Monday, May 7, 2012

Beer-Lambert Law


1. To verify the Beer-Lambert Law

2. To determine the composition of complexes by using Job Method


Job method is also known as method of continuous variation. This method is used to determine the composition of a complex which is formed by two reacting species. It is most effective to be applied when only a single complex is formed in the solution. Job’s method is based on the concept that equimolar solution of metal-ion and ligand are mixed gradually by using different volume ratio. As the concentration of metal ion increase, the concentrations of ligand will decerease. It maintains the total number of mole reactants to be constant in a series of mixture of reactants. In this experiment, the mixture is made up of different fraction of nickel sulfate and ligand ethylene diamine. A wavelength at which the complex absorbs the strongest, λmax is selected. Then, the absorbance of each solution in the series at the wavelength of maximum absorbance is determined by using spectrometric method.

Job Method is often used to determine the soluble Ni2+ - en complexes in the solution. The “n” value of the complexes also can be calculated.

Z + nL à ZLn

where Z represents Ni2+ ion, L refers to the ethylene diamine (en). Different complexes could be formed in a mixture of metal Ni2+ ion and ligand en, for example, Ni(en)2+, Ni(en)22+, Ni(en)32+ and many more. The equilibrium constant of each Ni2+ - en complexes are shown in the following:


where K1, K2 and K3 are the equilibrium constant for each reaction respectively. Species that formed the most in the solution depends on the relative value of the equilibrium constant. If the value of K2 is bigger than K1, that means the concentration of Ni(en)22+ is higher than Ni(en)2+. In this experiment, every solution prepared contains the same concentration of Z and L. this is to ensure that the value of equilibrium constant of the formation of Z(L)n is large and the absorption for the species is maximum when the concentration of ligands en is exactly “n” times the concentration of ion Z. The value of “n” can be calculated if the concentration rate of L/Z is known for the solution that gives the maximum absorption.

Measurement of optical density (absorbance) at the λmax will show the maximum when the ratio of ethylene diamine to nickel sulfate is equally present in the particular mixture. This is because the solution contains the highest concentration of complex. So, in the graph of absorbance against mole fraction of ligand in the mixture will show a region starting with zero and increasing as the mole fraction of ligand increases as well as the concentration of complex. The absorbance of complex will also increase at the same time. At this region with positive slope in the graph, the ligand ethylene diamine is acting as limiting reagent. Further addition of mole fraction of ligand will decrease the mole fraction of nickel sulfate in the mixture. Since the nickel sulfate is insufficient to form complex with excess ethylene ligand, thus the absorbance due to less formation of complex then falls. The diagram 1 below shows the general trend of continuous variation of complex.


Diagram 1

According to Beer-Lambert law, the equation can be expressed as A = εcl where A is the absorbance, ε is refers to the molar absorptivity of liquid (L mol-1 cm-1), c is concentration of absorbing material (mol L-1) and l is the optical path length (cm). The amount of attenuation is depends on the concentration of absorbing molecules and path length over which absorption occurs. The absorbance of the complexes formed is directly proportional to the concentration of the complexes formed in the solution. The value of “n” could be calculated by using the formula as below:



10ml volumetric flask, dropper, pipette


UV-Vis spectrometer, 0.4M ligand ethylene diamine, 0.4M nickel sulfate solution, distilled water


1. 100cm3 of nickel sulfate (NiSO4.6H2O) with the concentration of 0.4M and 100cm3 of ligand-en with concentration of 0.4M were prepared.

2. The spectrums of each stock solution that has been prepared were obtained in the range of 500-65-nm.

3. Solutions with a total volume of 10cm3 were prepared in which the mole fraction of en and X is 0.0, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 by using the stock solutions of NiSO4.6H2O and ethylene diamine.

4. The values of Y with, at least five different wavelengths were calculated and graph of X vs. Y was plotted for each results.

5. The value of X was determined when Y is at the maximum for each graph. By using the value of X in equation (6), the n values for Ni(en)n2+ complexes were calculated.

Results and calculations:

Table 1 Absorbance (A) at different wavelength, λ (nm)


In order to plot the graph of X versus Y, the equation of Y = [A – (1-X) Az]b is used.

where Az is the absorption of pure Ni2+ at the selected wavelength, b is optical path length

Table 2 Absorbance (Y) at Different Wavelength, λ (nm)


From Graph 1,

At λ= 530 nm, X = 0.8.

n1 = X / (1 - X)

= 0.8/ (1 - 0.8)

= 4

From Graph 2,

At λ = 545 nm, X = 0.715

n2 = X / (1 - X)

= 0.715 / (1 – 0.715)

= 2.51

From Graph 3,

At λ = 578 nm, X = 0.655

n3= X / (1 - X)

= 0.655/ (1 – 0.655)

= 1.90

From Graph 4,

At λ = 622 nm, X = 0.5

n4= X / (1 - X)

= 0.5/ (1 – 0.5)

= 1

From Graph 5,

At λ = 640 nm, X = 0.455

n5= X / (1 - X)

= 0.455/ (1 – 0.455)

= 0.83

Average of value of n = (4 + 2.51 +1.90 + 1 + 0.83) / 5

= 2.048

Thus, the n value for Ni(en)n2+ complexes = 2 since the n value must be an integer.


The reaction between nickel sulfate and ligand ethylene diamine produces nickel(II) bis(ethylenediamine) complex as product. This metal complex is a cationic complex. This is because the en anion carrying 0 charge since it is a neutral ligand while Ni2+ carrying +2 charge. The en ligand did not loss any proton during the formation of Ni-en complex so that it is a neutral ligand. Hence, the net charge of the Ni(II) complex is +2. The ethylene diamine ligand is a bidendate ligand which each en ligand coordinated to the Ni2+ metal via two dative bonds. The lone pair electron was donated from each nitrogen atom in ethylenediamine to form the two coordination bonding to Ni(II) metal. Since en ligand are weakly coordinated to the metal species, the en ligand is easily to be bonded to the Ni(II) metal so that the reaction can be took place at room temperature because the reaction is just required a small amount of energy.

In this experiment, the value of n was determined. Thus, the composition of the Ni(II) complex also was determined based on the value of n obtained. The ratio of Ni(II) cation to the ethylenediamine ligand in the metal complex is 1:2. For each metal complex in the solution, the Ni2+ metal is coordinated with two ethylenediamine ligand. The Ni(II) complex is predicted has the geometry of tetrahedral with the Ni(II) in the centre of complex. In the structure of complex, two ethylenediamine neutral ligands were coordinated surrounding to the Ni2+ metal centre. The ethylenediamone ligand is known as bidentate ligand (chelating ligand) which has can forms two coordinating point to the metal. The chelating effect allows the ethylenediamine bonded strongly to the Fe(III) complex.

Based on the data obtained, Beer-Lambert law was verified. This is because the data indicated that the absorbance is directly proportional to the concentration of complex formed and the path length over which absorption occurs. The path length is defined as 1cm in the experiment, because the curvette size is generally manufactured in 1cm. Since the path length is being held constant, thus the absorbance increases as the concentration of complex formed in the solution increases.

Precaution steps:

1. Gloves and goggles must be worn in order to prevent direct exposure to any chemicals.

2. The readings of apparatus must be taken parallel to the eyes in order to avoid parallax error which can cause the deviation in mole fraction.


  1. This is a good post but I had to refresh my basics of the derivation of beer-lambert law in order to gain more from the post.

  2. Good post. Great guideline for my own report, but where are the graphs?

  3. Is bearts lembart law is used for qualitative analysis?