[]

Application of Beer’s Law

2011

Tootoonchi FY C06209263

Thien Tran

Introduction

The purpose of this experiment was to use spectrometric analysis to find the concentration of iron in parts per million (ppm) of an unknown sample. Spectrometric (or colorimetric) analysis is done by conducting quantitative measurements of trace metals on the ppm basis by using the interactions of a ligand and a metal to form a complex. This method is effective because Iron, like many transition metals, forms several intensively colored complex ions. A ligand is an ion or molecule that binds to a central metal atom to form a complex [1]. Spectrometric analysis measures the intensity of the color produced and this is related to the concentration by Beer’s law (A=ε∗b∗C) where A is the absorbance, ε is the molar absorptivity, b is the path length in cm, and C is the molar concentration. 1,10-Phenanthroline acts as the ligand and when it is added to iron to produce a bright color. In order to reduce the iron (Fe+3→F e+2), hydroxylamine is added as the soluble hydrochloride, NH2OH·HCl. The iron needs to be reduced because the concentration is that of Fe+2. The spectrophotometer precisely measures quantitatively how much light passes through the solution. The absorbance (A) is related to the percent transmittance (%T) by the equation A = log (100/%T). The maximum absorbance for the complex occurs around a wavelength of 510 nanometers. Because the absorbance is directly proportional to the concentration, we can interpolate and obtain the value of the unknown.

Procedure

First, 0.0, 1.0, 2.0, 4.0, and 8.0 mL of a solution of 50ppm Fe(H2O)62+ were added to five

volumetric flasks. The first was left as a blank in order to compare the iron solutions and correct any interference from other metals that may be present. Also, 5 mL of NH4Ac, 5mL of NH2OH∙HCL (reduces Fe3+ to Fe2+) and 10mL of 1,10-phenanthroline (phen) were added to each flask. Sixth and seventh flasks were filled with the same solutions in the first five, except the Fe(H2O)6

2+ stock solution. This was replaced with two vials filled with solutions of unknown iron concentration. The number of the first unknown sample was #8 and the second was #9. For the addition of these solutions, the unknown was poured into the sixth and seventh volumetric flasks and rinsed three times with distilled water, and then poured into the flask in order to ensure that all of the iron had been extracted from the vial. Then, distilled water was added to each of the volumetric flasks to a final volume of exactly 100mL. The flasks then sat for a period of 45 minutes in order to allow the color to fully develop.

After waiting the specified time, a sample from each of the flasks was added to the cuvettes until the solutions reached the bottom of the logo on the cuvette. Before each cuvette was placed in the slot of the spectrophotometer, it needed to be calibrated. First, the machine to 510 nanometers for wavelength and calibrated it to 0% transmittance with the slot empty. The blank cuvette was then inserted and the machine was adjusted to 100% transmittance. This was done to ensure that the machine would only read the absorbance of the iron and not anything else present in the solutions. The mode of the display was then changed to output absorbance rather than transmittance. Each cuvette was then placed into the slot of the machine, and the corresponding absorbance or each was recorded.

After determining the absorbance of each solution, values (except of the blank) of the concentrations of iron (ppm) were plotted with the absorbance. The concentration of iron was found by multiplying the volume of the iron added by the original concentration (50 ppm) and

then dividing by the total volume in the flask (100 mL). Using the plotted points, a linear fit line was created in MATLAB, as seen in figure 1. This shows the linear curve fit with a confidence interval of 95%. The equation of this line was then used to determine the ppm of the iron solution of unknown concentration.

Figure 1. Best fit line for Absorbance vs. Concentration in ppm

Equations

Variables:C=Concentration∈ parts permillion V=Volume of FeSolution Added phen=1,10−phenanthroline A=Absorbance ε = molar absorptivityb = path length in cm%T = percent transmittance of the solution

(1) 2 Fe2+¿+N H2OH ∙HCl+2O F−¿→2 Fe2+¿+N

2+2H

+¿+4 H2O+2C l

−¿¿¿¿¿¿

(2) Fe ¿¿

(3) A=ε∗b∗c(4) A=log(100 /%T )

(5) CF e2+¿=50.0∙ V

100¿

(6) A=0.190C−0.00760(7) y=0.16 x+0.0242

Data Collection

Solution #

Volume of Concentrated Fe

solution added (mL)

NH4Ac NH2OH•HCl phen [Fe2+] (ppm) Absorbance

Blank 0.00 5.00 5.00 10.00 0.00 0.0001 1.05 5.00 5.00 10.00 0.525 0.0962 1.92 5.00 5.00 10.00 0.96 0.1753 3.96 5.00 5.00 10.00 1.98 0.3664 7.99 5.00 5.00 10.00 4.00 0.6548 Unknown 5.00 5.00 10.00 1.55* 0.2729 Unknown 5.00 5.00 10.00 2.77* 0.468

*Concentration calculated using linear fit

Calculations

The [Fe2+] concentration in parts per million was calculated using equation (4) for each volume:

CF e2+¿=50.0∙ 1.05

100=0.525ppm ¿

CF e2+¿=50.0∙ 1.92

100=0.96 ppm¿

CF e2+¿=50.0∙ 3.96

100=0.1 .98 ppm¿

CF e2+¿=50.0∙ 7.99

100=0.4 .00 ppm ¿

The concentrations of the two unknowns were calculated using the generated linear fit equation in MATLAB (7), by rearranging and solving for x:

x=(0. 272−0.0242)

0.16=1.55 ppm

x=(0.468−0.0242)

0.16=2.77 ppm

Discussion

How Error Can Be IntroducedSince this experiment consisted of carefully and accurately preparing various amounts of

different solutions in flasks, the main source of error came from misreading these measurements. The largest source of error may have come from determining exactly how much solution was taken from the burets. Also, reading the meniscus in the graduated cylinder was not identical for each measurement, leading to different amounts of ammonium acetate, hydroxylamine, and phen. The last significant source of error came from the condition of the cuvettes. They were not entirely clean, and each cuvette had a different degree of “dirtiness” that could not be removed.

How This Error Will Change Our ResultIf incorrect amounts of each solute are added, then the absorbance will be inaccurate. For

example, if the actual amount of iron added was less than what was recorded, then the absorbance value will be lowered as well. If the cuvettes were not entirely clean and identical, the spectrophotometer would have showed that less light passed through, outputting larger values for absorbance and therefore raising the concentration.

How to Prevent This ErrorTo prevent the different amounts of solute added, different instruments with slimmer

necks may be used to measure the various solutions. This would allow less room for error in reading the meniscus, since the larger graduated cylinders gave too much room for error when doing small measurements such as 5 mL. Also, the cuvettes may be intensively cleaned prior to adding any of the solutions, so that they are identical for the most part, and will allow the same amount of light through. This will give accurate readings for the absorbance, so that concentration may be calculated accordingly.

Although there were several sources of error, the linear fit line produced showed little discrepancies. The linear correlation value was 0.995, which is relatively close to 1, indicating that our data points resembled a linear relationship very well.

References

[1] http://en.wikipedia.org/wiki/Ligand