Molar absorbivity, also known as the molar extinction coefficient, measures the ability of a chemical species to absorb a given wavelength of light. This information allows you to perform a comparative analysis between different chemical compounds without having to take into account the differences in concentration or size of the solution during the measurements. This is a widely used data in chemistry, which should not be confused with the extinction coefficient that is most commonly used in physics. The standard unit of molar absorbivity is liters per mole per centimeter (L mol-1 cm-1).
Steps
Method 1 of 2: Calculate Molar Absorbivity Using the Equation
Step 1. Understand the Beer-Lambert law of absorbivity:
A = ɛlc. The standard equation for absorbance is A = ɛlc, where A represents the amount of light emitted by the chosen wavelength and absorbed by the sample under test, ɛ is the molar absorbivity, l is the distance traveled by the light through the chemical solution under examination and c is the concentration of the absorbent chemical species per unit volume of the solution (ie the "molarity").
- Absorbance (formerly known as "optical density") can also be calculated using the ratio between the intensity of a reference sample and that of the unknown sample. It is expressed by the equation A = log10(THEor/ I).
- Intensity is measured using a spectrophotometer.
- The absorbance of a solution varies according to the length of the light wave passing through it. Some wavelengths are absorbed more than others, based on the composition of the solution under examination, so it is good to remember to always indicate which wavelength was used to perform the calculation.
Step 2. Use the inverse formula of the Lambert-Beer equation to calculate molar absorbivity
According to the algebraic rules, we can divide the absorbance by the length and the concentration in order to isolate the molar absorbivity in a member of the initial equation, obtaining: ɛ = A / lc. At this point, we can use the equation obtained to calculate the molar absorbivity of the wavelength of light used for the measurement.
The absorbance of the different measurements may vary depending on the concentration of the solution and the shape of the container that was used to measure the intensity of the light. Molar absorbivity compensates for these variations
Step 3. Using a spectrophotometer you can measure the values to be substituted for the respective variables present in the equation
The spectrophotometer is an instrument that measures the amount of light, at a specific wavelength, that is able to pass through the solution or compound under examination. A part of the light will be absorbed by the studied solution, while the remainder will pass through it completely and will be used to calculate its absorbance.
- Prepare the solution to be studied using a known degree of concentration which will be substituted for the variable c of the equation. The unit of measurement of concentration is the mole (mol) or the mole per liter (mol / l).
- To measure the variable l, you need to physically measure the length of the tube or container used to store the solution. In this case the unit of measurement is centimeters.
- Use a spectrophotometer to measure the absorbance, A, of the test solution, based on the wavelength chosen for the measurement. The unit of measurement for wavelength is the meter, but since most waves have a much shorter length, in reality, the nanometer (nm) is used much more often. Absorbance is not associated with any unit of measure.
Step 4. Replace the measured values with the relevant variables in the equation, then perform the calculations to obtain the molar absorption coefficient
Use the values obtained for the variables A, c and l and replace them within the equation ɛ = A / lc. Multiply l by c, then divide A by the result of that product to calculate molar absorbivity.
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For example, let's assume we are using a test tube with a length of 1 cm and measuring the absorbance of a solution with a concentration degree equal to 0.05 mol / L. The absorbance of the solution in question, when it is crossed by a wave of length equal to 280 nm, is 1, 5. So what is the molar absorbivity of the solution in question?
ɛ280 = A / lc = 1.5 / (1 x 0.05) = 30 L mol-1 cm-1
Method 2 of 2: Calculate Molar Absorbivity Graphically
Calculate Molar Absorptivity Step 5 Step 1. Measure the intensity of the light wave as it passes through different concentrations of the same solution
Make 3-4 samples of a solution at different concentrations. It uses a spectrophotometer to measure the absorbance of each of the solution samples when a specific wavelength of light passes through them. Start testing the solution sample with the lowest concentration and then move on to the one with the highest concentration. The order in which you take your measurements is not important, but it serves to keep track of which absorbance to use during the various calculations.
Calculate Molar Absorptivity Step 6 Step 2. Draw a graph of the trend of the measurements by concentration and absorbance
Using the data obtained from the spectrophotometer, plot each point on a line graph. Reports the concentration on the X axis and the absorbance on the Y axis, then uses the measured values as the coordinates of each point.
Now join the points obtained by drawing a line. If your measurements are correct, you should get a straight line indicating that, as expressed by the Beer-Lambert law, absorbance and concentration are related by a proportional relationship
Calculate Molar Absorptivity Step 7 Step 3. Determine the slope of the trend line defined by the various points obtained from the instrumental measurements
To calculate the slope of a straight line, the appropriate formula is used which involves subtracting the respective X and Y coordinates of two points chosen from the straight line in question and then calculating the Y / X ratio.
- The equation for the slope of a line is (Y2 - Y1) / (X2 - X1). The highest point of the line under examination is identified by index 2, while the lowest point is indicated by index 1.
- For example, let's assume that the absorbance of the solution under test, at a concentration of 0.2 mol, is equal to 0.27, while that at a concentration of 0.3 mol is 0.41. The absorbance represents the Cartesian coordinate Y, while the concentration represents the Cartesian coordinate X of each point. Using the equation to calculate the slope of a straight line we will obtain (Y2 - Y1) / (X2 - X1) = (0, 41-0, 27) / (0, 3-0, 2) = 0, 14/0, 1 = 1, 4, which represents the slope of the drawn line.
Calculate Molar Absorptivity Step 8 Step 4. Divide the slope of the line by the length of the light wave path (in this case the depth of the tube) to obtain the molar absorbivity
The final step of this method for calculating the molar absorption coefficient is to divide the slope by the length of the path taken by the light wave used for the measurements. In this case, we will have to use the length of the tube used for the measurements made with the spectrophotometer.
In our example, we have obtained a slope of 1, 4 of the line that represents the relationship between absorbency and chemical concentration of the solution under examination. Assuming that the length of the tube used for the measurements is 0, 5 cm, we will obtain that the molar absorbivity is equal to 1, 4/0, 5 = 2, 8 L mol-1 cm-1.
