2.2.2

Beer-Lambert Law

Test yourself on Beer-Lambert Law

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The Beer-Lambert Law

The Beer-Lambert law tells us about the absorption of light by a solution.

Absorption of light

Absorption of light

The Beer-Lambert law gives the equation for the absorption of light $A$ as:
- $A = \epsilon bc$
Where $\epsilon$ is the molar absorptivity of the solution, $b$ is the path length of the light as it moves through the solution, and $c$ is the concentration of the solution.

Experiments

Experiments

The molar absorptivity $\epsilon$ is a measure of how much a particular wavelength of light is absorbed by one mole of a substance.

Application

Application

The single largest application of the spectrophotometer is for quantitative analysis.
The prerequisite for such analysis is a known absorption spectrum of the compound under investigation.
- Of particular importance is the maximum absorption (at λmax), which can be easily obtained by plotting absorbance vs. wavelength at a fixed concentration.
Next, a series of solutions of known concentration are prepared and their absorbance is measured at λmax.

Application - 2

Application - 2

Plotting absorbance vs. concentration, a calibration curve can be determined and fit using linear regression (least-squares fit).
An unknown concentration can be deduced by measuring absorbance at the absorption maximum and comparing it to the standard curve.
- Caution: The Beer-Lambert Law is only obeyed (the standard curve is linear) for reasonably dilute solutions.
Only those points in the linear range of the standard curve may be used for accurate concentration determination.

Example

Example

Typical results are shown in the table for the absorbance of [Ti(H₂O)₆]³⁺ measured at 490 nm.

Graphs

Graphs

After plotting absorbance vs concentration, we can see that if a solution has a measured absorbance of 0.450 its concentration is 1.5 mg/mL.

1

Principles of Science I

1.1

Structure & Bonding

1.1.1Atomic Model 1.1.2Electron Shells, Sub-Shells & Orbitals 1.1.3Ionic Bonding 1.1.4Representing Ionic Bonds 1.1.5Covalent Bonding 1.1.6Representing Covalent Bonds 1.1.7Metallic Bonding 1.1.8Intermolecular Forces 1.1.9Intermolecular Forces 2 1.1.10End of Topic Test - Bonding 1.1.11Relative Masses 1.1.12The Mole 1.1.13Molar Calculations 1.1.14Molar Calculations 2 1.1.15Empirical & Molecular Formulae 1.1.16Balanced Equations 1.1.17Percentage Yield 1.1.18End of Topic Test - Amount of Substance

1.2

Properties of Substances

1.2.1The Periodic Table 1.2.2Ionisation Energy 1.2.3Factors Affecting Ionisation Energies 1.2.4Trends of Ionisation 1.2.5Trends in the Periodic Table 1.2.6Polarity 1.2.7Metals & Non-Metals 1.2.8Alkali Metals 1.2.9Alkaline Earth Metals 1.2.10Reactivity of Alkaline Earth Metals 1.2.11Redox 1.2.12Transition Metals 1.2.13Redox Reactions of Transition Metals

1.3

Cell Structure & Function

1.3.1Introduction to Cells 1.3.2Prokaryotes 1.3.3Organelles of Eukaryotic Cells 1.3.4Organelles of Eukaryotic Cells 2 1.3.5Organelles in Plant Cells 1.3.6Microscopy 1.3.7End of Topic Test - Cell Structure

1.4

Cell Specialisation

1.4.1Cell Specialisation 1.4.2Blood Cells 1.4.3Plant Cells 1.4.4Gametes

1.5

Tissue Structure & Function

1.5.1Human Gas Exchange 1.5.2Blood Vessels 1.5.3Atherosclerosis 1.5.4Skeletal Muscle 1.5.5Slow & Fast Twitch Fibres 1.5.6Neurones 1.5.7Speed of Transmission 1.5.8Action Potentials 1.5.9End of Topic Test - Neurones & Action Potentials 1.5.10Synapses 1.5.11Types of Synapse 1.5.12Medical Application 1.5.13End of Topic Test - Synapses 1.5.14Chemical Brain Imbalances 1.5.15Effect of Drugs on the Brain

