ions

Topic overview Electron pair repulsion and VSEPR theory Shapes and bond angles up to four electron pairs Shapes with five and six electron pairs Polar bonds and polar molecules

Redox

Topic overview Rules for assigning oxidation states Oxidation states in peroxides, hydrides and Roman numeral names Oxidation, reduction and electron transfer Oxidising agents, reducing agents and disproportionation Half-equations and combining them into redox equations

The Halogens

Topic overview Colours, physical states and solubility of the halogens Chlorine with water and the treatment of drinking water Disproportionation of the halogens with sodium hydroxide Oxidising ability and displacement reactions Solid halides with concentrated sulfuric and phosphoric acid

Acid-Base Titrations

Topic overview Strong and weak acids and bases Concentration, molarity and units Preparing a standard solution Titration technique, mean titres and uncertainty Indicators and the end point Titration calculations

Qualitative Tests

Topic overview Chemical tests for the gases Flame tests for metal cations Testing for the ammonium ion, sulfate and carbonate Distinguishing the halides, and the starch test for iodine

Formulae and Amounts of a Substance

Topic overview Empirical and molecular formulae Calculating formulae from composition data Molar gas volume and reacting gas volumes Percentage yield Atom economy

Nomenclature and Isomerism in Organic Chemistry

Topic overview Homologous series and functional groups IUPAC rules for naming organic compounds Structural, displayed and skeletal formulae Structural isomerism Geometrical isomerism and E–Z notation

Alkanes

Topic overview Alkanes as saturated hydrocarbons Boiling points of alkanes and van der Waals' forces Boiling points of branched isomers Complete and incomplete combustion of alkanes Pollutants from alkane fuels and the atmosphere Catalytic converters Radicals, homolytic fission and heterolytic fission Free radical substitution of alkanes

Alkenes

Topic overview Unsaturated hydrocarbons and the bromine water test Sigma and pi bonds in the carbon–carbon double bond Electron density at C=C, reactivity and catalytic hydrogenation Addition of chlorine and bromine to alkenes Addition of hydrogen chloride and hydrogen bromide Electrophiles, heterolytic fission and the addition mechanism Carbocation stability and Markovnikov addition Addition polymerisation of alkenes

Halogenoalkanes

Topic overview Classification and boiling points of halogenoalkanes Laboratory preparation of a halogenoalkane from an alcohol Nucleophiles and hydrolysis with aqueous alkali Reactions with ammonia and with potassium cyanide Relative rates of hydrolysis and carbon–halogen bond enthalpy Elimination using ethanolic potassium hydroxide CFCs and the ozone layer

Alcohols

Topic overview Hydrogen bonding, boiling point and solubility of alcohols Classifying alcohols and preparing them from halogenoalkanes Combustion of alcohols and their use as fuels Reactions with sodium, hydrogen bromide and phosphorus pentachloride Oxidation with acidified potassium dichromate(VI)

Infrared Spectroscopy

Topic overview Molecular vibrations and the absorption of infrared radiation Characteristic absorptions and the wavenumber scale Identifying functional groups from infrared spectra Distinguishing compounds and following reactions by infrared

Energetics

Topic overview Exothermic and endothermic changes Standard conditions and the standard enthalpy change Enthalpy level diagrams Standard enthalpies of combustion and formation Standard enthalpy of neutralisation Measuring enthalpy changes by experiment Enthalpy calculations using q = mcΔT Hess's Law and enthalpy cycles Indirect enthalpy calculations using Hess's Law Average bond enthalpies and their limitations

Kinetics

Topic overview Reaction rate and the factors that change it Collision theory and activation energy The Maxwell–Boltzmann distribution of molecular energies Catalysts and the activation energy barrier

Equilibrium

Topic overview Reversible reactions and dynamic equilibrium Changing conditions and the position of equilibrium The equilibrium constant Kc and its units The magnitude of Kc and the extent of reaction Industrial processes and compromise conditions

Group II Elements and Their Compounds

Topic overview s-block character and electronic configuration Trends in atomic radius and first ionisation energy Reactions of the elements with oxygen, water and dilute acids The oxides and their reactions with water and dilute acids Thermal stability of the carbonates and hydroxides Uses of magnesium oxide, calcium carbonate and lime Solubility trends and solubility curves

Lattice Enthalpy, Entropy and Free Energy

Topic overview Lattice enthalpy and the factors that control it Born–Haber cycles for Group I halides Born–Haber cycles for Group II halides and oxides Enthalpy of hydration and enthalpy of solution Calculations on dissolving ionic compounds Entropy and the limits of enthalpy change Standard entropy change calculations Free energy and the temperature of feasibility

Rates of Reaction

Topic overview Rate of reaction, order and the rate constant Deducing rate equations from initial rate data Concentration–time graphs and half-lives Rate–concentration graphs and orders Rate-determining steps, SN1 and SN2 Experimental methods and the effect of temperature on the rate constant

Equilibrium and Acid-Base Equilibria

Topic overview Equilibrium concentrations from initial amounts Kc expressions, values and units Brønsted–Lowry acids, bases and conjugate pairs Kw, pH and the pH of strong acids and bases Ka, pKa and the pH of weak acids Buffer solutions and how they resist pH change Calculating the pH of a buffer solution Titration curves, indicators and the pH of salt solutions

