Analyzing Absorbance and Concentration Correlation in Solutions

Abstract

This study explores the correlation between color intensity and absorbance in solutions, specifically focusing on Coomassie Blue's behavior at a wavelength of 595 nm.

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Through various experiments and calculations, including the application of Beer-Lambert's law, this paper presents a quantitative analysis of how absorbance changes with concentration, the effect of pathlength on absorbance, and the implications of these findings in concentration measurements of β-carotene solutions.

Materials and Methods

The analysis involved preparing solutions of varying concentrations of Coomassie Blue, measuring their absorbance at 595 nm, and calculating the molar concentration of β-carotene in a sample solution.

The experiments were conducted using a UV-Vis spectrophotometer with a 1.0 cm pathlength cuvette.

In one sentence describe the trend you see between the colour intensity and the absorbance values recorded? What can you conclude from this observation? From the recorded results, it can be seen that generally as the intensity of the Coomassie Blue solution increases, so does the value of absorbance at a wavelength of 595 nm. It can be inferred from these results that as the concentration of Coomassie Blue (the absorbing species) increase, there would be a greater number of molecules present in the solution to interact with the passing light; and thus, absorbance is directly proportional to the concentration of a dilute solution.

2a. Slope value for the trendline = 47.495 mL/mg

2b. Convert the unit for the slope (mg/mL)-1 to M-1

Given information: Mm = 854 g/mol

Calculation:

47.495mL/mg × (1000 mg)/(1 g ) × (1 L)/(1000 mL) = 47.495 L g-1

(47.495 L)/(1 g) × (854 g)/(1 mol) = 40,560.73 L mol-1 = 4.

06 x 104 M-1

2c. Knowing that the pathlength of 1.0 cm was used for the absorbance readings, explain what this slope value means with respect to the absorbance property of Coomassie Blue and the Beer-Lambert law equation. Based on the value of the slope (4.06 x 104 M-1) and the pathlength (1cm), it can be said that the value of the slope represents the molar absorptivity coefficient (measured in units of M-1cm-1). The molar absorptivity coefficient is a measure of the absorbance of a solution at a particular wavelength under the conditions such that the concentration is 1M and the pathlength is 1cm too. In terms of the Beer-Lambert Law, the value of the slope is thus represented by the symbol, ε.

2d. Using what you calculated above, what is the expected absorbance of a 25 µM Coomassie blue solution when using a 1 cm pathway?

Coomassie Blue solution = 25 µM

l (pathway) = 1 cm

ε = 4.06 x 104 M-1cm-1

Calculation:

Abs = ε l C

= ((4.06 x (10)^4 M )^(-1) (cm)^(-1))× 1.0 cm × 25 µM × (1M/(1000000µM ))

= 1.0

Therefore, the expected absorbance of a 25 µM Coomassie blue solution when using a 1 cm pathway is 1.0.

3a. If you were to use a cuvette with a 2.0 pathlength to measure the various solutions you made in the lab how would (i) your absorbance values be affected; and (ii) how would you slope be affected (when compared to a 1.0 cm pathlength)? Briefly explain your reasoning.

According to the Beers Lambert equation, absorbance is proportional to both the concentration of the species and the pathlength (1). If the pathlength were to double then, so would the value of absorbance for each particular solution (where the concentration for each solution has not changed). This is possible because as the path length increases, there is a greater amount of molecules that would interact with the transmitting light (1).

If the values of absorbance were to double, the slope of the graph would also double and look much steeper in comparison to the slope of the graph where the pathway was only 1cm.

3b. Does the molar extinction coefficient change for Coomassie Blue as the pathlength of the cuvette changes?

Although the pathlength of the cuvette changes, the molar extinction coefficient does not. This is because according to Beer’s law, the molar extinction coefficient is simply a constant value that indicates the ability of the substance to absorb light at a particular wavelength, under the conditions of pathlength and concentration being 1cm and 1M respectively. Thus, absorbance is thus only affected by two variables: concentration or pathlength.

4a. What is the molar concentration of a 2.00 µg/mL solution of β-carotene?

Given:

Molar weight = 537 g/ mol

ε = 140,000 M-1cm-1

wavelength = 453 nm

Molar concentration of β-carotene:

(2.00µg)/mL × (1000 mL)/(1 L) × (1 g)/(1000000 µg ) × (1 mol)/(537 g) = 3.72 x 10-6 M

Therefore the value of the molar concentration of a 2.00 µg/mL solution of β-carotene is 3.72

x 10-6 M.

4b. What is the expected absorbance value for a solution containing 2.00 µg/mL of β-carotene when measured at 453 nm with a 1.0 cm pathlength?

Abs = ε l C

= (140,000M^(-1) (cm)^(-1))× 1.0 cm × (3.72 x 〖10〗^(-6) M)

= 0.52

In conclusion, the expected absorbance is 0.52.

4c. What is the expected % transmission for a solution containing 2.00 µg/mL of β-carotene when measured at 453nm with a 1.0cm pathlength?

% transmittance = 10-Abs x 100%

= 10-0.52 x 100%

= 30.1999

= 30.2 %

Therefore, the expected % transmission is 30.2 %

4d. What is the % (m/v) concentration of the 2.00 µg/mL of β-carotene?

% (m/v) = ((2.00µg)/mL × (1 g)/(1000000 µg )) × 100%

= 0.000002 x 100%

= 0.0002 %

= 2.00 x 10-4 %

Thus, the overall % (m/v) concentration of the 2.00 µg/mL of β-carotene is 2.00 x 10-4 %.

5. When monitoring the volume measurements by mass, what was the expected mass for 700µL, 150 µL, 70.0 µL, and 15.0 µL? Briefly explain your reasoning?

700µL × (1 L)/(1000000µL) ×(1000 g)/(1 L)=0.7 g

150µL × (1 L)/(1000000µL) ×(1000 g)/(1 L)=0.15 g

70.0µL × (1 L)/(1000000µL) ×(1000 g)/(1 L)=0.0700 g

15.0µL × (1 L)/(1000000µL) ×(1000 g)/(1 L)=0.0150 g

Based on monitoring the measurements of volume by mass, the expected values for 700µL, 150 µL, 70.0 µL, and 15.0 µL are 0.7 g, 0.15g, 0.0700g and 0.0150g respectively. This can be calculated through the use of conversion factors that expresses the relationship between two different units as a ratio. Specifically, since the density of water is approximately 1 g/ml, it can be written as an equivalent ratio of 1000g/L and be used to convert µL to L.

Discussion

The experimentally determined linear relationship between the absorbance and concentration of Coomassie Blue confirms the Beer-Lambert law's applicability in analyzing dilute solutions. The findings indicate that absorbance can serve as a reliable metric for determining the concentration of a solution, provided the pathlength and molar absorptivity are known. The conversion of slope values and subsequent calculations further illustrate the direct impact of concentration and pathlength on absorbance, essential for accurate chemical analysis.

Conclusion

This study underscores the critical role of absorbance in assessing solution concentration, validating the Beer-Lambert law's principle that absorbance is proportional to concentration and pathlength. The methodology and calculations presented provide a foundational approach for analyzing the concentration of solutions in various scientific fields, ensuring precise and accurate measurements essential for research and development.