Beer's Law relates the absorbance of light to the concentration of a solution. It's the foundation of spectrophotometry and analytical chemistry for determining unknown concentrations.
A = εbc
Absorbance = molar absorptivity × path length × concentration
Units: Dimensionless (no units)
Amount of light absorbed by the sample
💡 Related to transmittance: A = -log(T) = -log(I/I₀)
Units: L/(mol·cm) or M⁻¹cm⁻¹
How strongly a substance absorbs light at a specific wavelength
Also called: extinction coefficient, molar extinction coefficient
Units: cm (centimeters)
Distance light travels through the sample
💡 Standard cuvettes are usually 1.00 cm
Units: M (mol/L) or mM
Molar concentration of the absorbing species
This is what we usually solve for in Beer's Law!
A = εbc
c = A / (εb)
Most common use!
ε = A / (bc)
b = A / (εc)
T = I / I₀
I = intensity of transmitted light
I₀ = intensity of incident light
A = -log(T)
Or: A = log(I₀/I) = log(1/T)
A = 2 - log(%T)
Example: 50% T → A = 2 - log(50) = 0.301
A = εbc
c = A / (εb)
c = 0.520 / [(1.30 × 10⁴ L/mol·cm)(1.00 cm)]
c = 0.520 / (1.30 × 10⁴)
c = 4.00 × 10⁻⁵ M
Answer: c = 4.00 × 10⁻⁵ M = 0.0400 mM = 40.0 μM
Determine unknown concentrations by measuring absorbance (most common use)
Measure protein, DNA, and enzyme concentrations using UV-Vis spectroscopy
Blood tests, drug concentrations, and diagnostic assays
Water quality analysis - detect pollutants and nutrients
Even with standard 1.00 cm cuvettes, you must include b in calculations. c = A/ε is WRONG - it's c = A/(εb).
If ε is in L/(mol·cm), then c must be in M and b in cm. Don't use mM or mm without converting units.
Beer's Law is linear only for A between ~0.1 and 1.0. Very high or very low absorbances are unreliable.
ε is wavelength-dependent! Use the wavelength where the substance absorbs maximally (λmax).
To determine the concentration of a colored or absorbing solution by measuring how much light it absorbs (A = εbc).
Between 0.1 and 1.0 for best accuracy. Above 1.5, very little light gets through. Below 0.05, signal is too weak.
ε tells you how strongly a compound absorbs light. High ε means you can detect very low concentrations. It's unique for each substance at each wavelength.
Yes, if only one component absorbs at your chosen wavelength. For mixtures where multiple species absorb, absorbances are additive: Atotal = A₁ + A₂ + ...
High concentrations, chemical reactions, stray light, fluorescence, or suspended particles can all cause non-linear A vs c plots.