Beer's Law

The relationship on the preceding page relates the amount of light transmitted through the sample to the concentration and cell width. We frequently like to think in terms of how much light is absorbed by the sample, so we define a new term, absorbance (A):

 (4)

Making all of the appropriate substitutions, we get:

 (5)

or,

 (6)

This equation is known as Beer's Law, which shows the linear relationship between the absorbance and the concentration of the absorbing species. In chemical analyses, the following three methods can utilize Beer's Law:

1. Absolute Calculations

   Absorptivity or molar absorptivity is calculated by measuring the absorbance of a standard of known concentration in a cell known cell width. This calculated value is then used to determine an unknown concentration of the same absorbing species from the absorbance measurement at that concentration.

2. Working Curve Analysis

   The absorbance of a series of three to five standard solutions are measured and plotted on graph paper against the concentrations of these standards. This is known as a Beer's Law plot. The absorbance of an unknown concentration is then measured, and its concentration is determined directly from the plot. This method is more commonly used than the absolute calculation, because experimental error will average out over the number of standards.

   

   Figure 3: Beer's Law Plot

   

   Figure 4: Example of change in color as concentration of solution increases.

3. Standard Addition Analysis

   This method is used when certain matrix interferences may cause problems with the measurements. The assumption is that the interference will act equally on the analyte and on an standard added to analyte. In this case, the sample is measured (A₁), and then a second portion of the sample is spiked with a standard and this is measured (A₂).

   

   We will use the first two methods in the laboratory experiment.