HANDS-ON APPROACH TO LAMBERT - BEER'S LAW

Objective

The objective of this activity is to introduce the Lambert - Beer's Law through a hands-on approach.

Experiment 1: The influence of the light path length through the absorption medium (b) on transmittance

The purpose of this experiment is to find out the impact of the increasing number of layers of pink filter foil »Medium pink« (LEE filters) on transmittance. The measurements will be made using the Spektra^TM spectrometer, and the green LED.

Take a colourless, transparent filter foil as a blank. Insert the foil into the measuring chamber and set the transmittance at 100.0.
Replace the blank with the pink filter foil. Record the transmittance and plot the result in the graph.
In subsequent steps of the experiment add one more pink foil each time (up to 8). Measure the transmittance of each set of foils and plot the results in the graph.

Φ - radiation power

Φ_i = ?

Transmittance: T = Φ_i / Φ₀

Φ₀

Plot the results in the graph below.

Define the relationship between the transmittance and the light path length through the absorption medium (b).

T ∝

Experiment 2: The influence of the increased concentration of solution (c) on transmittance

The purpose of the experiment is to find the relationship between the transmittance and the concentration of a solution.

Hazards

	KMnO₄ is harmful if swallowed, inhaled or absorbed through the skin. It is a powerful oxidant and reacts vigorously with organic substances. Use goggles and a lab coat, and avoid contact with skin. Do not dispose of the substance into the environment. Risk phrases: 22, 8, 50/53 Safety phrases: 60, 61

Procedure

Prepare nine solutions of KMnO₄ of different concentrations in the hollows of a blister, as shown in the table below. The transmittance is measured against deionized water, using the green LED. The results must be presented in a graphic form.

KMnO₄()	-*	1	2	3	4	5	6	7	8	9
H₂O ()	9	8	7	6	5	4	3	2	1	0

Blue boxes marked with * denote a blank.
The concentration of the stock solution of KMnO₄ is 10 mmol/L.

Plot the results in the graph below.

Define the relationship between the transmittance and the concentration of the solution (c).

T ∝

Experiment 3: Impact of different substances/species on transmittance

The purpose of this experiment is to demonstrate how the transmittance changes if the dichromate ions in the solution are changed into chromate ions.

Cr₂O₇^2–+ 2 OH^–		2 CrO₄^2–+ H₂O
(orange)		(yellow)

Hazards

	NaOH is a corrosive substance, causing burns of eyes, skin, and digestive system irritant. Avoid contact with skin and eyes. Use goggles and a lab coat for personal protection. Risk Phrase: 34 Safety phrases: 23, 24/25, 26, 36/37/39, 28A
	K₂Cr₂O₇ is highly toxic and dangerous for the environment. Contact with skin may cause over sensitisation. The substance is toxic if ingested. For personal protection use gloves and goggles, do not dispose of the substance into the environment. Risk Phrases: 49-46-21-25-26-37/38-41-43-50/53 Safety phrases: 53-45-60-61

Procedure

Take a blister and prepare a blank and five dichromate solutions. Also prepare a blank and five solutions of chromate in different concentrations. The preparation procedure is presented in the table below. Use the stock solution of K₂Cr₂O₇, 11 mmol/L, and deionised water, and the solution of NaOH, 2 mol/L.

	Blank	Dichromate solutions
K₂Cr₂O₇()	-	1	2	3	4	5
NaOH ()	-	-	-	-	-	-
H₂O ()	9	8	7	6	5	4
	Blank	Chromate solutions
K₂Cr₂O₇()	-	1	2	3	4	5
6 NaOH ()	2	2	2	2	2	2
H₂O ()	7	6	5	4	3	2

Measure the transmittance of dichromate and chromate solutions with the SPEKTRA^TM spectrometer using the blue LED against the blank. Plot the results into the graph.

Plot the results in the graph below.

If the proportional factor k, which depends on the substance, is introduced into the exponential part of the relationship T ∝ e^-cbthe formula is as follows:

T =

In practice the exponential relationship between the measured physical quantity and concentration can be difficult to use. Linear relationships are better suited for practical applications.

The exponential relationship T ∝ e^-kcbcan be transformed into a linear one by using logarithmic transformation. Afterwards the natural logarithm is transformed into decadic logarithm, and instead of k/2,303 we introduce a molar absorption coefficient (ε) and a new term, i.e. - absorbance (A). This relationship is called Lambert - Beer's Law.

A = ε c b

Lambert - Beer's Law

Symbol A stands for absorbance, c for the concentration of a solution (mol L^-1), b is the light path length through the absorption medium (cm). Symbol ε denotes molar absorption coefficient of a species at a certain wavelength, and defined conditions. The equation above shows that the unit for molar absorption coefficient is L mol^-1 cm^-1.

Complete the following relationship between the absorbance and transmittance. (Hint. The absorbance is related to the transmittance in a similar way as the pH to the concentration of oxonium ions in the solution.)

A = ________T

Calculate the absorbance from the transmittance values given in the table. Transmittance can be expressed as the share of 1, or in percent. When calculating the transmittance, it must be expressed as the share of 1.

c (mmol/L)	0.04	0.12	0.20	0.28	0.36
T	0.826	0.570	0.408	0.298	0.205
A

In the chart on the left side the values of transmittance are plotted against the concentration. Plot the values for the absorbance at different concentrations in the chart on the right.

Developed and prepared by: Nata�a Gros, University of Ljubljana, Faculty of Chemistry and Chemical Technology and Margareta Vrta�nik, University of Ljubljana, Faculty of Natural Sciences and Engineering