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How to Calculate Molar Absorptivity Download ArticleExplore this Article methods 1 Calculating Molar Absorptivity with the Equation 2 Calculating Molar Absorptivity Using a Line-of-Best-Fit Other Sections Questions & Answers Video Related Articles References Article Summary Co-authored by Ronitte Libedinsky, MS
Last Updated: June 27, 2024 Fact Checked
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This article was co-authored by Ronitte Libedinsky, MS. Ronitte Libedinsky is an Academic Tutor and the Founder of Brighter Minds SF, a San Francisco, California based company that provides one-on-one and small group tutoring. Specializing in tutoring mathematics (pre-algebra, algebra I/II, geometry, pre-calculus, calculus) and science (chemistry, biology), Ronitte has over 10 years of experience tutoring to middle school, high school, and college students. She also tutors in SSAT, Terra Nova, HSPT, SAT, and ACT test prep. Ronitte holds a BS in Chemistry from the University of California, Berkeley, and an MS in Chemistry from Tel Aviv University. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 847,147 times.
Molar absorptivity, also known as the molar extinction coefficient, is a measure of how well a chemical species absorbs a given wavelength of light. It allows you to make comparisons about the probability of electrons transition between levels for different compounds without taking into account differences in concentration or solution length during measurements.[1]XResearch source It is commonly used in chemistry and should not be confused with the extinction coefficient, which is used more often in physics. The standard units for molar absorptivity are liters per mole centimeter (L mol-1 cm-1).[2]XResearch source
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Method 1 Method 1 of 2:
Calculating Molar Absorptivity with the Equation
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1 Understand the Beer-Lambert law for absorbance, A = ɛ x l x c. The standard equation for absorbance is A = ɛ x l x c, where A is the amount of light absorbed by the sample for a given wavelength, ɛ is the molar absorptivity, l is the distance that the light travels through the solution, and c is the concentration of the absorbing species per unit volume.[3]XResearch source
Absorbance can also be calculated using the ratio between the intensity of a reference sample and the unknown sample. It is given by the equation A = log10(Io/I).[4]XResearch source
Intensity is obtained using a spectrophotometer.
The absorbance of a solution will change based on the wavelength that is passed through the solution. Some wavelengths will be absorbed more than others depending upon the makeup of the solution. Remember to state which wavelength is being used for your calculation.[5]XResearch source
2 Rearrange the Beer-Lambert equation to solve for molar absorptivity. Using algebra we can divide absorbance by the length and the concentration to get molar absorptivity on one side of the equation: ɛ = A/lc.[6]XResearch source We can now use this basic equation to calculate molar absorptivity for a given wavelength.
Absorbance between readings can vary due to the concentration of the solution and the shape of the container used to measure intensity. Molar absorptivity compensates for these variations.[7]XResearch source
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3 Obtain values for the variables in the equation using spectrophotometry. A spectrophotometer is a piece of equipment that passes a specific wavelength of light through a substance and detects the amount of light that comes out. Some of the light will be absorbed by the solution and the remaining light that passes through can be used to calculate the absorbance of that solution.
Prepare a solution of known concentration, c, for analysis. Units for concentration are molar or moles/liter.[8]XResearch source
To find l, measure the length of the cuvette, the piece that holds the liquid samples in the spectrophotometer. Units for path length are measured in centimeters.
Using a spectrophotometer, obtain a measurement for absorbance, A, at a given wavelength. The unit for wavelength is meters, but most wavelengths are so small, they are actually measured in nanometers (nm). Absorbance has no units.
4 Plug in the values for the variables and solve the equation for molar absorptivity. Using the values you obtained for A, c, and l, plug them into the equation ɛ = A/lc. Multiply l by c and then divide A by the product to solve for molar absorptivity.
For example: Using a cuvette with a length of 1 cm, you measured the absorbance of a solution with a concentration of 0.05 mol/L. The absorbance at a wavelength of 280 nm was 1.5. What is the molar absorptivity of this solution?
