Determining the Concentration of a Solution Beer\'s Law PDF

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Caitlin'Bettenay'

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21st'November'2016'

‘Determining the Concentration of a Solution: Beer’s Law’

Lab #7 - Fall Term - 2016

Lecturer: Bryce Clifton Caitlin Bettenay

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21st'November'2016'

Determining the Concentration of a Solution: Beer’s Law ABSTRACT: Throughout the experiment ‘Determining the Concentration of a Solution: Beer’s Law’, Allura Red standard solutions were prepared and a colorimeter was used to measure the absorbance of each of solution. Furthermore, the relationship between the absorbance and concentration of a solution was found and this was used to determine the concentration of Allura Red in commercially available beverages (in this case red Gatorade). The result of the experiment showed that the concentration of Allura Red in red Gatorade is 15.75×10'( .

INTRODUCTION: The following experiment has been designed to determine the relationship between the absorbance and concentration of five Allura Red standard solutions. This was then used to determine the concentration of Allura Red in commercially available beverages - in this case – Red Gatorade. The method includes preparing five solutions of Allura Red with different concentrations ranging from 6×10'* 𝑀,𝑡𝑜 ,2×10'0 𝑀. Each standard solution will then be transferred to a small, rectangular cuvette that will be placed into the colorimeter. The amount of light that passes through the solution and strikes the photocell will used to compute the absorbance of each solution. After the absorbance of each solution was recorded, and used to make a graph of absorbance vs. concentration. The calibration curve will then be calculated and finally, the linear relationship between absorbance and concentration for each solution will be determined. This relationship is also known as Beer's law. In order to conduct this experiment and fully understand it, further research is required.

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A calibration curve is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration. When light passes through a solution, certain ions may absorb some of the light, reducing the amount of light that passes through the solution. This absorbance of light is responsible for the colours that we see: a solution that absorbs red light will appear green, its opposite. This experiment is designed to understand Beer’s Law which states: for a specified wavelength: 𝐴 = 𝐸𝑏𝑐 as can be seen in figure 1, where A is absorbance, E is molar absorption constant, b is path length of light and C is concentration in mol/L. This equation outlines that under ideal conditions, a substance’s concentration and its absorbance are directly proportional: a high-concentration solution absorbs more light, and solutions of lower concentrations absorb less light as concentration and absorbance are proportional. These concepts will be explored and tested in order to determine an unknown concentration of Allura red in a Figure'1:'Diagram'displaying'the' Beer-Lambert'Law'and'brief' explanation'

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solution (in this case, red Gatorade).

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DATA:

Table 1: Table displaying the volume of Allura Red (mL), and the concentration of Allura red (M) with the volume of the solution (mL) and the concentration of the solution. Volume'of' Allura'Red' (mL): 1

Concentration' Volume'of' of'Allura'red' the'solution' (M): (mL): 1.0×10'6

6

100

Concentration'of'solution'(M):'

𝑀7 𝑉7 = 𝑀9 𝑉9 , 𝑀7 = 1.0×10'6 𝑉7 = 6𝑚𝐿 𝑀9 = 𝑥 𝑉9 = 100𝑚𝐿 ∴ 1.0×10'6 ,6 = 100𝑥, 6.0×10'6 𝑥= 100 𝑥 = 6.0×10'*

2

9

1.0×10'6

100

9.0×10'*

3

12

1.0×10'6

100

1.2×10'0

4

15

1.0×10'6

100

1.5×10'0

5

20

1.0×10'6

100

2.0×10'0

Table 2: Table displaying the relationship between concentration (M) and absorbance for the five Allura Red standard solutions Allura'Red'Solution'#:'' Concentration'(M):

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Absorbance:'

1

6.0×10* '

0.057

2

9.0×10

'*

0.059

3

1.2×10'0

0.090

4

1.5×10'0

0.113

5

2.0×10'0

0.157

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Graph 1: Graph displaying the concentration of a solution: Beer’s Law through the relationship between the absorbance and concentration (mol/L)

CALCULATIONS: Calculations to determine the concentration of Gatorade: 𝐴𝑏𝑠𝑜𝑟𝑏𝑡𝑖𝑜𝑛,(𝑦) = ,𝑚,×,𝑥, + ,𝑏, 𝑚, = ,7583, 𝑏, = ,0.001279, 𝑥 = 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝐴𝑏𝑠𝑜𝑟𝑏𝑡𝑖𝑜𝑛:,7583𝑥 + 0.001279 = 0.187, , (𝐴𝑏𝑠𝑜𝑟𝑏𝑎𝑛𝑐𝑒,– ,𝑏), , 𝑥= 𝑚 , 0.187 − 0.001279 𝑥= 7583 , 𝑥 = 3.15×10'( Due to the fact that the original concentration of Gatorade was multiplied by 5 (20mL was used), this answer needs to be multiplied by 5 in order to get the true concentration of Gatorade. , , ∴ 𝑇ℎ𝑒,𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛,𝑜𝑓,𝐺𝑎𝑡𝑜𝑟𝑎𝑑𝑒 ,𝑖𝑠:,3.15×10'( ×5 = 15.75×10'(

