Chemistry · General chemistry II · Concept
The Beer–Lambert law and absorbance
A solution that absorbs light lets through a fraction T of it, and its absorbance is A = −log T. The Beer–Lambert law says absorbance is proportional to concentration: A = εbc, where ε is the molar absorptivity at that wavelength and b the path length. A calibration line from standard solutions turns a measured absorbance into a concentration.
Transmittance and absorbance
In absorption spectroscopy, a spectrophotometer compares the light leaving a sample with the light entering it. Transmittance T is that fraction, often given as a percentage. Absorbance is A = −log T: a sample that transmits 10% has A = 1, and one that transmits 1% has A = 2.
Absorbance is proportional to concentration
ε, the molar absorptivity, depends on the substance and the wavelength; b is the path length, usually 1.00 cm; c is the molar concentration. Doubling the concentration doubles the absorbance, not the transmittance.
Choose the wavelength
Measure where the substance absorbs strongly, usually at the peak of its absorption spectrum, and use the same wavelength for every standard and sample. For a colored solution the peak lies in the visible range: the color you see is the light the solution does not absorb.
Calibration curves
In practice εb is found by measuring standards of known concentration and fitting a straight line of absorbance against concentration. The slope is εb, and an unknown’s concentration is read from its absorbance on that line.
Limits of the law
The straight line holds for dilute solutions. At high concentrations, or when the absorbing species reacts, associates or scatters light, the absorbance bends away from the line, so a reading beyond the range of the standards is not trustworthy.
Common mistakes
- Treating transmittance as proportional to concentration: absorbance is, while transmittance falls off exponentially.
- Putting a percentage into A = −log T: 35.5% transmittance is T = 0.355.
- Using a molar absorptivity measured at a different wavelength.
- Reading an unknown far above the highest standard, where the line may no longer hold.
Key terms
- Beer–Lambert law
- A = εbc: absorbance is proportional to concentration c and path length b. It holds best for dilute solutions measured at one chosen wavelength.
- Absorbance
- How much light a sample absorbs: A = −log₁₀T, where T is the fraction of light transmitted. It has no units and rises with concentration.
- Transmittance
- The fraction of light that passes through a sample: the transmitted intensity divided by the incoming (reference) intensity, from 0 to 1, or 0% to 100%.
- Molar absorptivity
- The constant ε in A = εbc: how strongly a substance absorbs light at one wavelength. Its units, often L/(mol·cm), must match those of the concentration and path length.
- Calibration
- Measuring known standards to build a curve that turns an instrument’s reading into a quantity, such as absorbance into concentration. Readings outside the range of the standards aren’t reliable.
- Spectrophotometry
- Measuring how much light a sample absorbs or transmits at chosen wavelengths. With a calibration curve or a known ε, the absorbance gives the concentration.
Work through an example
A dye solution in a 1.00 cm cell transmits 35.5% of the light at the dye’s measuring wavelength, where ε = 1.50 × 10⁴ L mol⁻¹ cm⁻¹. Find the dye’s concentration.
Find a concentration from transmittance →Sources and scope
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