Verification of the Beer-Lambert Law for Solutions of Copper Sulphate and Determination of the Concentration of a Given Solution of Copper Sulphate
Introduction
The determination of elements concentrations in water media is an important task in industry, medicine, and environmental protection. The main requirements are accuracy, simplicity of operations, speed and cost of the analysis (Hunt 1995). The spectroscopic analysis is widely applied for routine measurements and research needs (Lindon 2010). The experiment is dedicated to determination of copper sulphate in water using the molecular absorption (Kenkel 2003). The first stage of the experiment performs absorbance measurements of the solutions with the known concentrations. Basing on these data, the concentration – absorbance graph is plotted; if the plot is linear, then the Beer-Lambert law is verified. The second stage is about absorption measurement of the solution with the unknown concentration and determination of the concentration.
The determination is based on the absorption of radiation laws practical application. The energy absorbance depends on the concentration of the compound, intensity of the light and path-length of the solution (Krupadanam 2001). The basic law that is used for molecular absorbance analysis is Beer-Lambert law, which is the combination of laws proposed by two scientists. The Lambert law states that 'the intensity of the light transmitted by a solution diminishes exponentially as the path-length, of the solution increases linearly' (Krupadanam 2001). The Beer's law studies the effect of concentration. Beer has explored that the concentration increase is proportional to increase in absorption and has the same effect as the light absorbing path (Zijlstra, Buursma & Assendelft 2000). The combined Beer-Lambert law states that the absorbance of the solution is linearly related to the concentration, and the path-length of the radiation. There is much mathematical background beyond the laws, and the numerous integral and differential formulae are applied to obtain the final form of the law (Svanberg 2004, Robinson 1996):
I=I0e-abc,
where I and I0 are the amounts of light that pass through the solution and the light falling on the solution prior to the absorption, respectively; a – molar absorbance, b – path-length, and c – concentration of the analyte. Typically, the simplified form of the law are used (Krupadanam 2001):
where A is the absorbance, and it is A=lnII0 .
There are several limitations to application of the Beer-Lambert law: the light should be monochromatic, the solution has to be diluted and should not exhibit stray fluorescence. The suspensions cannot be analysed as the dispersed particles cause additional absorption and the deviations from law are observed (Khopkar 2012).
Aim
The lab assignment aims to verify the Beer-Lambert law using the experiment with CuSO4 solutions and determine the concentration of the unknown solution.
Experimental Procedure
Verification of the Beer-Lambert Law
The standard 0.1 M solution of CuSO4 is used for the experiment. The series of dilutions using 1, 2, 3, 4 and 5 ml of CuSO4 dissolved in 25 ml volumetric flasks. The standard solutions with concentrations 0.004 M, 0.008 M, 0.012 M, 0.016 M, and 0.02 M are obtained.
The solution of CuSO4 is placed into the beaker, and the spectra is obtained. Using the spectra, the maximum absorbance λmax is determined. After this, the spectrophotometer is set at λmax, and the stock solutions are measured.
Determination of the Concentration of the Unknown CuSO4 Solution
The volume of unknown solution (5 ml) is placed into the 25 ml flask, and diluted to the mark. The absorbance of the solution is measured, and the results are recorded.
Results and Discussion
Verification of the Beer-Lambert Law
The maximum absorbance is observed at λmax = 800 nm. The experimental results for absorbance measurements of CuSO4 solutions of different concentration are presented in Table 1.
Figure 1 presents the graphical interpretation of the experimental data. The graphical interpretation is the calibration line, which is the CuSO4 concentration and absorbance dependence.
Figure 1: Calibration Line for Concentration of CuSO4 and Absorbance.
The calibration line that was obtained basing on the experimental data illustrates the linear dependence between the concentration of CuSO4 solution and its and absorbance. The linearity is confirmed with a determination coefficient R2 = 0.9994, which is close to 1. It shows that the calibration line with the equation Absorbance = 0.0122·Concentration - 0.0018 corresponds the experimental data by 99.94%, and this is the perfect fit (Meier & Zund 2000). Therefore, the experiment was conducted with high accuracy and the calibration line can be used to determine the concentration of unknown solution (Miller & Miller 2010). The high linearity of the plot verifies the Beer-Lambert law.
Determination of Concentration of the Unknown Solution
The unknown solution absorbance was measured at 800 nm, and its absorbance was 0.117. Using the equation of the calibration line obtained from the previous section, the concentration of the unknown solution is determined:
Absorbance = 0.0122·Concentration - 0.0018
Concentration = (Absorbance + 0.0018) / 0.0122.
Substituting the absorbance of the unknown solution into the equation (Freiser & Freiser 2011):
Concentration = (0.117 + 0.0018) / 0.0122 = 9.7 mM.
Alternatively, the determination can be performed using the graphical method. For this, the line at Absorbance = 0.117 is drawn; from the intersection point of the absorbance line and calibration line, a perpendicular is dropped on concentration axis. This is the concentration of the unknown solution. The procedure is presented in Figure 2. However, this method is less accurate (Nemcová, Čermáková & Gasparič, 1996).
Figure 2: Graphical Method for Unknown Concentration Determination.
Since the unknown solution was dissolved prior to determination, and the dilution factor is 5 (25 ml volumetric flask and 5 ml sample, 25 ml / 5 ml = 5), the obtained concentration should be multiplied by 5: 9.7 nm · 5 = 48.5 mM. Therefore, the concentration of the unknown solution of CuSO4 is 48.5 mM, or 0.0485 M.
Conclusions
The Beer-Lambert law was verified by obtaining the absorbances of CuSO4 solutions of different concentrations. The concentration - absorbance plot shows high linearity, which is confirmed with high determination coefficient. This is the sign of accurate experiments performance and absence of the systematic errors. Basing on the equation of concentration - absorbance plot, the concentration of the unknown solution was calculated. Using the equation of the calibration line is the convenient and reliable method for determination of the unknown solutions concentrations. The experiment can be improved if the concentration of unknown solution is measured by another, more reliable, method and the experimental error is calculated.
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