Isomerism

Topic overview Structural isomerism between different families Chiral centres and optical isomers Representing optical isomers in three dimensions Plane polarised light, optical activity and racemic mixtures Stereochemistry, drug action and receptor sites

Aldehydes and Ketones

Topic overview Structure and naming of aldehydes and ketones Boiling points and solubility of carbonyl compounds Preparation from primary and secondary alcohols Reaction with hydrogen cyanide and the nucleophilic addition mechanism Racemic mixtures from nucleophilic addition 2,4-dinitrophenylhydrazine and the identification of carbonyls Distinguishing aldehydes from ketones, and reduction with lithal

Carboxylic Acids

Topic overview Structure, naming and physical properties of carboxylic acids Preparation from primary alcohols and aldehydes Formation by hydrolysis of esters and nitriles Salt formation with carbonates, hydroxides and ammonia Reactions with alcohols, phosphorus pentachloride and lithal

Derivatives of Carboxylic Acids

Topic overview Esters and acyl chlorides: structure and naming Boiling points and solubility of monoesters Making esters from alcohols with carboxylic acids or acyl chlorides The laboratory preparation of a liquid ester Fats and oils as esters of glycerol Transesterification, biodiesel and margarine Reactions of acyl chlorides with water and alcohols

Aromatic Chemistry

Topic overview The structure of benzene and delocalised π electrons The stability of benzene compared with alkenes Electrophilic substitution: bromination and nitration of benzene Friedel–Crafts reactions and the nitration of methyl benzoate

Spectroscopy and Chromatography

Topic overview The mass spectrum: molecular ion and base peak Fragmentation and the formulae of fragment ions High resolution mass spectrometry Nuclear magnetic resonance and the TMS standard Chemically equivalent hydrogens and chemical shift Integration curves Spin–spin splitting and the n+1 rule Deducing a structure from an nmr spectrum Paper and thin-layer chromatography Gas–liquid chromatography

Volumetric Analysis

Topic overview Iodine–thiosulfate titrations Manganate(VII) titrations Deducing titration equations from half-equations Back titration

Transition Metals

Topic overview The characteristic properties of the transition metals Electronic configurations of the metals and their ions Complexes, ligands and coordination number Oxidation number, redox and disproportionation Monodentate, bidentate and polydentate ligands Ligand strength and the entropy of ligand replacement Ligand replacement in copper(II) complexes The colours of the aqueous transition metal ions Hydroxide precipitates with sodium hydroxide Precipitates with aqueous ammonia and their dissolution Vanadium and the interconversion of its oxidation states

Electrode Potentials

Topic overview Standard electrode potential Types of half-cell Cell representation and calculating emf Non-rechargeable, rechargeable and fuel cells The hydrogen–oxygen fuel cell Electrode potentials and reactivity

Amines

Topic overview Structure and classification of amines Physical properties of amines Preparing aliphatic and aromatic amines Amines as bases Reaction with ethanoyl chloride and identifying amines Diazonium salts and coupling Colour and delocalisation

Amides and Polymers

Topic overview The amide group and its preparation Reactions of amides The basicity of amides Condensation polymerisation Polyesters and polyamides in use Comparing addition and condensation polymers

Amino Acids and Proteins

Topic overview The structure of amino acids Optical activity Zwitterions and physical properties Reactions of amino acids Peptides and protein structure Enzymes as catalysts Temperature, pH and enzyme activity Enzymes in analysis and industry

Chemistry in Medicine

Topic overview Indigestion remedies Analysing an indigestion remedy by back titration Treating the skin Silver nitrate and cisplatin Aspirin: synthesis and analysis Chromatography in identifying drugs Haemoglobin, carbon monoxide and edta Drugs, testing and judgement

Kinetics

The Maxwell–Boltzmann distribution of molecular energies

3 things to know
Unit AS 2

Overview

Shape of the Maxwell–Boltzmann curve and how the Maxwell–Boltzmann curve changes when the temperature is raised.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What does the peak of the Maxwell–Boltzmann curve represent?

Key term

What does the total area under the Maxwell–Boltzmann curve represent?

Key term

Why does only a small fraction of the molecules lie beyond the activation energy at room temperature?

Questions from this subtopic

Each one with the model answer underneath.

1
What does the Maxwell–Boltzmann distribution show?
Model answer
It shows how the energies of the molecules in a sample of gas are spread out at a particular temperature.
2
Why does the Maxwell–Boltzmann curve begin at the origin?
Model answer
No molecule in the sample is completely without energy, so the number of molecules having zero energy is zero.
3
Describe the shape of the Maxwell–Boltzmann curve.
Model answer
The curve rises steeply from the origin to a peak and then falls away more gradually, with a long tail that approaches the energy axis without ever touching it.
4
What does the peak of the curve represent?
Model answer
The peak lies at the most probable energy, the energy possessed by more molecules than any other single value.
5
Why does the tail of the curve never meet the energy axis?
Model answer
There is no upper limit to the energy a molecule may have, although very high energies become vanishingly rare.
6
What does the total area under the curve represent?
Model answer
The total area represents the total number of molecules in the sample.

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