1.6

Working with Waves

1.6.1Progressive Waves 1.6.2Wave Speed & Phase Difference 1.6.3Longitudinal & Transverse Waves 1.6.4Stationary Waves 1.6.5Stationary Waves 2 1.6.6Applications of Stationary Waves 1.6.7Interference 1.6.8Diffraction 1.6.9Diffraction Gratings 1.6.10Application of Diffraction Gratings

1.7

Waves in Communication

1.7.1Refraction at a Plane Surface 1.7.2Internal Reflection & Fibre Optics 1.7.3Applications of Total Internal Reflection 1.7.4Properties 1.7.5Gamma, X-Ray & UV Light 1.7.6Visible Light 1.7.7Infrared, Microwave & Radio Waves 1.7.8Intensity 1.7.9Digital & Analogue Signals 1.7.10Communication Channels

2

Practical Scientific Procedures and Techniques

2.1

Titration

2.1.1pH Curves & Titrations 2.1.2pH Curves & Titrations 2 2.1.3Buffer Solutions

2.2

Colorimetry

2.2.1Measuring Rates 2.2.2Beer-Lambert Law

2.3

Chromatography

2.3.1Overview of Chromatography 2.3.2Thin-Layer Chromatography 2.3.3Column Chromatography 2.3.4Gas Chromatography

3

Science Investigation Skills

3.1

Scientific Processes

3.1.1Aims, Hypotheses & Sampling 3.1.2Pilot Studies & Design 3.1.3Ethics 3.1.4Variables & Control 3.1.5Demand Characteristics & Investigator Effects 3.1.6Features of Science 3.1.7Scientific Report 3.1.8Scientific Report 2

3.2

Data Handling & Analysis

3.2.1Types of Data 3.2.2Descriptive Statistics 3.2.3Presentation & Display of Data

3.3

Enzymes in Action

3.3.1Overview of Protein Structure 3.3.2Enzymes 3.3.3Factors Affecting Enzyme Activity 3.3.4Enzyme-Controlled Reactions

3.4

Diffusion

3.5

Plants & Their Environment

3.5.1Factors Affecting Plant Growth 3.5.2Measuring Number & Distribution of Species

3.6

Energy Content in Fuels

3.6.1Fractions 3.6.2Burning Hydrocarbons 3.6.3Combustion 3.6.4Energy 3.6.5Energy at Home 3.6.6Calorimetry

3.7

Electrical Circuits

3.7.1Circuit Diagrams & Components 3.7.2Diodes, LDRs & Thermistors 3.7.3Resistance 3.7.4Electrical Work 3.7.5Ohm's Law 3.7.6Domestic Uses of Electricity 3.7.7Fuses

4

Principles of Science II

4.1

Extracting Elements

4.1.1Atom Economy

4.2

Relating Properties to use of Substances

4.2.1Group 2 Chemistry 4.2.2End of Topic Test - Group 2 4.2.3Electrolysis 4.2.4Electrolysis Examples 4.2.5Extracting Metals 4.2.6Transition Metals 4.2.7Variable Oxidation States 4.2.8Heterogeneous Catalysts 4.2.9Homogeneous Catalysts

4.3

Organic Chemistry

4.3.1Naming Compounds 4.3.2Functional Groups 4.3.3Isomerism 4.3.4Hydrocarbons 4.3.5Structure of Alkanes 4.3.6Boiling Points of Alkanes 4.3.7Alkenes 4.3.8Curly Arrows & Mechanisms 4.3.9Cracking 4.3.10Combustion 4.3.11Free Radical Substitution of Alkanes 4.3.12Electrophilic Addition of Alkenes

