Beer-Lambert Law
A = εlc relates absorbance to concentration. ε = molar absorptivity (L·mol⁻¹·cm⁻¹), l = path length, c = concentration. Foundation of UV-Vis spectrophotometry.
Why This Chemistry Calculation Matters
Why: Beer-Lambert law is the basis of quantitative UV-Vis spectroscopy. Measure A to determine concentration; ε is compound- and wavelength-specific.
How: A = ε × l × c. A = -log₁₀(T) = -log₁₀(I/I₀). %T = 100 × 10^(-A). Valid for dilute solutions.
- ●A = 1 means 10% transmittance; A = 2 means 1% T.
- ●ε (epsilon) in L·mol⁻¹·cm⁻¹; varies with λ.
- ●Optimal A range 0.1–1.0 for accurate measurement.
- ●Path length l typically 1 cm in cuvettes.
Sample Examples
Input Parameters
Understanding the Beer-Lambert Law
What is the Beer-Lambert Law?
The Beer-Lambert Law (also known as Beer's Law or the Beer-Lambert-Bouguer Law) is a fundamental relationship in spectroscopy that relates the absorption of light to 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 through the solution.
A = εbc
Where: A = Absorbance, ε = Molar Absorptivity (L/(mol·cm)), b = Path Length (cm), c = Concentration (mol/L)
How Does It Work?
Light Absorption
When light passes through a solution, molecules absorb specific wavelengths. The more concentrated the solution or the longer the path, the more light is absorbed.
Absorbance Measurement
A spectrophotometer measures how much light passes through (transmittance) and calculates absorbance as A = -log₁₀(T), where T is the ratio of transmitted to incident light.
Molar Absorptivity
Each compound has a characteristic molar absorptivity (ε) at a given wavelength, which indicates how strongly it absorbs light. Higher ε means stronger absorption.
Linear Range
The law holds best for absorbance values between 0.1 and 1.0. Outside this range, deviations may occur due to stray light, detector limitations, or chemical effects.
When to Use This Calculator
- Determining unknown concentrations from absorbance measurements
- Calculating required dilutions for spectrophotometric analysis
- Converting between absorbance and transmittance values
- Enzyme assays (NADH consumption, product formation)
- DNA and protein quantification
- Water quality testing and environmental analysis
- Pharmaceutical and clinical chemistry applications
Key Formulas
Beer-Lambert Law:
A = ε × b × c
Transmittance to Absorbance:
A = -log₁₀(T) = -log₁₀(%T/100)
Concentration from Absorbance:
c = A / (ε × b)
Molar Absorptivity:
ε = A / (b × c)
📚 Official Data Sources
⚠️ Disclaimer: This calculator uses IUPAC-recommended spectrophotometric conventions. For precise work, consult the latest NIST absorption data and analytical chemistry references.
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Frequently Asked Questions
Why should absorbance be between 0.1 and 1.0?
At low absorbance (less than 0.1), the relative error in measurement is high because small differences in light intensity cause large percentage errors. At high absorbance (greater than 2.0), very little light reaches the detector, leading to poor signal-to-noise ratio and potential stray light effects.
What causes deviations from Beer's Law?
Deviations can be chemical (association/dissociation, pH changes), instrumental (stray light, non-monochromatic light, wide slits), or due to sample issues (fluorescence, scattering, refractive index changes at high concentrations).
How do I choose the right wavelength?
Use the wavelength of maximum absorbance (λmax) for highest sensitivity. This is where the molar absorptivity is highest and small concentration changes produce the largest absorbance differences. Also ensure minimal interference from other compounds in the sample.
⚠️For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
A = εlc. Absorbance proportional to concentration.
— IUPAC
A = -log₁₀(T). T = I/I₀ transmittance.
— NIST
ε in L·mol⁻¹·cm⁻¹. Wavelength-dependent.
— Spectroscopy
Optimal A 0.1–1.0. %T = 100 × 10^(-A).
— Analytical