## Beer-Lambert Law Calculator

The **Beer-Lambert Law Calculator** is a powerful tool used to determine the **concentration** of a substance in a solution based on its **light absorption** properties.

`This law, also known as `**Beer's Law** or the **Beer-Lambert-Bouguer Law**, establishes a linear relationship between the **concentration** of a solution and its **absorbance** of light.

## Beer-Lambert Law Chart

Concentration (mol/L) | Path Length (cm) | Molar Absorptivity (L/mol·cm) | Absorbance |
---|---|---|---|

0.001 | 1 | 5000 | 0.500 |

0.002 | 1 | 5000 | 1.000 |

0.003 | 1 | 5000 | 1.500 |

0.004 | 1 | 5000 | 2.000 |

0.005 | 1 | 5000 | 2.500 |

## Beer-Lambert Law Equation

The **Beer-Lambert Law** is expressed by the equation:

**A = εbc**

Where:

Ais theabsorbance(dimensionless)εis themolar absorptivity(L/mol·cm)bis thepath lengthof the sample (cm)cis theconcentrationof the solution (mol/L)

Let’s consider an example using this formula. Suppose you have a solution of **methylene blue** with a molar absorptivity of **95,000 L/mol·cm** at **664 nm**.

You measure its absorbance in a **1 cm** cuvette and get a reading of** 0.285**. To find the concentration:

c = A / (εb)

c = 0.285 / (95,000 × 1)

c ≈ 3 × 10^(-6) mol/L or 3 μM

## How to calculate molar absorptivity?

**Molar absorptivity** (ε) is a measure of how strongly a chemical species absorbs light at a given wavelength.

To calculate it, you need to rearrange the Beer-Lambert equation:

`ε = A / (bc)`

For example, let’s say you prepare a **0.002 M solution** of **potassium permanganate** and measure its absorbance in a **1 cm cuvette** at **525 nm**.

**If the absorbance reading is 0.786, you can calculate the molar absorptivity:**

ε = 0.786 / (1 cm × 0.002 M)

ε = 393 L/mol·cm

`This value indicates how effectively `**potassium permanganate** absorbs light at **525 nm**, which is useful for future concentration determinations or comparing the absorptive properties of different substances.

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