AP®ChemistryCollege BoardRevision NotesUnit 3: Properties of Substances & MixturesSpectroscopyBeer-Lambert Law

Beer-Lambert Law (College Board AP® Chemistry): Revision Note

Written by: Martín

Reviewed by: Stewart Hird

Updated on 23 October 2026

Beer-Lambert Law

Principles of the Beer-Lambert Law

Each light-absorbing species absorbs light most strongly at particular wavelengths
Chemists use the absorbing properties of chemical compounds for quantitative analysis, using solutions as samples
The amount of light absorbed by a sample is called absorbance
Absorbance (A) depends on three variables:
- Molar absorptivity (ε), in M^-1 cm^-1: how strongly a molecule or ion absorbs light of a specific wavelength
- Length in cm (b): The length of the path in which light travels through the sample
- Both the path length and the concentration are proportional to the number of light-absorbing particles in the light path, so increasing either increases the absorbance
- Concentration (c), in M: how much absorbing material is present in the sample
Absorbance has no units. It is directly proportional to molar absorptivity, path length and concentration, as the Beer–Lambert law shows:

$A = ε b c$

Beer-Lambert Law in Experiments

In most experiments, the path length (b) and the wavelength of light are held constant, so absorbance (A) is proportional only to the concentration of the absorbing molecules or ions
This mathematical relation can be used to build a calibration curve
A calibration curve is a method used to calculate the concentration of an unknown sample, by comparing its absorbance with the absorbance of standards
Standards are solutions with known concentration

Building a calibration curve

Prepare a series of standard solutions.
Set the spectrophotometer to the wavelength of maximum absorbance (λ_max, the optimum wavelength) for the species, which gives the most sensitive measurement, then measure the absorbance of each standard.
Plot an Absorbance vs Concentration curve.
Draw a straight line of best fit; for a solution that obeys the Beer–Lambert law it passes through, or very close to, the origin.

Example of a calibration curve

Graph of absorbance at a chosen wavelength against concentration, with five green points from standard solutions lying close to a straight blue line labeled calibration curve.

Graph showing a calibration curve Absorbance vs Concentration

Examiner Tips and Tricks

Calibration-curve questions give you the absorbance of an unknown: read its concentration from the line, or use the line’s equation — both routes can earn the point
Absorbance measures light absorbed by the colored species, so a lower absorbance means a lower concentration of that species in the light path — not a reaction with the light, the water or another reagent
Water left in the cuvette dilutes the sample, so the absorbance and the calculated concentration both come out lower

Worked Example

A student has prepared an experiment to determine the concentration of X (aq) in an unknown sample. The absorbance at different concentrations is shown below:

Graph of absorbance at 420 nm against concentration of X in M: five standards at (0.002, 0.11), (0.004, 0.22), (0.006, 0.33), (0.008, 0.44) and (0.010, 0.55), joined by a dashed straight line.

Calibration curve built using standard samples of X

If the absorbance of the unknown sample is 0.275 at 420 nm, what is the concentration of X in the unknown sample?

Answer:

Step 1: Set up the equation of the line to show the relation between absorbance and concentration

$A = mc + b$

Step 2: Calculate the gradient (m) for the equation of the line of the calibration curve, using the data for two nearest standard solutions

$Data point 1 (0.002, 0.10)$

$Data point 2 (0.004, 0.22)$

$m = \frac{A_{2} - A_{1}}{c_{2} - c_{1}}$

$m = \frac{0.22 - 0.1}{0.004 - 0.002}$

m = 60

Step 3: Calculate the y axis intercept (b) for the calibration curve by replacing A and c with one of the data points used in Step 1

$Data point 1 (0.002, 0.10)$

$A = 60 c + b$

$0.10 = 60 (0.002) + b$

$0.10 - 60 (0.002) = b$

$b = - 0.02$

Step 4: Complete the equation of the line for the calibration curve using the calculated values of m and b

$A = 60 c - 0.02$

Step 5: Rearrange the equation of the line in terms of the concentration (c)

$A = 60 c - 0.02$

$A + 0.02 = 60 c$

$c = \frac{A + 0.02}{60}$

Step 4: Calculate the concentration of X in the unknown sample, using the absorbance given in the problem statement by replacing its value in the equation obtained in st

$c = \frac{A + 0.02}{60}$

c=0.275+0.0260

c=4.92×10-3 M

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