Measuring concentration with light
When light passes through a colored solution, part of it is absorbed. The more molecules are in the beam, the more light is absorbed. The Beer-Lambert law turns this into a straight-line relationship between absorbance and concentration, the principle behind every UV-visible spectrophotometer and many medical and environmental tests.
The formulas
- Absorbance A = ε × l × c
- Concentration c = A ÷ (ε × l)
- Transmittance T = 10^(−A), or A = −log₁₀ T
Here ε is the molar absorptivity (L·mol⁻¹·cm⁻¹), a property of the substance at a given wavelength, l the path length of the cuvette in cm, and c the concentration in mol/L.
Worked example
NADH absorbs strongly at 340 nm with ε = 6,220 L·mol⁻¹·cm⁻¹. A sample in a 1 cm cuvette reads A = 0.500.
- c = 0.500 ÷ (6,220 × 1) = 8.04 × 10⁻⁵ mol/L = 80.4 µmol/L.
- Transmittance = 10^(−0.5) = 31.6% of the light gets through.
This measurement is the basis of many enzyme assays, which follow NADH appearing or disappearing over time.
Absorbance and transmittance
| Absorbance | Light transmitted |
|---|---|
| 0 | 100% |
| 0.1 | 79% |
| 0.5 | 32% |
| 1 | 10% |
| 2 | 1% |
| 3 | 0.1% |
Staying in the linear range
Most instruments are accurate for absorbances between about 0.1 and 1.0, sometimes up to 1.5. Above that, so little light reaches the detector that stray light and noise dominate; below 0.1, the signal is weak. If a reading is too high, dilute the sample and multiply the result by the dilution factor.
Calibration curves
In practice, ε is often unknown or depends on the instrument. The standard method is to measure several standards of known concentration, plot absorbance against concentration, and read unknown samples from the line. The slope of the line equals ε × l.
Common values of ε
| Substance | Wavelength | ε (L·mol⁻¹·cm⁻¹) |
|---|---|---|
| NADH | 340 nm | 6,220 |
| DNA (per nucleotide, average) | 260 nm | about 6,600 |
| Potassium permanganate | 525 nm | about 2,400 |
| p-Nitrophenolate | 405 nm | about 18,000 |
When the law fails
Deviations appear in concentrated solutions, when molecules associate or react, with turbid samples that scatter light, and when the light is not monochromatic. Always use a blank of the solvent to zero the instrument.