Final answer:
To apply Beer's law to determine the concentration of a dye, measure the absorbance with a spectrophotometer, use the known molar absorptivity and path length, and rearrange the Beer-Lambert formula to solve for the dye concentration in the sample.
Step-by-step explanation:
To apply Beer's law for determining the concentration of a dye in a laboratory setting, you will first need to understand the Beer-Lambert law, which is expressed as A = εcl, where A is the absorbance, ε (epsilon) is the molar absorptivity, c is the concentration, and l is the path length of the cuvette containing the sample. For example, if the absorbance is measured and the molar absorptivity and path length are known, the concentration can be calculated by rearranging the Beer-Lambert law to c = A / (εl).
In a practical sense, you would measure the absorbance of the dye solution using a spectrophotometer at a wavelength where the dye has a known absorption peak. Then, using the provided molar absorptivity value for the dye and the path length of the cuvette (usually 1 cm), you would plug these values into the Beer-Lambert law to calculate the concentration of the dye.
As an example, given a molar absorptivity (ε) of 14,150 M⁻¹cm⁻¹ and an absorbance reading from your spectrophotometer, you would rearrange the formula to solve for concentration c and express it in the desired units of M/min or any other units relevant to your experiment.