Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann Distribution of Energies

The Maxwell-Boltzmann distribution of energies is a handy little graph showing the energy distribution of all the molecules in a gas.

The graph

The number of molecules is on the y-axis.
The kinetic energy of the molecules is on the x-axis.

The origin

The curve passes through the origin (0,0).
- This is because no molecules have zero energy.

The peak

There is a peak in the middle.
- This represents the most likely energy of any molecule.
There are more molecules with this energy than with any other energy.

The area under the graph

The area under the graph gives the total number of molecules.
- You can think of this as like adding up the number of molecules with every particular energy.

Molecule energies

The average energy is to the right of the maximum (peak).
The tail of the graph is asymptotic to the x-axis.
- This means it tends to zero, but never touches the x-axis.
- This reflects that there is a small possibility of having a very high energy molecule.

Activation energies

We can mark the activation energy on the Maxwell-Boltzmann distribution. This allows us to view the number of molecules with the energy to react.
- On the left-hand side of the activation energy mark, molecules have less energy than the activation energy and so they can't react.
- On the right-hand side, molecules have more energy than the activation energy and so they can react.

1Physical Chemistry

1.1Atoms, Molecules & Stoichiometry

1.1.1Relative Masses

1.1.2The Mole

1.1.3Mass Spectrometry

1.1.4Empirical & Molecular Formulae

1.1.5Balanced Equations

1.1.6Molar Volume

1.1.7End of Topic Test - Amount of Substance

1.2Atomic Structure

1.2.1Fundamental Particles

1.2.2Isotopes & Mass Number

1.2.3Electron Shells, Sub-Shells & Orbitals

1.2.4Electron Configuration

1.2.5Ionisation Energy

1.2.6Factors Affecting Ionisation Energies

1.2.7Trends of Ionisation

1.2.8Specific Impacts on Ionisation Energies

1.2.9Electron Affinity

1.2.10End of Topic Test - Atomic Structure

1.2.11A-A* (AO2/3) - Atomic Structure

1.3Chemical Bonding

1.3.1Ionic Bonding

1.3.2Covalent & Dative Bonding

1.3.3Shapes of Molecules

1.3.4Intermolecular Forces

1.3.5Intermolecular Forces 2

1.3.6Electronegativity

1.3.7Bond Length, Bond Energy, & Bond Polarity

1.3.8Metallic Bonding

1.3.9Physical Properties

1.3.10End of Topic Test - Bonding

1.3.11A-A* (AO2/3) - Bonding

1.4States of Matter

1.4.1Simple Covalent Molecules

1.4.2The Ideal Gas Equation

1.4.3States of Matter

1.4.4Particle Diagrams

1.4.5The Liquid State

1.4.6Giant Ionic Lattices

1.4.7Giant Metallic Lattices

1.4.8Giant Covalent Structures

1.4.9Graphene & Fullerene

1.4.10Recycling

1.5Chemical Energetics

1.5.1Calorimetry

1.5.2Bond Enthalpies

1.5.3Enthalpy Changes

1.5.4Hess' Law

1.5.5Born-Haber Cycles

1.5.6Born-Haber Cycle Calculations

1.5.7Entropy

1.5.8Free Energy

1.5.9End of Topic Test - Energetics

1.6Electrochemistry

1.6.1Electrochemical Cells

1.6.2Electrochemical Series

1.6.3Commercial Application

1.6.4Nernst Equation

1.6.5Redox

1.7Equilibria

1.7.1Dynamic Equilibrium & Le Chatelier

1.7.2Kc

1.7.3Kp

1.7.4pH

1.7.5The Ionic Product of Water

1.7.6Weak Acids & Bases

1.7.7Introduction to Solubility Equilibria

1.7.8Solubility Equilibria Calculations

1.7.9Free Energy of Dissolution

1.7.10pH and Solubility

1.7.11Common-Ion Effect

1.7.12End of Topic Test - Kp & Electrochemistry

1.7.13A-A* (AO2/3) - Electrochemical Cells

1.8Partition Coefficient

1.8.1Kpc

1.9Reaction Kinetics

1.9.1Collision Theory

1.9.2Orders, Rate Constants & Equations

1.9.3Rate Graphs

1.9.4Rate Determining Step

1.9.5Maxwell-Boltzmann Distribution

1.9.6Catalysts

1.9.7Homogeneous Catalysts

1.9.8Heterogeneous Catalysts

1.9.9End of Topic Test - Kinetics

1.9.10End of Topic Test - Rate Equations

1.9.11A-A* (AO2/3) - Rate Equations

2Inorganic Chemistry

2.1The Periodic Table

2.1.1The Periodic Table

2.1.2Trends in the Periodic Table

2.1.3End of Topic Test - Periodicity & Trends

2.1.4Ceramics

2.1.5Period 3 Elements & Oxides

2.1.6Period 3 Oxides

2.1.7End of Topic Test - Period 3

2.2Group 2

2.2.1Group 2 Chemistry

2.3Group 17

2.3.1Introduction to Halogens

2.3.2Reactions of Halogens

2.3.3Chlorine & Chlorate(I)

