The Beer–Lambert law is a fundamental relationship in IB Chemistry Topic 11 (Measurement & Data Processing). It explains how the amount of light absorbed by a solution depends on its concentration. This law forms the basis of colorimetry and spectrophotometry—techniques used to determine concentrations of unknown solutions with high accuracy. Once you understand how absorbance, concentration, and path length are linked, quantitative analysis becomes much easier.
What Is the Beer–Lambert Law?
The Beer–Lambert law states that absorbance is directly proportional to the concentration of a solution and the path length of the light through it.
The equation is:
A = ε c l
Where:
- A = absorbance (no units)
- ε = molar absorptivity (L mol⁻¹ cm⁻¹)
- c = concentration of solution (mol L⁻¹)
- l = path length of cuvette (cm)
In simple terms:
More concentrated solutions absorb more light.
What Absorbance Means
When light passes through a colored solution, some wavelengths are absorbed.
Absorbance measures how much light is absorbed rather than transmitted.
Important points:
- Absorbance increases with concentration.
- A = 0 → no light absorbed (solution is clear).
- Higher A values → darker solution.
Absorbance is logarithmic, not linear, but Beer–Lambert makes the relationship effectively linear for practical lab use.
Why the Beer–Lambert Law Works
Two principles combine to make the law valid:
1. Beer’s Law (concentration)
Each particle absorbs a tiny portion of light.
More particles = more absorption.
2. Lambert’s Law (path length)
A longer path gives more chances for light to be absorbed.
Together, they explain why absorbance depends on both solution depth and concentration.
What Is Molar Absorptivity (ε)?
Molar absorptivity measures how strongly a substance absorbs light at a given wavelength.
High ε value:
- Substance absorbs strongly
- Even small concentrations produce high absorbance
Low ε value:
- Substance is weakly absorbing
- Needs higher concentration to absorb the same amount
ε depends on wavelength, so measurements must be taken at the maximum absorbance wavelength (λmax).
How the Beer–Lambert Law Is Used
1. Determining unknown concentrations
This is the most common use in IB experiments.
Process:
- Prepare a calibration curve using known concentrations.
- Measure absorbance of unknown sample.
- Use the graph to find its concentration.
This method is widely used in environmental testing, food chemistry, and medical analysis.
2. Monitoring reaction progress
Absorbance changes over time if reactants or products are colored.
This allows real-time analysis of reaction rates.
3. Identifying substances
Specific compounds absorb at specific wavelengths.
Matching absorbance patterns helps identify substances.
Creating a Calibration Curve
A calibration curve plots:
- Absorbance (y-axis)
- Concentration (x-axis)
This graph should be a straight line through the origin if Beer–Lambert is followed.
Steps:
- Prepare several standard solutions.
- Measure absorbance at λmax.
- Plot the values and draw a best-fit line.
- Use the line to determine the concentration of unknown samples.
Calibration curves are core IB skills.
Limitations of the Beer–Lambert Law
The law breaks down when:
- Concentration is too high (particles interact).
- The solution scatters light (cloudy samples).
- The wavelength is not at λmax.
- The cuvette has fingerprints or scratches.
- The light source is unstable.
IB questions often test knowledge of these limitations.
Common IB Misunderstandings
“Absorbance and concentration are always perfectly linear.”
Only true at low to moderate concentrations.
“Absorbance has units.”
Absorbance is unitless.
“Any wavelength can be used.”
Measurements must be at λmax for accuracy.
“The calibration curve must go through zero.”
Ideally yes, but small deviations can occur due to instrument error.
FAQs
Why does absorbance increase with concentration?
More particles absorb more light, reducing transmitted intensity.
Why is λmax used?
It maximizes sensitivity and accuracy of measurement.
Can Beer–Lambert be used for colorless solutions?
Only if the species absorbs UV light—requires a UV spectrophotometer.
Conclusion
The Beer–Lambert law links absorbance to concentration through a simple proportional relationship. It forms the basis of quantitative analysis in chemistry, allowing accurate determination of unknown concentrations through spectrophotometry. Mastering this law is essential for IB Chemistry experiments, data processing, and exam success.
