1.9.5

Maxwell-Boltzmann Distribution

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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 graph

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

The origin

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

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

  • 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

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

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.
Jump to other topics
1

Physical Chemistry

1.1

Atoms, Molecules & Stoichiometry

1.1.1Relative Masses1.1.2The Mole1.1.3Mass Spectrometry1.1.4Empirical & Molecular Formulae1.1.5Balanced Equations1.1.6Molar Volume1.1.7End of Topic Test - Amount of Substance
1.2

Atomic Structure

1.2.1Fundamental Particles1.2.2Isotopes & Mass Number1.2.3Electron Shells, Sub-Shells & Orbitals1.2.4Electron Configuration1.2.5Ionisation Energy1.2.6Factors Affecting Ionisation Energies1.2.7Trends of Ionisation1.2.8Specific Impacts on Ionisation Energies1.2.9Electron Affinity1.2.10End of Topic Test - Atomic Structure1.2.11A-A* (AO2/3) - Atomic Structure
1.3

Chemical Bonding

1.3.1Ionic Bonding1.3.2Covalent & Dative Bonding1.3.3Shapes of Molecules1.3.4Intermolecular Forces1.3.5Intermolecular Forces 21.3.6Electronegativity1.3.7Bond Length, Bond Energy, & Bond Polarity1.3.8Metallic Bonding1.3.9Physical Properties1.3.10End of Topic Test - Bonding1.3.11A-A* (AO2/3) - Bonding
1.4

States of Matter

1.4.1Simple Covalent Molecules1.4.2The Ideal Gas Equation1.4.3States of Matter1.4.4Particle Diagrams1.4.5The Liquid State1.4.6Giant Ionic Lattices1.4.7Giant Metallic Lattices1.4.8Giant Covalent Structures1.4.9Graphene & Fullerene1.4.10Recycling
1.5

Chemical Energetics

1.5.1Calorimetry1.5.2Bond Enthalpies1.5.3Enthalpy Changes1.5.4Hess' Law1.5.5Born-Haber Cycles1.5.6Born-Haber Cycle Calculations1.5.7Entropy1.5.8Free Energy1.5.9End of Topic Test - Energetics
1.6

Electrochemistry

1.6.1Electrochemical Cells1.6.2Electrochemical Series1.6.3Commercial Application1.6.4Nernst Equation1.6.5Redox
1.7

Equilibria

1.7.1Dynamic Equilibrium & Le Chatelier1.7.2Kc1.7.3Kp1.7.4pH1.7.5The Ionic Product of Water1.7.6Weak Acids & Bases1.7.7Introduction to Solubility Equilibria1.7.8Solubility Equilibria Calculations1.7.9Free Energy of Dissolution1.7.10pH and Solubility1.7.11Common-Ion Effect1.7.12End of Topic Test - Kp & Electrochemistry1.7.13A-A* (AO2/3) - Electrochemical Cells
1.8

Partition Coefficient

1.8.1Kpc
1.9

Reaction Kinetics

1.9.1Collision Theory1.9.2Orders, Rate Constants & Equations1.9.3Rate Graphs1.9.4Rate Determining Step1.9.5Maxwell-Boltzmann Distribution1.9.6Catalysts1.9.7Homogeneous Catalysts1.9.8Heterogeneous Catalysts1.9.9End of Topic Test - Kinetics1.9.10End of Topic Test - Rate Equations1.9.11A-A* (AO2/3) - Rate Equations
2

Inorganic Chemistry

2.1

The Periodic Table

2.1.1The Periodic Table2.1.2Trends in the Periodic Table2.1.3End of Topic Test - Periodicity & Trends2.1.4Ceramics2.1.5Period 3 Elements & Oxides2.1.6Period 3 Oxides2.1.7End of Topic Test - Period 3
2.2

Group 2

2.2.1Group 2 Chemistry
2.3

Group 17

2.3.1Introduction to Halogens2.3.2Reactions of Halogens2.3.3Chlorine & Chlorate(I)2.3.4End of Topic Test - Group 172.3.5A-A* (AO2/3) - Periodicity, Group 2 & 17
2.4