4.4

Energy Changes in Industry

4.4.1The Kelvin Scale 4.4.2Enthalpy Changes 4.4.3Calorimetry 4.4.4Bond Enthalpies 4.4.5Hess' Law

4.5

The Circulatory System

4.5.1The Circulatory System 4.5.2Blood Vessels 4.5.3Blood Transfusion & the ABO Rhesus System 4.5.4The Heart 4.5.5The Cardiac Cycle 4.5.6Cardiac Output 4.5.7Coordination of Heart Action 4.5.8Heart Dissection 4.5.9Controlling Heart Rate 4.5.10Electrocardiograms 4.5.11Cardiovascular Disease 4.5.12Investigating Heart Rates

4.6

Ventilation & Gas Exchange

4.6.1Human Gas Exchange 4.6.2Ventilation 4.6.3Measuring Gas Exchange 4.6.4Controlling Ventilation Rate 4.6.5Lung Disease 4.6.6Lung Disease Data

4.7

Urinary System

4.7.1Kidneys & Control of Water Balance 4.7.2Kidneys & Osmoregulation 4.7.3Kidneys & Blood Pressure 4.7.4Urine 4.7.5Kidney Failure & Urinalysis 4.7.6Dialysis 4.7.7Transplants

4.8

Cell Transport

4.8.1Cell Membrane Structure 4.8.2Diffusion 4.8.3Osmosis 4.8.4Active Transport

4.9

Thermal Physics

4.9.1Power & Efficiency 4.9.2Work & Energy 4.9.3Conservation of Energy 4.9.4Pressure 4.9.5First Law of Thermodynamics 4.9.6Second Law of Thermodynamics 4.9.7Heat Engines, Heat Pumps & Refrigerators 4.9.8Non-Flow Processes 4.9.9p-V Diagrams 4.9.10Ideal Gases 4.9.11Ideal Gases 2 4.9.12Thermal Energy Transfer 4.9.13Thermal Energy Transfer Experiments

4.10

Materials

4.10.1Density 4.10.2Stress & Strain 4.10.3Properties of Materials 4.10.4Elasticity 4.10.5Plasticity 4.10.6Energy in Materials 4.10.7Young Modulus

4.11

Fluids

4.11.1Fluid Flow 4.11.2Viscosity 4.11.3Density 4.11.4Continuity Equation 4.11.5Bernoulli's Equation 4.11.6Non-Newtonian Fluids

5

Contemporary Issues in Science

5.1

Contemporary Issues in Science

5.1.1Sustainability 5.1.2Genetic Engineering 5.1.3Uses of Genetic Modification 5.1.4Stem Cell Therapy 5.1.5Cloning 5.1.6Cloning 2 5.1.7Nanotechnology 5.1.8Ecosystems

5.2

Analysing Scientific Information

5.2.1Validity 5.2.2Peer Review

Jump to other topics

1

Principles of Science I

1.1

Structure & Bonding

1.1.1Atomic Model 1.1.2Electron Shells, Sub-Shells & Orbitals 1.1.3Ionic Bonding 1.1.4Representing Ionic Bonds 1.1.5Covalent Bonding 1.1.6Representing Covalent Bonds 1.1.7Metallic Bonding 1.1.8Intermolecular Forces 1.1.9Intermolecular Forces 2 1.1.10End of Topic Test - Bonding 1.1.11Relative Masses 1.1.12The Mole 1.1.13Molar Calculations 1.1.14Molar Calculations 2 1.1.15Empirical & Molecular Formulae 1.1.16Balanced Equations 1.1.17Percentage Yield 1.1.18End of Topic Test - Amount of Substance

1.2

Properties of Substances

1.2.1The Periodic Table 1.2.2Ionisation Energy 1.2.3Factors Affecting Ionisation Energies 1.2.4Trends of Ionisation 1.2.5Trends in the Periodic Table 1.2.6Polarity 1.2.7Metals & Non-Metals 1.2.8Alkali Metals 1.2.9Alkaline Earth Metals 1.2.10Reactivity of Alkaline Earth Metals 1.2.11Redox 1.2.12Transition Metals 1.2.13Redox Reactions of Transition Metals

1.3

Cell Structure & Function

1.3.1Introduction to Cells 1.3.2Prokaryotes 1.3.3Organelles of Eukaryotic Cells 1.3.4Organelles of Eukaryotic Cells 2 1.3.5Organelles in Plant Cells 1.3.6Microscopy 1.3.7End of Topic Test - Cell Structure

1.4

Cell Specialisation

1.4.1Cell Specialisation 1.4.2Blood Cells 1.4.3Plant Cells 1.4.4Gametes

1.5

Tissue Structure & Function

1.5.1Human Gas Exchange 1.5.2Blood Vessels 1.5.3Atherosclerosis 1.5.4Skeletal Muscle 1.5.5Slow & Fast Twitch Fibres 1.5.6Neurones 1.5.7Speed of Transmission 1.5.8Action Potentials 1.5.9End of Topic Test - Neurones & Action Potentials 1.5.10Synapses 1.5.11Types of Synapse 1.5.12Medical Application 1.5.13End of Topic Test - Synapses 1.5.14Chemical Brain Imbalances 1.5.15Effect of Drugs on the Brain

1.6

Working with Waves

1.6.1Progressive Waves 1.6.2Wave Speed & Phase Difference 1.6.3Longitudinal & Transverse Waves 1.6.4Stationary Waves 1.6.5Stationary Waves 2 1.6.6Applications of Stationary Waves 1.6.7Interference 1.6.8Diffraction 1.6.9Diffraction Gratings 1.6.10Application of Diffraction Gratings

1.7

Waves in Communication

1.7.1Refraction at a Plane Surface 1.7.2Internal Reflection & Fibre Optics 1.7.3Applications of Total Internal Reflection 1.7.4Properties 1.7.5Gamma, X-Ray & UV Light 1.7.6Visible Light 1.7.7Infrared, Microwave & Radio Waves 1.7.8Intensity 1.7.9Digital & Analogue Signals 1.7.10Communication Channels

2

Practical Scientific Procedures and Techniques

2.1

Titration

2.1.1pH Curves & Titrations 2.1.2pH Curves & Titrations 2 2.1.3Buffer Solutions

2.2

Colorimetry

2.2.1Measuring Rates 2.2.2Beer-Lambert Law

2.3

Chromatography

2.3.1Overview of Chromatography 2.3.2Thin-Layer Chromatography 2.3.3Column Chromatography 2.3.4Gas Chromatography

3

Science Investigation Skills

3.1

Scientific Processes

3.1.1Aims, Hypotheses & Sampling 3.1.2Pilot Studies & Design 3.1.3Ethics 3.1.4Variables & Control 3.1.5Demand Characteristics & Investigator Effects 3.1.6Features of Science 3.1.7Scientific Report 3.1.8Scientific Report 2

3.2

Data Handling & Analysis

3.2.1Types of Data 3.2.2Descriptive Statistics 3.2.3Presentation & Display of Data

3.3

Enzymes in Action

3.3.1Overview of Protein Structure 3.3.2Enzymes 3.3.3Factors Affecting Enzyme Activity 3.3.4Enzyme-Controlled Reactions

3.4

Diffusion

3.5

Plants & Their Environment

3.5.1Factors Affecting Plant Growth 3.5.2Measuring Number & Distribution of Species

3.6

Energy Content in Fuels

3.6.1Fractions 3.6.2Burning Hydrocarbons 3.6.3Combustion 3.6.4Energy 3.6.5Energy at Home 3.6.6Calorimetry

3.7

Electrical Circuits

3.7.1Circuit Diagrams & Components 3.7.2Diodes, LDRs & Thermistors 3.7.3Resistance 3.7.4Electrical Work 3.7.5Ohm's Law 3.7.6Domestic Uses of Electricity 3.7.7Fuses

