Beer-Lambert Law Calculator

The fundamental principle governing this calculation is the Beer-Lambert law, which states that absorbance is directly proportional to the concentration of the absorbing species and the distance the light travels through the solution. The primary equation is expressed as A = ε × b × c, where A represents absorbance, ε is the molar absorption coefficient (or molar absorptivity), b is the path length, and c is the concentration. Additionally, absorbance can be derived from transmittance using the logarithmic relationship A = 2 - log₁₀(T), where T is expressed as a percentage, or simply A = -log₁₀(τ) for fractional transmittance.

Imagine you are analyzing an unknown copper sulfate solution using a standard spectrophotometer with a glass cuvette. You record an absorbance (A) of 0.650 at a specific wavelength. The path length (b) of your cuvette is exactly 1.0 cm, and the known molar absorptivity (ε) of copper sulfate at this wavelength is 50.0 L/(mol·cm). To find the concentration (c), you rearrange the formula to c = A / (ε × b). Substituting the values gives c = 0.650 / (50.0 × 1.0), which equals 0.013 moles per liter (M). This straightforward process reveals the exact molarity of your sample in seconds.

Ensure your units are consistent before running calculations; path lengths are typically measured in centimeters, and concentrations in moles per liter. Be mindful of instrument limitations, as the Beer-Lambert law tends to lose linearity at high concentrations where molecular interactions alter absorption behavior. Always perform a blank calibration using your pure solvent to eliminate background interference from the cuvette and solvent itself.