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RESULTS: As can be from Table 1, the five standard solutions of Allura Red were calculated by the formula 𝑀7 𝑉7 = 𝑀9 𝑉9 . Using this formula, the concentrations (M) were determined to be, 6.0×10'* , 9.0×10'* , 1.2×10'0 , 1.5×10'0 and 2.0×10'0 . Which were 6mL, 9mL, 12mL, 15mL and 20mL volume of Allura Red respectively. Table 2 displays the concentration and absorbance of the five Allura Red standard solutions and as can be seen from the table, as the concentration increases, so does the absorption. Graph 1 displays the concentration of a solution: Beer’s Law through the relationship between the absorbance and concentration (mol/L). As can be seen, the line of best fit equation can help to determine the absorption by using 𝑦,(𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛) = ,𝑚,×,𝑥, + ,𝑏 which was solved in the Calculations section of this report to be 0.187. Furthermore, the overall trend of the data demonstrated that as the concentration increased, so did the absorption.

DISCUSSION: Throughout the experiment, ‘Determining the Concentration of a Solution: Beer’s Law’, Allura Red standard solutions were prepared and a colorimeter was used to measure the absorbance of each of solution. Furthermore, the relationship between the absorbance and concentration of a solution was found and this was used to determine the concentration of Allura Red in commercially available beverages (in this case red Gatorade). As can be seen from the Data, results and Calculations sections, the findings strongly support Beer’s Law as defined in the introduction of this report. According to the equation given by Beer’s law, the relationship between concentration and absorbance should be directly proportional to each other. This is particularly evident in Table 2 and Graph 1 when looking at the trend line of the data as when the concentration increases, the absorbance level also increases. Through utilizing the linear relationship between concentration and absorbance known as Beer’s law, it was determined that the concentration of the Gatorade was 15.75×10'( . Although the linear correlation of the graph is accurate, the non-zero intercept

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suggests that there may have been various errors in the lab. One methodology error involved the cuvette. Although wiped off before being placed in the colorimeter each time, it may not have been perfectly clean. This may have slightly affected the results as anything left on the cuvette would decrease the light that could pass and would result in a higher measured absorbance. If this happened on the first few solutions of known concentration it would have decreased the slope of the graph, resulting in a larger calculated concentration for the unknown. If this problem had occurred on either of the two more concentrated solutions, it would have increased the slope of the line, causing a decrease in the calculated value for the unknown concentration. If this had occurred with the Gatorade, the higher measured absorbance would have led a calculated concentration that was too high. In future testing it would seem appropriate to take greater care in wiping down the equipment to ensure that these methodology errors can be avoided and the most reliable data can be obtained. Another error that may have affected the results was when each solution was placed in the cuvette, traces of the prior solution may have still been present. For each of the solutions of known concentration, this would have decreased their concentration and therefore their absorbance, lowering the line on the graph. This would have led to a lower intercept value and a higher calculated concentration for the Gatorade. In future testing it would seem appropriate to take greater care in washing the equipment to ensure that these methodology errors can be avoided and the most reliable data can be obtained. Although these errors may have affected the results, they did not affect the overall trend lines of the data therefore the data gathered is still reliable and valid and Beer’s Law is still evident in this experiment which supports the information found in the introduction of this report.

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FURTHER QUESTIONS: 1. How many molecules of Allura Red would you consume if you drank one 20 ounce bottle of Gatorade? Concentration of Allura Red: 0.0001,𝑚𝑜𝑙/𝑚𝐿 𝑀, = ,0.0001,𝑚𝑜𝑙/𝑚𝐿, 𝑉, = ,20,𝑜𝑧, = ,0.591,𝐿, = ,591,𝑚𝐿 , 𝑛, = ,𝑀×𝑉, = ,0.0001,𝑚𝑜𝑙/𝑚𝐿 ,×,591,𝑚𝐿, = ,0.0591,𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 There are 0.0591 molecules of Allura Red in one 20 ounce bottle of Gatorade.

2. What mass of Allura Red you would consume if you drank one 20 ounce bottle of Gatorade? If your value is greater than the mass of one 20 ounce bottle, be sure to recheck your calculations.

𝑀𝑜𝑙𝑎𝑟,𝑚𝑎𝑠𝑠,𝑜𝑓,𝐴𝑙𝑙𝑢𝑟𝑎,𝑅𝑒𝑑:,496.42,𝑔/𝑚𝑜𝑙, 0.0591,𝑚𝑜𝑙,×,496.42,𝑔/𝑚𝑜𝑙, = ,29.34,𝑔 , There are 29.34 grams of Allura Red in one 20 ounce bottle of Gatorade. As the mass of one 20 ounce is equal to 567 grams, the calculations are reasonable.

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