2.3.4End of Topic Test - Group 17

2.3.5A-A* (AO2/3) - Periodicity, Group 2 & 17

2.4Transition Metals

2.4.1General Properties

2.4.2Titrations

2.4.3Shapes of Complex Ions

2.4.4Variable Oxidation States

2.4.5Ligands

2.4.6Colours of Ions

2.4.7Stereoisomerism of Complex Ions

2.4.8Cisplatin

2.4.9Ligand Substitutions & Kstab

2.4.10End of Topic Test - Transition Metals

2.4.11A-A* (AO2/3) - Transition Metals

2.5Nitrogen & Sulfur

2.5.1Nitrogen & Ammonia

2.5.2Formulated vs Manure Fertilisers

2.5.3Nitrogen Containing Fertilisers

2.5.4Fertilizers & Eutrophication

2.5.5Common Atmospheric Pollutants & Their Properties

2.5.6Catalytic Converters

2.5.7Atmospheric Oxides

3Organic Chemistry & Analysis

3.1Introduction to Organic Chemistry

3.1.1Naming Conventions

3.1.2Mechanism

3.1.3Isomerism

3.1.4End of Topic Test - Introduction to Organic Chem

3.2Hydrocarbons

3.2.1Fractional Distillation

3.2.2Cracking

3.2.3Combustion

3.2.4Chlorination

3.2.5End of Topic Test - Alkanes

3.2.6Introduction to Alkenes

3.2.7Reactions of Alkenes

3.2.8Polymerisation Reactions

3.2.9End of Topic Test - Alkenes

3.2.10Arenes

3.2.11Evidence for Structure of Arenes

3.2.12Reactions of Benzene

3.2.13End of Topic Test -Arenes

3.3Halogen Derivatives

3.3.1Properties of Haloalkanes

3.3.2Substitution Reactions of Haloalkanes

3.3.3Environmental Impacts of Haloalkanes

3.3.4End of Topic Test - Halogenoalkanes

3.4Hydroxy Compounds

3.4.1Types of Alcohol

3.4.2Oxidation 1

3.4.3Oxidation 2

3.4.4Elimination

3.4.5Acids & Esters

3.4.6Acyl Chlorides & Acylation

3.4.7Phenols & Their Reactions

3.4.8End of Topic Test - Alcohols

3.5Carbonyl Compounds

3.5.1Carbonyls

3.5.2Hydrogen Bonding & Carbonyls

3.5.3Aldehydes & Ketones

3.5.4Tri-Iodomethane Reaction

3.5.5End of Topic Test -Carbonyls

3.6Carboxylic Acids & Derivatives

3.6.1Properties of Carboxylic Acids

3.6.2Esters

3.6.3Acyl Chlorides

3.6.4End of Topic Test - Carboxylic Acids

3.7Nitrogen Compounds

3.7.1Nature & Preparation of Amines

3.7.2Basicity & Nucleophilicity

3.7.3Amides

3.7.4Reactions of Amino Acids

3.7.5Amino Acids

3.8Polymerisation

3.8.1Properties of Addition Polymers

3.8.2Condensation Polymerisation

3.8.3Effects of Side-Chains on Polymers

3.8.4Hydrolysis of Ester & Amide Groups

3.8.5Proteins

3.8.6DNA

3.8.7Adhesive & Conducting Polymers

3.8.8End of Topic Test - Amines & Proteins

3.9Analytical Techniques

3.9.1Chromatography

3.9.2High-Performance Liquid Chromatography

3.9.3Gas Chromatography

3.9.4IR Spectroscopy

3.9.5Uses of IR Spectroscopy

3.9.6Mass Spectrometry

3.9.7Mass Spectrometry Analysis

3.9.8Nuclear Magnetic Resonance

3.9.9Carbon-13 NMR

3.9.10Proton NMR I

3.9.11Proton NMR II

3.9.12End of Topic Test - Analytical Techniques

3.9.13A-A* (AO2/3) - Analytical Techniques

3.10Organic Synthesis

3.10.1Chirality & Drug Synthesis

3.10.2Organic Synthesis

3.10.3Examples of Synthetic Routes

3.10.4End of Topic Test - Organic Synthesis

Jump to other topics