1.5.2

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

  • No molecules have zero energy, so the curve passes through the origin at (0,0).
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

Atomic Structure

1.1.1Fundamental Particles1.1.2Isotopes & Mass Number1.1.3Mass Spectrometry1.1.4Electron Shells, Sub-Shells & Orbitals1.1.5Electron Configuration1.1.6Ionisation Energy1.1.7Factors Affecting Ionisation Energies1.1.8Trends of Ionisation1.1.9Specific Impacts on Ionisation Energies1.1.10End of Topic Test - Atomic Structure1.1.11A-A* (AO3/4) - Atomic Structure
1.2

Amount of Substance

1.2.1Relative Masses1.2.2The Mole1.2.3The Ideal Gas Equation1.2.4Empirical & Molecular Formulae1.2.5Balanced Equations1.2.6Percentage Yield1.2.7A-A* (AO3/4) - Percentage Yield1.2.8Atom Economy1.2.9End of Topic Test - Amount of Substance1.2.10A-A* (AO3/4) - Substances & Yield1.2.11Diagnostic Misconceptions - Moles
1.3

Bonding

1.3.1Ionic Bonding1.3.2Covalent & Dative Bonding1.3.3Carbon Structures1.3.4Metallic Bonding1.3.5Physical Properties1.3.6Shapes of Molecules1.3.7Polarity1.3.8Intermolecular Forces1.3.9Intermolecular Forces 21.3.10End of Topic Test - Bonding1.3.11Exam-Style Question - Shape of Molecules1.3.12A-A* (AO3/4) - Bonding1.3.13Diagnostic Misconceptions - Ions1.3.14Diagnostic Misconceptions - Ionic & Covalent1.3.15Diagnostic Misconceptions - Phase Change1.3.16Diagnostic Misconceptions - Boiling1.3.17Diagnostic Misconceptions - Polar Bonds
1.4

Energetics

1.4.1Enthalpy Changes1.4.2Bond Breaking and Making1.4.3Enthalpy Changes: Standard Conditions1.4.4Calorimetry1.4.5Hess' Law1.4.6Bond Enthalpies1.4.7End of Topic Test - Energetics1.4.8Diagnostic Misconceptions - Calorimetry
1.5

Kinetics

1.5.1Collision Theory1.5.2Maxwell-Boltzmann Distribution1.5.3Increasing Rates1.5.4End of Topic Test - Kinetics
1.6

Equilibria

1.6.1Le Chatelier1.6.2Equilibrium Constants1.6.3A-A* (AO3/4) - Energetics, Kinetics, Equilibria1.6.4End of Topic Test - Equilibria1.6.5Diagnostic Misconceptions - Solids
1.7

Redox

1.7.1Redox1.7.2End of Topic Test - Redox
2

Physical Chemistry 2 (A2 Only)

2.1

Thermodynamics (A2 Only)

2.1.1Born-Haber Cycles (A2 Only)2.1.2Born-Haber Cycle Calculations (A2 Only)2.1.3Entropy (A2 Only)2.1.4Free Energy (A2 Only)2.1.5End of Topic Test - Thermodynamics2.1.6A-A* (AO3/4) - Thermodynamics
2.2

Rate Equations (A2 Only)

2.2.1Rate Equations (A2 Only)2.2.2Rate Equations 2 (A2 Only)2.2.3The Arrhenius Equation (A2 Only)2.2.4Experimental Methods for Rates (A2 Only)2.2.5End of Topic Test - Rate Equations2.2.6Exam-Style Question - Rates2.2.7A-A* (AO3/4) - Rate Equations
2.3

The Equilibrium Constant Kp (A2 Only)

2.3.1Properties of Kp (A2 Only)
2.4

Electrochemical Cells (A2 Only)

2.4.1Electrochemical Cells (A2 Only)2.4.2Electrochemical Series (A2 Only)2.4.3Commercial Application (A2 Only)2.4.4End of Topic Test - Kp & Electrochemistry2.4.5A-A* (AO3/4) - Electrochemical Cells2.4.6Diagnostic Misconceptions - Salt Bridges2.4.7Diagnostic Misconceptions - Electrode, Electrolyte
2.5

Acids & Bases (A2 Only)

2.5.1Brønsted-Lowry Acids & Bases (A2 Only)2.5.2pH (A2 Only)2.5.3The Ionic Product of Water (A2 Only)2.5.4Weak Acids & Bases (A2 Only)2.5.5pH Curves & Titrations (A2 Only)2.5.6pH Curves & Titrations 2 (A2 Only)2.5.7Buffer Solutions (A2 Only)2.5.8End of Topic Test - Acids & Bases2.5.9Exam-Style Question - Weak Acids2.5.10A-A* (AO3/4) - Acids & Bases2.5.11Diagnostic Misconceptions - Ammonia is an Alkali2.5.12Diagnostic Misconceptions - Water's Neutrality2.5.13Diagnostic Misconceptions - Concentrate & Strength
3

Inorganic Chemistry

3.1

Periodicity & Trends

3.1.1The Periodic Table3.1.2Trends in the Periodic Table3.1.3End of Topic Test - Periodicity & Trends3.1.4Diagnostic Misconceptions - Atomic Radius
3.2

