Colorimetric Analysis

(Beer's law or Spectrophotometric Analysis)

##### Along with operating the instruments, Beer's law also involves calculations to actually figure out the concentration of a solution from the absorbance measurements made by using the colorimeter (or spectrophotometer). There are three methods that can be used depending on what information is available. They involve using proportionality, graphing and Beer's Law.

Proportionality Example

The proportionality approach to these kinds of problems focuses on the idea that the absorbance of a solution is directly proportional to its concentration. When using this approach it is necessary to be sure that the values given are for different concentrations of the same chemical measured under the SAME conditions (BOTH wavelength and the path length).

Question: A solution with a concentration of 0.14M is measured to have an absorbance of 0.43. Another solution of the same chemical is measured under the same conditions and has an absorbance of 0.37. What is its concentration?

The solution to this problem can be set up using the equation shown below, which simply says that the ratio of the concentrations is proportional to the ratio of absorbances. We can use c1 to represent the unknown concentration. You can derive this equation from Beer's law (Absorbance = e L c)

C1 / C2 = A1 / A2

(ONLY for absorbances that are measured/predicted at the SAME Wavelength)

Therefore,

C1 = (A1 / A2) * C2

Substitute all the values as follow:

A1 = 0.37; A2= 0.43 & C2=0.14M

Thus, C1 = 0.12M

Graphing Example

The graphing method is called for when several sets of data involving STANDARD SOLUTIONS are available for concentration and absorbance. This is probably the most common way of Beer's law analysis based on experimental data collected in the laboratory.

Graphing the data allows you to check the assumption that Beer's Law is valid by looking for a straight-line relationship for the data.

Question: What is the concentration of a 1.00 cm (path length) sample that has an absorbance of 0.60?

 Concentration (M) Absorbances 0.20 0.27 0.30 0.41 0.40 0.55 0.50 0.69

The solution to the problem here is to graph the data and draw a straight line through the points. If the data points are on or close to the line, that will confirm that the absorbance and concentration are proportional and Beer's Law is valid for this situation.

Recall that Beer's law is expressed as Absorbance = e L c. To find the concentration for a solution that has an absorbance of 0.60, you will first need to find the slope of the BEST-FIT line. From the slope of the best-fit line together with the absorbance, you can now calculate the concentration for that solution (i.e. Concentration = Absorbance / Slope)

Notice that the SLOPE of the best-fit line in this case is actually the PRODUCT of the molar absorptivity constant and the path length (1.00cm).

Beer's Law Example

Here is an example of directly using the Beer's Law Equation (Absorbance = e L c) when you were given the molar absorptivity constant (or molar extinction coefficient). In this equation, e is the molar extinction coefficient. L is the path length of the cell holder. c is the concentration of the solution.

Note: In reality, molar absorptivity constant is normally not given. The common method of working with Beer's law is in fact the graphing method (see above).

Question: The molar absorptivity constant of a particular chemical is 1.5/M·cm. What is the concentration of a solution made from this chemical that has an absorbance of 0.72 with a cell path length of 1.1cm?

To find the concentration, simply plug in the values into the Beer's law equation.