ɛ280 = A/lc = 1.5/(1 x 0.05) = 30 L mol-1 cm-1
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Calculating Molar Absorptivity Using a Line-of-Best-Fit
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1 Measure the intensity of transmitted light through varying concentrations of solution. Make up three to four concentrations of one solution. Using a spectrophotometer, measure the absorbance of one concentration of solution at a given wavelength. Start with the lowest concentration of solution and move to the highest. The order isn’t important, but keep track of which absorbance goes with which calculation.
2 Plot the concentration versus absorbance on a graph. Using the values obtained from the spectrophotometer, plot each point on a line graph. For each individual value, plot the concentration on the X-axis and absorbance on the Y-axis.[9]XResearch source
Draw a line between each of the points. If the measurements are correct, the points should form a straight line indicating absorbance and concentration are proportional to Beer’s Law.[10]XResearch source
3 Determine the slope of the line-of-best-fit through the data points. To calculate the slope of the line you take rise divided by run. Using two of your data points, subtract the X- and Y-values from each other, then divide Y/X.[11]XResearch source
The equation for the slope of a line is (Y2 - Y1)/(X2 - X1). The point higher on the line is given the subscript 2, while the lower point is given the subscript 1.
For example: The absorbance at a .2 molar concentration is 0.27 and at 0.3 molar is 0.41. The absorbance values are Y-values, while concentrations are X-values. Using the equation for a line (Y2 - Y1)/(X2 - X1) = (0.41-0.27)/(0.3-0.2) = 0.14/0.1 = 1.4 is the slope of the line.
4 Divide the slope of the line by the path length (depth of the cuvette) to calculate molar absorptivity. The final step to calculating molar absorptivity with data points is to divide by the path length. The path length is the depth of the cuvette used in the spectrophotometer.[12]XResearch source
Continuing our example: If 1.4 is the slope of the line and the path length is 0.5 cm, then the molar absorptivity is 1.4/0.5 = 2.8 L mol-1 cm-1.
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Question What is Beer Lambert's law? Mohsin257 Community Answer In simple words it states that light absorbed by the sample is directly proportional to the path length (l or x) and concentration. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 13 Helpful 35
Question Is the molar absorptivity constant, or does it change as the length of the cuvette changes? Community Answer It is constant. Units of molar absorptivity constant is in M^-1 cm^-1, which is essentially how much is absorbed per unit length. As the length of cuvette increases, more is absorbed as a whole, but the constant is independent of length of cuvette! Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 9 Helpful 20
Question How do I know the path length? Mohsin257 Community Answer It is known by sample compartment. Path-length is the area of the cell/sample compartment. It is mostly 1cm and depends on that compartment may be .5cm etc. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 19 Helpful 21
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Co-authored by: Ronitte Libedinsky, MS Chemistry and Biology Tutor This article was co-authored by Ronitte Libedinsky, MS. Ronitte Libedinsky is an Academic Tutor and the Founder of Brighter Minds SF, a San Francisco, California based company that provides one-on-one and small group tutoring. Specializing in tutoring mathematics (pre-algebra, algebra I/II, geometry, pre-calculus, calculus) and science (chemistry, biology), Ronitte has over 10 years of experience tutoring to middle school, high school, and college students. She also tutors in SSAT, Terra Nova, HSPT, SAT, and ACT test prep. Ronitte holds a BS in Chemistry from the University of California, Berkeley, and an MS in Chemistry from Tel Aviv University. This article has been viewed 847,147 times. 69 votes - 86% Co-authors: 20Updated: June 27, 2024 Views: 847,147 Categories: Chemistry CalculationsArticle SummaryX
To calculate molar absorptivity, make sure you first understand the Beer-Lambert law for absorbance. Then, rearrange the Beer-Lambert equation into an algebraic equation so you can solve for molar absorptivity. You can obtain the values for the variables in the algebraic equation by using spectrophotometry. Once you have the values, plug them in for the variables in your equation. Once those values are plugged in, solve the algebraic equation as you normally would. The answer you get is the molar absorptivity. If you want to learn how to calculate molar absorptivity with the line-of-best-fit, keep reading the article!Did this summary help you?YesNo
