Molar absorptivity, otherwise known as the molar attenuation coefficient, is a measure of how well a chemical species absorbs light of a certain wavelength. This allows comparisons between compounds without the need to consider differences in solution concentration and the width of the solution container when making measurements. Molar absorptivity is commonly used in chemistry and should not be confused with the exclusion coefficient which is more commonly used in the physical sciences. The standard unit of measure for molar absorptivity is liters per mole centimeter (L mol-1 cm-1).
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Method 1 of 2: Calculating Molar Absorptivity Using Equation
Step 1. Understand Beer-Lambert Law, A = bc
The standard equation for absorbance is A = bc, A is the amount of light of a certain wavelength absorbed by a chemical sample, is the molar absorptivity, b is the distance light must travel through the sample solution or the width of the container, and c is the concentration of the compound per unit volume..
- Absorbance can also be calculated using the ratio between the reference sample and the unknown sample. The equation that can be used is A = log10(Io/i).
- The intensity was obtained using a spectrophotometer.
- The absorbance of a solution will change based on the wavelength that passes through it. Certain wavelengths will be absorbed more than other wavelengths depending on the character of the solution. Don't forget to state the wavelength used in your calculations.
Step 2. Rearrange the Beer-Lambert Law equation to solve for the molar absorptivity
Using algebra, we can divide the absorbance value by the width of the solution container and the concentration level of the solution to determine the molar absorptivity in the equation: = A/bc. We can use this equation to calculate the molar absorptivity for a given wavelength.
Absorbance measurements carried out more than once can produce different readings due to differences in the concentration of the solution and the shape of the container used to measure the intensity. Molar absorptivity overcomes this kind of difference
Step 3. Find the value of the required variable in the equation using spectrophotometry
A spectrophotometer is a device that emits light with a certain wavelength through a solution and detects the amount of light that comes out. Some of the light will be absorbed by the solution and the remaining light that has passed through the solution is used to calculate the absorbance value of the solution.
- Prepare a solution of known concentration, c, for analysis. The unit of measure for the concentration of a solution is molar or mole/liter.
- To find b, measure the width of the container. The unit of measure for the container is centimeters (cm).
- Using a spectrophotometer, measure the absorbance value, A, using light of a certain wavelength. The unit of measurement for wavelength is the meter, but most wavelengths are so small that they are generally measured in nanometers (nm). Absorbance has no unit of measure.
Step 4. Enter the values of the variables that have been found into the molar absorptivity equation
Plug the values obtained for A, c, and b, into the equation = A/bc. Multiply b and c then divide A by the product of “b” and “c” to determine the value of the molar absorptivity.
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Example: Using a container 1 cm wide, you measure the absorbance value of a solution with a concentration of 0.05 mol/L. The absorbance value of the solution using a wavelength of 280 nm is 1.5. What is the molar absorptivity of this solution?
️280 = A/bc = 1.5/(1 x 0.05) = 30 L mol-1 cm-1
Method 2 of 2: Calculating Molar Absorptivity Using Linear Curves
Step 1. Measure the intensity of light emitted through a solution of various concentrations
Make three or four solutions of the same type, but with different concentrations. Using a spectrophotometer, measure the absorbance value of a solution with various levels of concentration using light of a certain wavelength. Start with the solution with the lowest concentration to the solution with the highest concentration. The order of operation is not important, but note carefully the pair of absorbance values and the calculation of the concentration level of the solution.
Step 2. Map the concentration level of the solution and the absorbance value into a graph
Using the values obtained from the spectrophotometer, plot each point onto a line graph. To get a point, use the concentration level of the solution for the X-axis and the absorbance value for the Y-axis.
Draw a line following the dots. If the measurement is carried out correctly, the dots will form a straight line indicating the absorbance value and the concentration level of the solution which is proportional to Beer's Law
Step 3. Determine the gradient of the straight line formed from the data points
To calculate the gradient of a line, divide the vertical change value by the horizontal change value. Using two data points, find the difference between the Y value and the X value, then divide the difference in the Y value by the difference in the X value (Y/X).
- The equation of the gradient of the line is (Y2 - Y1)/(X2 - X1). Higher data points are subscripted 2 and lower data points are given subscript 1.
- Example: With a solution concentration level of 0.27, the absorbance value is recorded as 0.2 molar and with a solution concentration level of 0.41, the absorbance value is 0.3 molar. The absorbance value is Y while the concentration level of the solution is X. Using the line equation (Y2 - Y1)/(X2 - X1) = (0, 41-0, 27)/(0, 3-0, 2) = 0, 14/0, 1 = 1, 4 is a straight line gradient.
Step 4. Divide the gradient of the line by the width of the solution container to obtain the molar absorptivity
The final step to obtain the molar absorptivity is to divide the gradient by the width. Width is the thickness of the solution container used in the spectrophotometric process.