Group 2

3.2.1Group 2 Chemistry3.2.2End of Topic Test - Group 2
3.3

Group 7

3.3.1Introduction to Halogens3.3.2Reactions of Halogens3.3.3Chlorine & Chlorate(I)3.3.4End of Topic Test - Group 73.3.5Exam-Style Question - Group 73.3.6A-A* (AO3/4) - Periodicity, Group 2 & 7
4

Inorganic Chemistry 2 (A2 Only)

4.1

Period 3 (A2 Only)

4.1.1Period 3 Elements & Oxides (A2 Only)4.1.2Period 3 Oxides (A2 Only)4.1.3End of Topic Test - Period 3
4.2

Transition Metals (A2 Only)

4.2.1General Properties (A2 Only)4.2.2Substitution Reactions (A2 Only)4.2.3Shapes of Complex Ions (A2 Only)4.2.4Colours of Ions (A2 Only)4.2.5Variable Oxidation States (A2 Only)4.2.6Titrations (A2 Only)4.2.7Homogeneous Catalysts (A2 Only)4.2.8Heterogeneous Catalysts (A2 Only)4.2.9End of Topic Test - Transition Metals4.2.10A-A* (AO3/4) - Transition Metals
4.3

Reactions of Ions in Aqueous Solutions (A2 Only)

4.3.1Acidity (A2 Only)4.3.2Identification (A2 Only)4.3.3End of Topic Test - Reactions of Ions in Solution
5

Organic Chemistry 1

5.1

Introduction

5.1.1Naming Conventions5.1.2Mechanism5.1.3Isomerism5.1.4End of Topic Test - Introduction to Organic Chem
5.2

Alkanes

5.2.1Fractional Distillation5.2.2Cracking5.2.3Combustion5.2.4Chlorination5.2.5End of Topic Test - Alkanes
5.3

Halogenoalkanes

5.3.1Substitution Reactions5.3.2Elimination Reactions5.3.3Ozone Depletion5.3.4End of Topic Test - Halogenoalkanes
5.4

Alkenes

5.4.1Introduction to Alkenes5.4.2Reactions of Alkenes5.4.3Polymerisation Reactions5.4.4Properties of Polymers5.4.5End of Topic Test - Alkenes
5.5

Alcohols

5.5.1Production of Alcohols5.5.2Oxidation of Alcohols5.5.3Oxidation of Alcohols - 25.5.4Elimination Reactions5.5.5End of Topic Test - Alcohols5.5.6Exam-Style Question - Alcohols
5.6

Organic Analysis

5.6.1Reactions5.6.2Reactions 25.6.3Mass Spectrometry5.6.4Infrared Spectroscopy5.6.5End of Topic Test - Organic Analysis
5.7

A-A* (AO3/4) - Organic 1

5.7.1A-A* (AO3/4) - Organic 1
6

Organic Chemistry 2 (A2 Only)

6.1

Optical Isomerism (A2 Only)

6.1.1Optical Isomerism (A2 Only)6.1.2End of Topic Test - Optical Isomerism
6.2

Aldehydes & Ketones (A2 Only)

6.2.1Aldehydes & Ketones (A2 Only)6.2.2End of Topic Test - Aldehydes & Ketones
6.3

Carboxylic Acids & Esters (A2 Only)

6.3.1Acids & Esters (A2 Only)6.3.2Acylation (A2 Only)6.3.3End of Topic Test - Carboxylic Acids & Esters
6.4

Aromatic Chemistry (A2 Only)

6.4.1Structure & Reactivity (A2 Only)6.4.2Reactions of Benzene (A2 Only)6.4.3End of Topic Test - Aromatic Chemistry
6.5

Amines (A2 Only)

6.5.1Nature & Preparation of Amines (A2 Only)6.5.2Basicity & Nucleophilicity (A2 Only)6.5.3End of Topic Test - Amines
6.6

Polymers (A2 Only)

6.6.1Condensation Polymers (A2 Only)6.6.2Biodegradability (A2 Only)
6.7

Biological Organic (A2 Only)

6.7.1Amino Acids (A2 Only)6.7.2Proteins (A2 Only)6.7.3DNA (A2 Only)6.7.4Anti-Cancer Drugs (A2 Only)6.7.5End of Topic Test - Biological Organic
6.8

Organic Synthesis (A2 Only)

6.8.1Organic Synthesis (A2 Only)6.8.2Examples of Synthetic Routes (A2 Only)6.8.3End of Topic Test - Polymers & Organic Synthesis
6.9

NMR Spectroscopy (A2 Only)

6.9.1Understanding NMR (A2 Only)6.9.2Carbon-13 NMR (A2 Only)6.9.3Hydrogen-1 NMR (A2 Only)6.9.4Hydrogen-1 NMR 2 (A2 Only)6.9.5End of Topic Test - NMR
6.10

Chromatography (A2 Only)

6.10.1Overview of Chromatography (A2 Only)6.10.2Thin-Layer Chromatography (A2 Only)6.10.3Column Chromatography (A2 Only)6.10.4Gas Chromatography (A2 Only)6.10.5End of Topic Test - Chromatography
6.11

A-A* (AO3/4) - Organic 2

6.11.1A-A* (AO3/4) - Organic 2

Practice questions on Maxwell-Boltzmann Distribution

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  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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Collision Theory

Increasing Rates