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Download Article Explore this Article methods 1 Calculating Molar Absorptivity with the Equation 2 Calculating Molar Absorptivity Using a Line-of-Best-Fit Other Sections Questions & Answers Video Related Articles References Article Summary Co-authored by Ronitte Libedinsky, MS 
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Co-authored by: Ronitte Libedinsky, MS Chemistry and Biology Tutor This article was co-authored by Ronitte Libedinsky, MS. Ronitte Libedinsky is an Academic Tutor and the Founder of Brighter Minds SF, a San Francisco, California based company that provides one-on-one and small group tutoring. Specializing in tutoring mathematics (pre-algebra, algebra I/II, geometry, pre-calculus, calculus) and science (chemistry, biology), Ronitte has over 10 years of experience tutoring to middle school, high school, and college students. She also tutors in SSAT, Terra Nova, HSPT, SAT, and ACT test prep. Ronitte holds a BS in Chemistry from the University of California, Berkeley, and an MS in Chemistry from Tel Aviv University. This article has been viewed 847,147 times. 69 votes - 86% Co-authors: 20 Updated: June 27, 2024 Views: 847,147 Categories: Chemistry Calculations Article SummaryX
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1 Understand the Beer-Lambert law for absorbance, A = ɛ x l x c. The standard equation for absorbance is A = ɛ x l x c, where A is the amount of light absorbed by the sample for a given wavelength, ɛ is the molar absorptivity, l is the distance that the light travels through the solution, and c is the concentration of the absorbing species per unit volume.[3] 
2 Rearrange the Beer-Lambert equation to solve for molar absorptivity. Using algebra we can divide absorbance by the length and the concentration to get molar absorptivity on one side of the equation: ɛ = A/lc.[6] We can now use this basic equation to calculate molar absorptivity for a given wavelength. 
3 Obtain values for the variables in the equation using spectrophotometry. A spectrophotometer is a piece of equipment that passes a specific wavelength of light through a substance and detects the amount of light that comes out. Some of the light will be absorbed by the solution and the remaining light that passes through can be used to calculate the absorbance of that solution. 
4 Plug in the values for the variables and solve the equation for molar absorptivity. Using the values you obtained for A, c, and l, plug them into the equation ɛ = A/lc. Multiply l by c and then divide A by the product to solve for molar absorptivity. 
1 Measure the intensity of transmitted light through varying concentrations of solution. Make up three to four concentrations of one solution. Using a spectrophotometer, measure the absorbance of one concentration of solution at a given wavelength. Start with the lowest concentration of solution and move to the highest. The order isn’t important, but keep track of which absorbance goes with which calculation. 
2 Plot the concentration versus absorbance on a graph. Using the values obtained from the spectrophotometer, plot each point on a line graph. For each individual value, plot the concentration on the X-axis and absorbance on the Y-axis.[9] 
3 Determine the slope of the line-of-best-fit through the data points. To calculate the slope of the line you take rise divided by run. Using two of your data points, subtract the X- and Y-values from each other, then divide Y/X.[11] 
4 Divide the slope of the line by the path length (depth of the cuvette) to calculate molar absorptivity. The final step to calculating molar absorptivity with data points is to divide by the path length. The path length is the depth of the cuvette used in the spectrophotometer.[12] 
Mohsin257 Community Answer In simple words it states that light absorbed by the sample is directly proportional to the path length (l or x) and concentration. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 13 Helpful 35 
Community Answer It is constant. Units of molar absorptivity constant is in M^-1 cm^-1, which is essentially how much is absorbed per unit length. As the length of cuvette increases, more is absorbed as a whole, but the constant is independent of length of cuvette! Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 9 Helpful 20 