?

Free Version
Moderate

# Beer-Lambert Law

ACTSCI-NAK03E

Spectrophotometry can be used to determine the concentration of food dye in an aqueous sample by measuring the amount of light the sample absorbs, as shown in the diagram below:

A narrow wavelength of the light produced by the light source is selected by the monochromator and sent throughout the sample in the cuvette. The ratio of the light coming through the cuvette and the light entering the cuvette is the absorbance (A).

$$A = \frac{\text{light exiting sample (I)}}{\text{light entering sample (I}_0)}$$

The absorbance can then be related to the concentration (c) by the Beer-Lambert equation:

A = abc

where “a” is the molar absorptivity constant and “b” is the width of the cuvette.

To analyze a sample, the optimal wavelength for maximum absorbance must be determined. This is done by measuring the absorbance of the sample at different wavelengths.

The graph below shows the absorption spectrum for two aqueous solutions one made of the food dye FD&C Blue #1 which had a concentration of 0.1 mol/L and a second solution made from the food dye Yellow #5, which also had a concentration of 0.1 mol/L.

Based on this information, a series of mixtures containing different concentrations of the two dyes were analyzed at two different wavelengths and the data in Table 1 was collected.

$\hspace {4cm}Table \ 1$

Sample Absorbance at 450 nm Absorbance at 620 nm
1 0.40 0.40
2 0.60 0.70
3 0.90 1.50
4 1.10 0.80

In a second experiment, the student measures the absorbance of five Blue #1 and five Yellow#5 solutions, at their optimal wavelengths, each with concentrations of $.10, .25, .50, .75,$ and $1.0$ moles per liter. The student plots the absorbances verses concentration:

Which of the following best explains why the absorbance of Blue #1 is higher than the absorbance of Yellow #5 at the same concentration?

A

There are more Blue #1 particles in the solution.

B

There are more Yellow #5 particles in the solution.

C

Blue #1 is more efficient at absorbing light than Yellow #5.

D

Yellow #5 is more efficient at absorbing light than Blue #1.