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Optical Method of Analysis Use of Beer’s Law

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The purpose of this analytical laboratory experiment is to determine the unknown concentration of potassium permanganate (KMnO4) solution by finding its absorbance through the use of spectrophotometer. The preparation of four known concentration of KMnO4 was done namely, 2.00×10-4M, 1.50×10-4M, 1.00×10-4M, 5.00×10-5M, respectively and is to be place on the spectrophotometer with the unknown and distilled water for the determination of each concentration’s absorbance. As the concentration is proportional with the absorbance of the solution, to determine the concentration of the solution is possible by drawing a graph of concentration against the absorbance. At the end of the experiment, the group found the concentration of the unknown sample is 2.50×10-4M.

I. Introduction

Spectrophotometry is a method to measure how much a chemical substance absorbs light by measuring the intensity of light as a beam of light passes through sample solution. The basic principle is that each compound absorbs or transmits light over a certain range of wavelength. This measurement can also be used to measure the amount of a known chemical substance. Spectrophotometry is one of the most useful methods of quantitative analysis in various fields such as chemistry, physics, biochemistry, material and chemical engineering and clinical applications.

A spectrophotometer is an instrument that measures the amount of photons (the intensity of light) absorbed after it passes through sample solution. With the spectrophotometer, the amount of a known chemical substance (concentrations) can also be determined by measuring the intensity of light detected. In this experiment, we use the spectrophotometer to determine the unknown concentration of potassium permanganate (KMnO4) solution.

The approach of this experiment on determining the concentration of the unknown is by finding the absorbance level of the different concentration of the solution. Relating the absorbance level and their respective concentration, we would be able to acquire the concentration of the unknown. The objective of this experiment is to became familiar with typical spectrophotometric analysis and to know the other way on how to know the concentration of a given solution.

II. Review of Related Literature

As stated by Christy P, The spectrophotometer was invented in 1940, by Arnold J. Beckman and his colleagues at National Technologies Laboratories, the company Beckman had started in 1935. They were led by project leader Howard H. Cary. The spectrophotometer was the company’s greatest discovery. Before 1940, the chemical analysis process was a long venture taking weeks to complete with only 25 percent accuracy according to the MIT’s “Inventor of the Week” archive. In 1940, when the Beckman DU Spectrophotometer was introduced, it simplified the process greatly, requiring only a few minutes for analysis.

According to the same source, this test offered 99.99 percent accuracy on the analysis. This instrument set the standard in chemical analysis. A study made by David R. Caprette: A spectrophotometer consists of two instruments, namely a spectrometer for producing light of any selected color (wavelength), and a photometer for measuring the intensity of light. The instruments are arranged so that liquid in a cuvette can be placed between the spectrometer beam and the photometer. The amount of light passing through the tube is measured by the photometer. The photometer delivers a voltage signal to a display device, normally a galvanometer.

The signal changes as the amount of light absorbed by the liquid changes. According to David B. Fankhauser, Ph.D., spectrophotometer is an instrument which measures the amount of light of a specified wavelength which passes through a medium. According to Beer’s law, the amount of light absorbed by a medium is proportional to the concentration of the absorbing material or solute present. Thus the concentration of a colored solute in a solution may be determined in the lab by measuring the absorbency of light at a given wavelength. Wavelength (often abbreviated as lambda) is measured in nm.

The spectrophotometer allows selection of a wavelength pass through the solution. Usually, the wavelength chose which corresponds to the absorption maximum of the solute. An excerpt of Dr. Laminar’s study: Spectrophotometric analysis for determining the amount of an inorganic compound in solution involves a reaction between an organic reagent and an analyte to form a colored complex. The reaction can be used to determine analyte concentrations assuming the color intensity and absorbance is proportional to the analyte concentration, the complex is stable, and the reagent does not significantly react with other constituents thereby causing interferences.

A spectrophotometer is the specific device which measures the absorption of a monochromatic light beam by a sample and added reagent. Beer-Lambert Law (also known as Beer’s Law) states that there is a linear relationship between the absorbance and the concentration of a sample. For this reason, Beer’s Law can only be applied when there is a linear relationship. Beer’s Law is written as:

where is the measure of absorbance (no units), is the molar extinction coefficient or molar absorptivity (or absorption coefficient), is the path length, and is the concentration. The molar extinction coefficient is given as a constant and varies for each molecule. Since absorbance does not carry any units, the units for must cancel out the units of length and concentration. As a result, has the units: L·mol-1·cm-1. The path length is measured in centimeters. Because a standard spectrometer uses a cuvette that is 1 cm in width, is always assumed to equal 1 cm. Since absorption, , and path length are known, we can calculate the concentration of the sample.

