Beer's Law is an equation that relates the attenuation of light to properties of a material. The law states the concentration of a chemical is directly proportional to the absorbance of a solution. The relation may be used to determine the concentration of a chemical species in a solution using a colorimeter or spectrophotometer. The relation is most often used in UV-visible absorption spectroscopy.

Note that Beer's Law is not valid at high solution concentrations.

### Other Names for Beer's Law

Beer's Law is also known as the **Beer-Lambert Law**, the **Lambert-Beer Law**, and the **Beer–Lambert–Bouguer law**.

### Equation for Beer's Law

Beer's Law may be written simply as:

**A = εbc**

where A is absorbance (no units)

ε is the molar absorbtivity with units of L mol^{-1} cm^{-1} (formerly called the extinction coefficient)

b is the path length of the sample, usually expressed in cm

c is the concentration of the compound in solution, expressed in mol L^{-1}

Calculating the absorbance of a sample using the equation depends on two assumptions:

- The absorbance is directly proportional to the path length of the sample (the width of the cuvette).
- The absorbance is directly proportional to the concentration of the sample.

### How To Use Beer's Law

While many modern instruments perform Beer's law calculations by simply comparing a blank cuvette with a sample, it's easy to prepare a graph using standard solutions to determine the concentration of a specimen.

The graphing method assumes a straight-line relationship between absorbance and concentration, which is valid for dilute solutions.

### Beer's Law Example Calculation

A sample is known to have a maximum absorbance value of 275 nm. Its molar absorptivity is 8400 M^{-1}cm^{-1}. The width of the cuvette is 1 cm.

A spectrophotometer finds A = 0.70. What is the concentration of the sample?

To solve the problem, use Beer's law:

A = εbc

0.70 = (8400 M^{-1}cm^{-1})(1 cm)(c)

Divide both sides of the equation by [(8400 M^{-1} cm^{-1})(1 cm)]

c = 8.33 x 10^{-5} mol/L