Beer-Lambert Law Calculator

Simulate a spectrophotometer. Calculate the absorbance or concentration of a solution based on its molar absorptivity and path length.

Solve For

Molar Absorptivity (ε)

L/(mol·cm)

Path Length (l)

Known Value (c or A)

Absorbance (A)

1.5000

Concentration (c)1.0000e-4 M

Transmittance (%T)3.16%

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Measuring Concentration with Light

The Beer-Lambert Law (often just called Beer's Law) is the fundamental principle behind spectrophotometry. It states that there is a direct, linear relationship between the absorbance of light by a solution and the concentration of that solution.

In simple terms: the darker the color of the liquid, the higher the concentration of the chemical dissolved inside it.

The Spectrophotometer

Chemists use a machine called a spectrophotometer to shine a specific wavelength of light through a small tube of liquid (a cuvette). A detector on the other side measures how much light successfully passed through the liquid (Transmittance). The machine mathematically converts this into Absorbance.

By knowing the Absorbance, we can perfectly calculate the unknown concentration of the liquid.

The Equation

\begin{aligned} A = \varepsilon \cdot l \cdot c \end{aligned}

Where:

Absorbance

\varepsilon

Molar Absorptivity (L/mol·cm)

Path Length (cm)

Concentration (M)

The Variables

Absorbance ( $A$ ): A unitless number indicating how much light was blocked.
Molar Absorptivity ( $\varepsilon$ ): A constant specific to the chemical being measured. It dictates how strongly that specific molecule absorbs light.
Path Length ( $l$ ): The width of the cuvette holding the liquid (almost universally exactly 1.0 cm).
Concentration ( $c$ ): The molarity of the solution.

Frequently Asked Questions

Standardization. Because $l=1$ , it effectively drops out of the math equation ( $A = \varepsilon \cdot c$ ), making manual calculations much simpler for laboratory technicians.

Yes. An absorbance of 1.0 means exactly 10% of the light made it through. An absorbance of 2.0 means only 1% made it through. Most spectrophotometers become highly inaccurate if the absorbance goes above 2.0 because the detector is receiving almost no light.

You must dilute the solution with pure solvent, measure the absorbance of the diluted liquid, and then mathematically multiply your result by your dilution factor.

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