III. Methodology

a. Materials and Equipment
* Standard KMnO4 solution
* Spectrophotometer
* Flasks
* 250mL volumetric flask
* Distilled H2O
* Wash Bottle
* Cuvettes
* Pipette
* Rubber Aspirator
b. Procedure

For the preparation of the aliquot of standard KMnO4 solution, we carefully measured a 2.53mL of standard KMnO4 (0.01975M) using a pipette and diluted it to the mark in a 250mL volumetric flask. After preparing the aliquot, we prepared four flasks containing 10mL, 30mL, 10mL and another 10mL of the solution respectively. We then diluted each with distilled water with 0mL, 10mL, 10mL, and 30mL respectively.

Each portion of each solution was transferred on different clean cuvettes and was placed on the carousel respectively. The zero (first one) in the carousel has the cuvette with distilled water and the last one has the unknown. We then used the spectrophotometer to find the wavelength in lambda max (ƛmax) and the instrument was then calibrated. The absorbance of the solutions was measured covering the wavelength range from 440nm to 770nm. The absorbance of each solution was recorded and a graph was made from the concentration of the solutions against their respective absorbance reading.

IV. Results and Discussion

The molarity of KMnO4 is dependent on the volume of the KMnO4 used and the volume of the distilled water added. In this table, it can be observed that the lower the amount of H2O and the higher the amount of the KMnO4 is, the higher the molarity is and the lower the amount of KMnO4 and the higher the amount of the H2O added, the lower the concentration is. The computation of the molarity can be seen on the appendix. Table 1: Data

| V of KMnO4 (2.00×10-4M)(mL)| V of H2o(mL)| VT(mL)| [M]f| Absorbance| B1| 10| 0| 10| 2.00×10-4| 0.168|
B2| 30| 10| 40| 1.50×10-4| 0.121|
B3| 10| 10| 20| 1.00×10-4| 0.084|
B4| 10| 30| 40| 5.00×10-5| 0.047|
unknown| | | | 2.50×10-4| 0.204|

The absorbance of each solution is determined by the use of spectrophotometer. While the molarity of the unknown is acquired through the use of graph and is reflected at Absorbance Graph. The computation of the concentration of the unknown is presented at the appendix.

V. Conclusion and Recommendation

From this experiment, we have determined the concentration of the unknown with the help of spectrophotometer and Beer’s Law. The experiment and familiarization with the spectrophotometer has been successfully done. In the preparation of the known concentration, it is best advised to have an accurate measurement because it can directly affect its absorbance.

Be sure to rinse first the cuvette with distilled water and the solution before filling it with the solution to be sure that there won’t be factors that can contaminate the solution, thus having different concentration. Handle the cuvettes carefully and hold it only on the rough side. Fingerprints on the smooth side can affect the transmission of light. In making the graph, having the R2 closed to our equal to 1 is ideal to be sure that the concentration of the unknown is still on the line.

VI. References
* Christy P. 2010. The History of Spectrophotometry. http://www.ehow.com/about_6595173_history-spectrophotometry.html. * David B. Fankhauser. 2007. Spectrophotometer Use. http://biology.clc.uc.edu/fankhauser/labs/microbiology/Growth_Curve/Spectrophotometer.htm. * Dr. Laminar. 1998. Spectrophotometric Analysis. http://www.public.asu.edu/~lwmays/classes/cee341/lab_example.pdf. * M.C. Nagan and J. M. McCormick. 2012. The Laboratory Report. http://chemlab.truman.edu/LabReports_files/LabReports.asp#Results. * History of Spectrophotometry. http://labsynergy.wordpress.com/2011/03/08/history-of-spectrophotometer/. * http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Reaction_Rates/Experimental_Determination_of_Kinetcs/Spectrophotometry. * http://www.ruf.rice.edu/~bioslabs/methods/protein/spectrophotometer.html#top

A. Computation of the Molarity of each solution of KMnO4 Formula used:
(VolumeKMnO4)(ConcentrationKMnO4) = (VolumeSolution)(ConcentrationSolution)

B1: (10mL)(2.00×10-4M) = (10mL)([M]f)
[M]f = 2.00×10-4M
B2: (30mL)(2.00×10-4M) = (40mL)([M]f)
[M]f = 1.50×10-4M
B3: (10mL)(2.00×10-4M) = (20mL)([M]f)
[M]f = 1.00×10-4M
B4: (10mL)(2.00×10-4M) = (40mL)([M]f)
[M]f = 5.00×10-5M

B. Computation of the molarity of the unknown solution
y = 792.8x + 0.0057
0.205 = 792.8x + 0.0057
0.205 – 0.0057 = 792.8x
x = 2.50×10-4 M

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