Short on time? This page is the recap. For explanations, diagrams and worked examples, use the full study guide.
Recap
- A solution absorbs light when its particles absorb photons of a matching energy. Absorbance, A, measures how much.
- The Beer-Lambert law: A = εbc.
- ε (molar absorptivity) says how strongly one species absorbs one wavelength. It depends on the species and the wavelength, not on concentration.
- b (path length) and c (concentration) together set how many absorbing particles the beam meets, so A is proportional to each.
- With the same cuvette and wavelength, A is proportional to c alone. A graph of A against c for standards is a straight line through the origin with gradient εb: a calibration curve.
- Set the spectrophotometer to λmax, the wavelength of maximum absorbance: biggest ε, most sensitive, least affected by small wavelength drift.
- Zero the instrument with a blank (cuvette plus solvent) first.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| A = εbc | A no unit; ε in M⁻¹ cm⁻¹; b in cm; c in M | find any one quantity from the other three |
| c = A ÷ (εb) | as above | find the concentration of an unknown |
| gradient of A against c = εb | gradient in M⁻¹ | get ε from a calibration curve (ε = gradient ÷ b) |
| c(original) = c(measured) × dilution factor | dilution factor = final volume ÷ sample volume | undo a dilution made before measuring |
Assumptions behind the numbers
- Only one species absorbs at the chosen wavelength (or the blank removes everything else).
- Path length and wavelength are the same for the standards and the unknown.
- The unknown’s absorbance lies within the range of the standards, where the line is straight.
- The solution is clear: nothing in it scatters light.
Mistakes to avoid
- Giving A a unit. It has none.
- Thinking ε changes with concentration. It does not.
- Picking the wavelength with the least absorbance. Use λmax.
- Forgetting the dilution factor after reading the calibration line.
- Wrong error direction. Smudges, bubbles, cloudiness and a longer cuvette raise A (c too high). Water droplets that dilute the sample lower A (c too low).
- Vague error answers. Say whether A goes up or down, then link to c.
Quick self-check
- A 3.00 × 10⁻⁵ M solution in a 1.00 cm cuvette has A = 0.450. What is ε? (1.50 × 10⁴ M⁻¹ cm⁻¹)
- A solution has A = 0.20 in a 1.00 cm cuvette. What is A in a 2.00 cm cuvette? (0.40)
- You halve the concentration and double the path length. What happens to A? (No change: the beam meets the same number of particles.)
- Air bubbles are stuck in the cuvette holding the unknown. Is the calculated c too high or too low? (Too high: bubbles scatter light, so A reads too high.)
Next: practice questions.