# How to Calculate Molar Absorptivity: 8 Steps

Molar absorptivity, also known as the molar extinction coefficient, is a unit that measures the ability of chemical species to absorb a given wave of light. During measurements, this unit allows you to compare compounds without taking into account differences in concentration or length of the solution. It is generally used in the field of chemistry and one should avoid confusing it with the extinction coefficient, which is used most often in physics. The standard units for molar absorptivity are liters per molar centimeter (L mol-1 cm-1).

## Steps

### Method 1 of 2: Calculate Molar Absorptivity Using an Equation

#### Step 1. Study the Beer-Lambert law for absorbance, A = ɛlc

The standard equation for absorbance is A = ɛlc, where A represents the amount of light absorbed by the sample in a given wave; ɛ, molar absorptivity; l the distance that light travels through the solution; and c, the concentration of the absorbent species per unit volume.

• You can also calculate absorbance using the relationship between the intensity of a reference sample and the unknown sample. The equation is expressed as follows: A = log10(Ior/ I).
• The intensity is obtained with the help of a spectrophotometer.
• The absorbance of a solution will change based on the wavelength that passes through it. Depending on the composition of the solution, some wavelengths will be absorbed more than others. Do not forget to indicate which wavelength you will use to make the calculation.

#### Step 2. Rearrange the Beer-Lambert equation to find the molar absorptivity

With the help of some algebraic calculations, we can divide the absorbance between the length and the concentration in order to pass the molar absorptivity to one side of the equation: ɛ = A / lc. Now we can use this basic equation to calculate the molar absorptivity of a given wavelength.

### The absorbance between readings can vary due to the concentration of the solution and the shape of the container where the intensity is measured. Molar absorptivity compensates for these variations

#### Step 3. Use spectrophotometry to find the values of the variables in the equation

A spectrophotometer is a device that makes a certain wavelength pass through a substance and thus detects the amount of light that comes out. The solution will absorb part of the light, while the rest that passes through it can be used to calculate the absorbance of said solution.

• Prepare a solution of a known concentration, c, for analysis. The units in which the concentration is expressed are the mole or moles per liter.
• To find l, measure the length of the bucket. Keep in mind that the unit to measure the trajectory is the centimeter.
• Use a spectrophotometer to obtain a measurement of the absorbance, A, at a given wavelength. The unit that represents wavelengths is the meter, but most of them are so small that they are actually measured in nanometers (nm). There is no unit to represent absorbance.

#### Step 4. Plug in the values of the variables and solve the equation to find the molar absorptivity

Plug the values you got for A, c, and l into the equation ɛ = A / lc. Now multiply l by c and then divide A by the product to find the molar absorptivity.

• Example: with a 1 cm long cuvette, you measured the absorbance of a solution that has 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

### Method 2 of 2: Calculate Molar Absorptivity Using the Compensation Line

#### Step 1. Measure the intensity of light transmitted through solutions of varying concentrations

Make three to four concentrations of a solution. Now use a spectrophotometer to measure the absorbance of a concentration at a certain wavelength. Start with the lowest until you finish with the highest. The order is irrelevant, but it keeps track of which absorbance fits a certain calculation.

#### Step 2. Use a graph to plot concentration versus absorbance

Use the values you obtained with the spectrophotometer to plot each point on a line graph. For each individual value, place the concentration on the "X" axis and the absorbance on the "Y" axis.

### Draw a line between each point. If the measurements are correct, the points should form a straight line indicating that the absorbance and concentration are proportional to the Lambert-Beer Law

#### Step 3. Use the data points to determine the slope of the compensation line

To calculate the slope of the line, you will need to divide the elevation by the path. Using two data points, subtract the “X” and “Y” values from each other, and then divide Y / X.

• The equation to find the slope of a line is as follows: (Y2 - AND1) / (X2 - X1). The highest point of the line is represented by the subscript 2, while the lowest point is represented by the subscript 1.
• Example: the absorbance at a molar concentration of 0.2 is 0.27, and at a concentration of 0.3 it is 0.41. The absorbance values are those found in "Y", while the concentrations are the values of "X". If we use the equation to calculate the slope of a line, we will obtain the following: (Y2 - AND1) / (X2 - X1) = (0, 41-0, 27) / (0, 3-0, 2) = 0, 14/0, 1 = 1, 4, figure that represents this slope.

#### Step 4. Divide the slope of the line by the path length (depth of the cuvette) to calculate the molar absorptivity

The last step in calculating molar absorptivity with data points is to divide the path length. This is the depth of the cuvette used in the spectrophotometer.

• Continuing with the previous 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.