Beer Lambert Law Calculator
Calculate absorbance, transmittance, concentration, path length, or molar absorptivity using Beer-Lambert law. Free online Beer's law calculator for spectroscopy.
What is Beer-Lambert Law?
The Beer-Lambert law, also known as Beer's law, describes the relationship between the absorption of light and the properties of the material through which the light is traveling. It states that the absorbance of a solution is directly proportional to its concentration and the path length of the light beam passing through it.
This fundamental principle of spectroscopy is expressed by the equation:
$$A = \varepsilon \times l \times c$$
where $A$ is the absorbance (unitless), $\varepsilon$ is the molar absorption coefficient or molar absorptivity (L/mol·cm), $l$ is the path length of the beam in the sample (cm), and $c$ is the concentration of the solution (mol/L).
Absorbance and Transmittance
Transmittance $T$ is the fraction of incident light that passes through the sample:
$$T = \frac{I}{I_0}$$
where $I_0$ is the intensity of the incident light and $I$ is the intensity of the transmitted light. Absorbance and transmittance are related by:
$$A = \log_{10}\left(\frac{1}{T}\right) = -\log_{10}(T)$$
An absorbance of 0 corresponds to 100% transmittance, while an absorbance of 1 corresponds to 10% transmittance. This logarithmic relationship means that each unit of absorbance represents a tenfold reduction in transmitted light intensity.
Applications of Beer-Lambert Law
The Beer-Lambert law has numerous practical applications in analytical chemistry and spectroscopy:
- Quantitative Analysis: Determining the concentration of unknown samples by measuring their absorbance at a specific wavelength.
- UV-Vis Spectroscopy: Identifying compounds based on their absorption spectra and characteristic molar absorptivity values.
- Pharmaceutical Analysis: Measuring drug concentrations in formulations and biological samples.
- Environmental Monitoring: Detecting pollutants and contaminants in water and air samples.
Frequently Asked Questions
What is the Beer-Lambert law equation?
The Beer-Lambert law equation is $A = \varepsilon \times l \times c$, where $A$ is absorbance, $\varepsilon$ is the molar absorptivity (L/mol·cm), $l$ is the path length (cm), and $c$ is the concentration (mol/L). Absorbance can also be expressed as $A = \log_{10}(I_0/I)$.
What is the unit of absorbance?
Absorbance is a dimensionless quantity — it has no units because it is derived from the ratio of incident to transmitted light intensity. However, it is sometimes reported in absorbance units (AU) for convenience.
How do I calculate concentration from absorbance?
To calculate concentration from absorbance, rearrange the Beer-Lambert law to $c = A / (\varepsilon \times l)$. First measure the absorbance of your sample, then divide by the product of the molar absorptivity and path length.
What causes deviation from Beer's law?
Deviations from Beer's law can occur at high concentrations due to molecular interactions, at very low concentrations due to instrumental limitations, when using polychromatic radiation, or when the sample undergoes chemical changes such as association or dissociation.
How do I convert transmittance to absorbance?
To convert transmittance to absorbance, use the formula $A = -\log_{10}(T)$, where $T$ is the transmittance expressed as a decimal (percentage divided by 100). For example, 50% transmittance equals an absorbance of $-\log_{10}(0.50) = 0.3010$ AU.
Apply the Beer-Lambert law with the Protein Concentration Calculator and explore water quality with the Chemical Oxygen Demand Calculator.
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