Transition Metals

2.4.1General Properties2.4.2Titrations2.4.3Shapes of Complex Ions2.4.4Variable Oxidation States2.4.5Ligands2.4.6Colours of Ions2.4.7Stereoisomerism of Complex Ions2.4.8Cisplatin2.4.9Ligand Substitutions & Kstab2.4.10End of Topic Test - Transition Metals2.4.11A-A* (AO2/3) - Transition Metals
2.5

Nitrogen & Sulfur

2.5.1Nitrogen & Ammonia2.5.2Formulated vs Manure Fertilisers2.5.3Nitrogen Containing Fertilisers2.5.4Fertilizers & Eutrophication2.5.5Common Atmospheric Pollutants & Their Properties2.5.6Catalytic Converters2.5.7Atmospheric Oxides
3

Organic Chemistry & Analysis

3.1

Introduction to Organic Chemistry

3.1.1Naming Conventions3.1.2Mechanism3.1.3Isomerism3.1.4End of Topic Test - Introduction to Organic Chem
3.2

Hydrocarbons

3.2.1Fractional Distillation3.2.2Cracking3.2.3Combustion3.2.4Chlorination3.2.5End of Topic Test - Alkanes3.2.6Introduction to Alkenes3.2.7Reactions of Alkenes3.2.8Polymerisation Reactions3.2.9End of Topic Test - Alkenes3.2.10Arenes3.2.11Evidence for Structure of Arenes3.2.12Reactions of Benzene3.2.13End of Topic Test -Arenes
3.3

Halogen Derivatives

3.3.1Properties of Haloalkanes3.3.2Substitution Reactions of Haloalkanes3.3.3Environmental Impacts of Haloalkanes3.3.4End of Topic Test - Halogenoalkanes
3.4

Hydroxy Compounds

3.4.1Types of Alcohol3.4.2Oxidation 13.4.3Oxidation 23.4.4Elimination3.4.5Acids & Esters3.4.6Acyl Chlorides & Acylation3.4.7Phenols & Their Reactions3.4.8End of Topic Test - Alcohols
3.5

Carbonyl Compounds

3.5.1Carbonyls3.5.2Hydrogen Bonding & Carbonyls3.5.3Aldehydes & Ketones3.5.4Tri-Iodomethane Reaction3.5.5End of Topic Test -Carbonyls
3.6

Carboxylic Acids & Derivatives

3.6.1Properties of Carboxylic Acids3.6.2Esters3.6.3Acyl Chlorides3.6.4End of Topic Test - Carboxylic Acids
3.7

Nitrogen Compounds

3.7.1Nature & Preparation of Amines3.7.2Basicity & Nucleophilicity3.7.3Amides3.7.4Reactions of Amino Acids3.7.5Amino Acids
3.8

Polymerisation

3.8.1Properties of Addition Polymers3.8.2Condensation Polymerisation3.8.3Effects of Side-Chains on Polymers3.8.4Hydrolysis of Ester & Amide Groups3.8.5Proteins3.8.6DNA3.8.7Adhesive & Conducting Polymers3.8.8End of Topic Test - Amines & Proteins
3.9

Analytical Techniques

3.9.1Chromatography3.9.2High-Performance Liquid Chromatography3.9.3Gas Chromatography3.9.4IR Spectroscopy3.9.5Uses of IR Spectroscopy3.9.6Mass Spectrometry3.9.7Mass Spectrometry Analysis3.9.8Nuclear Magnetic Resonance3.9.9Carbon-13 NMR3.9.10Proton NMR I3.9.11Proton NMR II3.9.12End of Topic Test - Analytical Techniques3.9.13A-A* (AO2/3) - Analytical Techniques
3.10

Organic Synthesis

3.10.1Chirality & Drug Synthesis3.10.2Organic Synthesis3.10.3Examples of Synthetic Routes3.10.4End of Topic Test - Organic Synthesis

Practice questions on Maxwell-Boltzmann Distribution

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    The peak on the Maxwell-Boltzmann distribution represents what?Multiple choice
  2. 2
    What represents the total number of molecules in the Maxwell-Boltzmann graph?Multiple choice
  3. 3
    What is the difference in the area under the Maxwell-Boltzmann distribution at high and low temperatures?Multiple choice
  4. 4
    If we raise the temperature, the curve on the Maxwell-Boltzmann distribution:True / false
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Rate Determining Step

Catalysts