4

Principles of Science II

4.1

Extracting Elements

4.1.1Atom Economy

4.2

Relating Properties to use of Substances

4.2.1Group 2 Chemistry 4.2.2End of Topic Test - Group 2 4.2.3Electrolysis 4.2.4Electrolysis Examples 4.2.5Extracting Metals 4.2.6Transition Metals 4.2.7Variable Oxidation States 4.2.8Heterogeneous Catalysts 4.2.9Homogeneous Catalysts

4.3

Organic Chemistry

4.3.1Naming Compounds 4.3.2Functional Groups 4.3.3Isomerism 4.3.4Hydrocarbons 4.3.5Structure of Alkanes 4.3.6Boiling Points of Alkanes 4.3.7Alkenes 4.3.8Curly Arrows & Mechanisms 4.3.9Cracking 4.3.10Combustion 4.3.11Free Radical Substitution of Alkanes 4.3.12Electrophilic Addition of Alkenes

4.4

Energy Changes in Industry

4.4.1The Kelvin Scale 4.4.2Enthalpy Changes 4.4.3Calorimetry 4.4.4Bond Enthalpies 4.4.5Hess' Law

4.5

The Circulatory System

4.5.1The Circulatory System 4.5.2Blood Vessels 4.5.3Blood Transfusion & the ABO Rhesus System 4.5.4The Heart 4.5.5The Cardiac Cycle 4.5.6Cardiac Output 4.5.7Coordination of Heart Action 4.5.8Heart Dissection 4.5.9Controlling Heart Rate 4.5.10Electrocardiograms 4.5.11Cardiovascular Disease 4.5.12Investigating Heart Rates

4.6

Ventilation & Gas Exchange

4.6.1Human Gas Exchange 4.6.2Ventilation 4.6.3Measuring Gas Exchange 4.6.4Controlling Ventilation Rate 4.6.5Lung Disease 4.6.6Lung Disease Data

4.7

Urinary System

4.7.1Kidneys & Control of Water Balance 4.7.2Kidneys & Osmoregulation 4.7.3Kidneys & Blood Pressure 4.7.4Urine 4.7.5Kidney Failure & Urinalysis 4.7.6Dialysis 4.7.7Transplants

4.8

Cell Transport

4.8.1Cell Membrane Structure 4.8.2Diffusion 4.8.3Osmosis 4.8.4Active Transport

4.9

Thermal Physics

4.9.1Power & Efficiency 4.9.2Work & Energy 4.9.3Conservation of Energy 4.9.4Pressure 4.9.5First Law of Thermodynamics 4.9.6Second Law of Thermodynamics 4.9.7Heat Engines, Heat Pumps & Refrigerators 4.9.8Non-Flow Processes 4.9.9p-V Diagrams 4.9.10Ideal Gases 4.9.11Ideal Gases 2 4.9.12Thermal Energy Transfer 4.9.13Thermal Energy Transfer Experiments

4.10

Materials

4.10.1Density 4.10.2Stress & Strain 4.10.3Properties of Materials 4.10.4Elasticity 4.10.5Plasticity 4.10.6Energy in Materials 4.10.7Young Modulus

4.11

Fluids

4.11.1Fluid Flow 4.11.2Viscosity 4.11.3Density 4.11.4Continuity Equation 4.11.5Bernoulli's Equation 4.11.6Non-Newtonian Fluids

5

Contemporary Issues in Science

5.1

Contemporary Issues in Science

5.1.1Sustainability 5.1.2Genetic Engineering 5.1.3Uses of Genetic Modification 5.1.4Stem Cell Therapy 5.1.5Cloning 5.1.6Cloning 2 5.1.7Nanotechnology 5.1.8Ecosystems

5.2

Analysing Scientific Information

5.2.1Validity 5.2.2Peer Review

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Measuring Rates

Overview of Chromatography