Absorbance Calculator (Beer-Lambert Law)
Calculate absorbance, transmittance, or concentration using the Beer-Lambert law from molar absorptivity and path length.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
A = -logโโ(I/Iโ) = ฮต ร l ร c
Absorbance equals the negative base-10 logarithm of the ratio of transmitted to incident light intensity. By Beer-Lambert Law, it also equals the product of molar absorptivity (ฮต), path length (l), and concentration (c).
Worked Examples
Example 1: Determining Concentration from Absorbance
Problem:A solution gives an absorbance of 0.45 at 520 nm. The molar absorptivity at this wavelength is 1500 L/(molยทcm) and the cuvette path length is 1 cm. Find the concentration.
Solution:Using Beer-Lambert Law: A = ฮต ร l ร c\nc = A / (ฮต ร l)\nc = 0.45 / (1500 ร 1)\nc = 3.0 ร 10โปโด mol/L\nTransmittance: T = 10^(-0.45) = 0.3548 = 35.48%
Result:Concentration = 3.0 ร 10โปโด M | Transmittance = 35.48%
Example 2: Absorbance from Light Intensities
Problem:A spectrophotometer measures incident light intensity Iโ = 1000 and transmitted intensity I = 250. Calculate the absorbance and percent transmittance.
Solution:Transmittance: T = I / Iโ = 250 / 1000 = 0.25\nPercent Transmittance: %T = 25%\nAbsorbance: A = -logโโ(T) = -logโโ(0.25) = 0.6021
Result:A = 0.6021 | T = 25.00% | 75% of light absorbed
Frequently Asked Questions
What is absorbance and how is it measured?
Absorbance (A) is a dimensionless quantity that measures how much light a sample absorbs at a particular wavelength. It is defined as the negative logarithm (base 10) of transmittance: A = -log10(T), where T = I/I0 is the ratio of transmitted light intensity (I) to incident light intensity (I0). Absorbance is measured using a spectrophotometer, which passes monochromatic light through a sample and detects how much light emerges. Higher absorbance values indicate more light absorbed. Typical absorbance values in analytical chemistry range from 0.1 to 1.0 for accurate measurements, as values above 2.0 mean over 99% of light is absorbed and measurements become unreliable.
What is the Beer-Lambert Law?
The Beer-Lambert Law (also called Beer's Law) is the fundamental equation governing light absorption in solutions. It states that absorbance is directly proportional to the concentration of the absorbing species and the path length of the sample: A = epsilon times l times c, where epsilon is the molar absorptivity (L/mol/cm), l is the path length in cm, and c is the molar concentration (mol/L). This linear relationship holds under certain conditions: the solution must be dilute, monochromatic light must be used, the absorbing species must not undergo chemical reactions, and there should be no scattering. Deviations from Beer's Law occur at high concentrations due to molecular interactions and refractive index changes.
How do I convert between absorbance and transmittance?
Absorbance (A) and transmittance (T) are inversely related through a logarithmic function. To convert transmittance to absorbance: A = -log10(T), where T is expressed as a decimal fraction (0 to 1). To convert absorbance to transmittance: T = 10^(-A). Percent transmittance (%T) is simply T multiplied by 100. For example, if %T = 50%, then T = 0.50 and A = -log10(0.50) = 0.301. If A = 1.0, then T = 10^(-1) = 0.10 or 10% transmittance, meaning 90% of light was absorbed. An absorbance of 2.0 corresponds to only 1% transmittance. This logarithmic relationship means that absorbance is more useful for quantitative analysis because it is linearly proportional to concentration.
What are common sources of error in absorbance measurements?
Several factors can introduce errors into absorbance measurements. Instrumental errors include stray light (light reaching the detector without passing through the sample), which causes negative deviations from Beer's Law at high absorbance values. Non-monochromatic light sources reduce accuracy because epsilon varies with wavelength. Chemical errors arise from concentration-dependent equilibria, solute-solvent interactions, and pH-dependent speciation changes. Sample preparation errors include fingerprints or scratches on cuvettes, air bubbles in the solution, and improper blank corrections. Temperature fluctuations affect both molar absorptivity and solution volume. To minimize errors, work in the absorbance range of 0.2 to 0.8, use matched cuvettes, calibrate with standards, and maintain consistent temperature throughout measurements.
References
Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy