Beer-Lambert Law

Beer-Lambert Law
Relationship Between Molar Concentration and Absorbance

Solution colour results from the absorbance of some light wavelengths by solutes dissolved in solution, while allowing other wavelengths to pass through (transmittance). The combination of the remaining wavelengths that pass through results in the colour of the solution.

A colorimeter can be used to determine the amount of light at a particular wavelength that is absorbed/transmitted by a solution. Depending on the concentration of the solute in the solution, more or less absorbance/transmittance will result.

A = lc

where A is the absorbance (no units) l is the length of the path (cm) c is the molar concentration (mol/L)
 is the molar absorptivity at a specific wavelength

Since the length of the path is set at 1 cm (size of the cuvette), the equation simplifies further to A = c. The relationship between absorbance and molar concentration is linear. When graphed, the slope of the line equals the molar absorptivity.

Table 1. Absorbance of standard Cu2+(aq) solutions at 635 nm
Sample Molar Concentration Percent Transmittance Absorbance Procedure
• Each group will prepare, through dilution, the concentrations in Table 1 using the standard 0.50 mol/L Cu(NO3)2(aq) solution.
• Calibrate the colorimeter at 635 nm with deionized water (pure solvent) as the blank solution.
• Fill a cuvette with each sample concentration and analyze their absorbance at 635 nm.

Analysis
• Graph molar concentration against absorbance.
• Draw the line of best fit and fine slope to determine the molar absorptivity of Cu2+(aq) at 635 nm.
Blank 0.00 mol/L 100 % 0
1 0.050 mol/L
2 0.10 mol/L
3 0.15 mol/L
4 0.20 mol/L
5 0.25 mol/L
6 0.30 mol/L
7 0.35 mol/L
8 0.40 mol/L
9 0.45 mol/L
10 0.50 mol/L

Use the value of the molar absorptivity of Cu2+(aq) at 635 nm to determine the concentration of two unknown Cu2+(aq) solutions based on the empirical absorbance measured for each solution at 635 nm.

Table 2. Absorbance of unknown Cu2+(aq) solutions at 635 nm
Sample Absorbance Percent Transmittance • Calculate the molar concentration for each solution.