Beer’s Law describes how a colored solution absorbs light as the light passes through it. It matters because chemists can use light measurements to determine the concentration of a substance without destroying the sample. A spectrophotometer shines a selected wavelength of light through a cuvette and compares the incoming and outgoing light intensities.
The darker or more concentrated the solution is, the more light it absorbs.
The law is written as A = εlc, where absorbance depends on molar absorptivity, path length, and concentration. Molar absorptivity describes how strongly a substance absorbs a specific wavelength of light, while path length is usually the width of the cuvette. In the useful linear range, a graph of absorbance versus concentration is a straight calibration curve.
The concentration of an unknown solution can be found by measuring its absorbance and comparing it to the calibration curve.
Key Facts
- Beer’s Law: A = εlc.
- Absorbance is defined by A = log10(I0 / I), where I0 is incident light intensity and I is transmitted light intensity.
- Transmittance is T = I / I0, and percent transmittance is %T = 100T.
- For a fixed substance and wavelength, absorbance is directly proportional to concentration: A ∝ c.
- For a fixed substance and concentration, absorbance is directly proportional to path length: A ∝ l.
- A calibration curve often has the form A = mc + b, where c is concentration and m is the slope.
Vocabulary
- Absorbance
- Absorbance is a measure of how much light a sample removes from a beam passing through it.
- Molar absorptivity
- Molar absorptivity is the constant ε that describes how strongly a chemical species absorbs light at a particular wavelength.
- Path length
- Path length is the distance light travels through the sample, often 1.00 cm in a standard cuvette.
- Calibration curve
- A calibration curve is a graph made from standards of known concentration that is used to find the concentration of an unknown.
- Spectrophotometer
- A spectrophotometer is an instrument that measures how much light a sample transmits or absorbs at selected wavelengths.
Common Mistakes to Avoid
- Using percent transmittance as if it were absorbance is wrong because absorbance is logarithmic, not linear with transmitted light.
- Forgetting to blank the spectrophotometer is wrong because the solvent, cuvette, and instrument background can add absorbance that should not be counted for the analyte.
- Using the wrong wavelength is wrong because ε depends on wavelength, and measurements are usually most sensitive near the wavelength of maximum absorbance.
- Assuming Beer’s Law is always linear is wrong because very concentrated solutions, chemical changes, stray light, or instrument limits can cause deviations.
Practice Questions
- 1 A solution has ε = 5200 L mol^-1 cm^-1, l = 1.00 cm, and c = 2.50 x 10^-5 mol/L. Calculate its absorbance.
- 2 A calibration curve is A = 14800c + 0.015, where c is in mol/L. An unknown solution has A = 0.459. Find the concentration of the unknown.
- 3 Two solutions of the same dye are measured at the same wavelength in identical cuvettes. One has twice the concentration of the other, but its absorbance is not twice as large. Give two possible reasons for this observation.