Worked example 1
A solution has an absorbance of 0.420 in a 1.00 cm cuvette. The molar absorptivity is 2100 L/(mol*cm). Find the concentration.
Try it first: Rearrange the law for the unknown before substituting numbers.
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Gases, Solutions & SpectroscopySpectroscopyContent level: Core 20 min
Spectroscopy and the Beer-Lambert Law
What you'll be able to do: Use A = abc to relate absorbance to concentration, and read a calibration curve to find an unknown.
Introduction
A coloured solution absorbs light, and the more concentrated it is the more it absorbs. Spectroscopy turns that everyday observation into a precise measurement of concentration.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- State and apply the Beer-Lambert law
- Explain why measurements are taken at λ max
- Construct and read a calibration curve
- Identify sources of deviation from linearity
Lesson
The law
A = abc, where A is absorbance, a is the molar absorptivity of the substance, b is the path length of the cuvette in centimetres, and c is the concentration in mol/L. Absorbance itself has no units, and molar absorptivity carries whatever units make the product dimensionless.
A = abc
With a and b held constant, absorbance is directly proportional to concentration. That single fact is what makes the whole technique work.
Choosing the wavelength
Every substance absorbs some wavelengths more than others. Measurements are taken at λ max, the wavelength of maximum absorbance, because the signal is largest there and small errors in wavelength setting have the least effect on the reading. A solution appears the complementary colour to the light it absorbs, so a solution that absorbs red light looks green.
Calibration curves
Prepare several standards of known concentration, measure the absorbance of each at λ max, and plot absorbance against concentration. The points fall on a straight line through the origin whose gradient equals the product ab. Measure the unknown, find its absorbance on the vertical axis, and read across then down to its concentration.
When linearity fails
At high concentration the particles begin to interact and the line bends away from the axis, so very concentrated samples should be diluted into the linear range. Cloudiness scatters light and inflates the apparent absorbance, and a smudged or mismatched cuvette does the same.
Key ideas
Definition
Absorbance
A unitless measure of how much light a sample removes from the beam.
Definition
Molar absorptivity
A constant describing how strongly one particular substance absorbs at a given wavelength.
Definition
Lambda max
The wavelength of maximum absorbance, used for the most sensitive measurement.
Rule
Proportionality
With fixed a and b, doubling the concentration doubles the absorbance.
Equation
Beer-Lambert law
A = abc
- A = absorbance, unitless
- a = molar absorptivity
- b = path length in cm
- c = concentration in mol/L
Worked examples
Worked example 2
Standards of 0.0020 M and 0.0040 M give absorbances of 0.30 and 0.60. An unknown reads 0.45. Find its concentration.
Try it first: Check whether the standards fall on a straight line through the origin.
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Common mistakes
Treating absorbance as having units.
Why it's wrong: Absorbance is a logarithmic ratio of light intensities, so it is dimensionless.
Check instead: Report absorbance as a bare number.
Extrapolating a calibration line beyond the standards.
Why it's wrong: Linearity is only demonstrated over the range that was measured.
Check instead: Dilute the unknown until it falls inside the calibrated range.
Assuming the solution is the colour it absorbs.
Why it's wrong: You see the transmitted light, which is the complementary colour.
Check instead: A green solution absorbs red light, not green.
Practice this skill
No practice questions are available for this topic yet. You can still practice the whole unit.
What you should now know
The Beer-Lambert law states that absorbance is proportional to molar absorptivity, path length and concentration. Because absorbance and concentration are linearly related, a set of standards produces a straight calibration line through the origin, and an unknown absorbance can be read back to a concentration. Measurements are made at the wavelength of maximum absorbance for the best sensitivity.
- A = abc links absorbance to concentration
- Absorbance is unitless and proportional to concentration
- Measure at λ max for the strongest, most reliable signal
- A calibration curve is a straight line through the origin
- Dilute concentrated or cloudy samples back into the linear range
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.