Laboratory Report: Demonstrating Beer's Law

Abstract

The objective of this laboratory experiment is to establish a linear relationship between the number of molecules capable of absorbing light in a solution and the amount of light absorbed by the solution. This experiment aims to validate Beer's law, expressed by the equation A = a x b x c, which predicts this linear relationship between absorbance (A), molar absorptivity (a), path length (b), and molar concentration (c). Through the dilution of a potassium permanganate (KMnO4) stock solution and subsequent measurement of absorbance values, we investigate this relationship.

Introduction

Beer's law, a fundamental principle in spectrophotometry, postulates that there exists a linear relationship between the concentration of a solute in a solution and the amount of light it absorbs at a specific wavelength. Mathematically, this relationship is described by the equation A = a x b x c, where A is the absorbance, a is the molar absorptivity, b is the path length through which the light travels in the solution, and c is the molar concentration of the solute.

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The objective of this experiment is to experimentally verify the validity of Beer's law by examining the absorbance of solutions with different molar concentrations. To do so, we prepared a series of diluted solutions from a stock solution of potassium permanganate (KMnO4) and measured their absorbance values using a spectrophotometer (Spec 20). By plotting the absorbance values against the molar concentrations of these solutions, we aim to establish a linear relationship, thereby confirming the principles of Beer's law.

Materials and Methods

Materials

• Potassium Permanganate (KMnO4)
• Diluted Solutions (various concentrations)
• Spectrophotometer (Spec 20)
• Cuvette

Experimental Procedure

In this experiment, the stock solution of potassium permanganate (KMnO4) with a known molarity was prepared before arriving at the laboratory.

The diluted solutions were then created as per the lab manual's instructions. To ensure consistency and minimize error, the same cuvette was employed throughout the experiment. This approach was chosen to eliminate potential variations in measurement due to differences in cuvette characteristics.

Data Calculations

To determine the molarity of each solution, the following calculations were performed:

Molarity of the Stock Solution (0.570 g KMnO4 in 0.500 L):

Molarity (M) = (grams of KMnO4 x (1 mole / molar mass (158.04g))) / Liters of stock solution

Molarity = (0.570 g KMnO4 x (1 mole / 158.04g)) / 0.500 L = 0.00721 M

Molarity of Solution #1:

Molarity of Solution 1 = (mL of stock solution x (moles of stock solution / liter)) / total liters of solution 1 (volumetric flask)

Molarity of Solution 1 = (5.00 mL stock solution x (0.00721 moles / 1000 mL)) / 0.10000 L = 0.000361 M

Molarity of Solution #2:

Molarity of Solution 2 = (mL of stock solution x (moles of stock solution / liter)) / total liters in solution 2 (volumetric flask)

Molarity of Solution 2 = (2.00 mL stock solution x (0.00721 moles / 1000 mL)) / 0.10000 L = 0.000144 M

Molarity of Solution #3:

Molarity of Solution 3 = (mL of solution 1 x (moles of solution 1 / 1 L)) / total liters in solution 3 (volumetric flask)

Molarity of Solution 3 = (50.00 mL solution 1 x (0.00721 moles / 1000 mL)) / 0.10000 L = 0.000181 M

Molarity of Solution #4:

Molarity of Solution 4 = (mL of solution 2 x (moles of solution 2 / 1 L)) / total liters in solution 4 (volumetric flask)

Molarity of Solution 4 = (50.00 mL solution 2 x (0.000144 moles / 1000 mL)) / 0.10000 L = 0.000072 M

Results

Discussion and Conclusion

The primary goal of this laboratory experiment was to validate Beer's law, which asserts that there is a linear relationship between the molar concentration of a solution and the amount of light it absorbs. This relationship is described by the equation A = a x b x c, where A represents absorbance, a is the molar absorptivity, b is the path length, and c is the molar concentration. By creating a series of diluted solutions from a stock solution of potassium permanganate (KMnO4) and measuring their absorbance values, we sought to confirm this linear relationship.

The results obtained in this experiment demonstrate that Beer's law holds true within the specified conditions. As shown in Figure 1, the absorbance values exhibit a linear increase as the molar concentration of the KMnO4 solutions increases. This behavior aligns with the predictions of Beer's law, which states that a higher molar concentration leads to increased absorbance due to a greater number of absorbing molecules in the solution.

However, it is essential to acknowledge potential sources of error that could have affected the accuracy of our results. One possible source of error is the dilution process. If any of the solutions were incorrectly diluted, it would introduce errors that propagate through subsequent dilutions. Additionally, the transfer of solution between containers may have left residual drops behind, leading to variations in the actual molar concentrations of the solutions. Lastly, variations in cuvette characteristics or inconsistencies in cuvette placement in the spectrophotometer may have contributed to minor deviations in the absorbance values.

In conclusion, this experiment successfully demonstrates that Beer's law holds true for the relationship between molar concentration and absorbance. The linear increase in absorbance with increasing molar concentration confirms the theoretical principles of Beer's law. To enhance the accuracy of future experiments, it is recommended to pay meticulous attention to the dilution process and ensure the complete transfer of solution between containers. Furthermore, measuring the absorbance of the stock solution could provide additional data points for a more comprehensive analysis.

Questions

1. A larger cuvette diameter will produce a higher absorbance value.

The diameter of the cuvette corresponds to the path length (b) in the Beer's law equation A = a x b x c. A larger path length results in a higher absorbance value because it effectively increases the distance through which light passes through the solution. This allows more absorbing molecules to interact with the light, leading to greater light absorption and a higher absorbance value.

2. To find the extinction coefficient, the equation A/cb = a is used. A larger cuvette diameter, or path length, would result in a smaller extinction coefficient.

The extinction coefficient (a) is determined using the equation A/cb = a, where A is the absorbance, c is the molar concentration, and b is the path length. If the path length (b) increases, the denominator of the equation becomes larger, leading to a smaller value for the extinction coefficient (a). Therefore, a larger cuvette diameter, which corresponds to a longer path length, results in a smaller extinction coefficient.

3. Solution 4 probably has the greatest error because it was the last solution to be diluted.

Solution 4 may indeed have a greater potential for error compared to the other solutions due to its position as the final solution in the dilution series. Any errors made during the dilution process of the earlier solutions would propagate and accumulate in Solution 4, affecting its accuracy. Therefore, Solution 4 is more susceptible to errors introduced in the preceding dilutions.