Beer-Lambert Law

Principles of the Beer-Lambert Law

Every chemical species absorbs light at a given wavelength
Chemists use the absorbing properties of chemical compounds for quantitative analysis, using solutions as samples
The amount of light absorbed by a sample is called absorbance
Absorbance (A) depends on three variables:
- Molar absorptivity in mol^-1 dm³ (ε): How strongly a molecule or ion absorbs light of a specific wavelength
- Length in cm (b): The length of the path in which light travels through the sample
- Concentration in M(c); How much absorbing material is present in the sample
Absorbance does not have units of measurement. and it is directly proportional to molar absorptivity, length, and concentration. Therefore, the Beer-Lambert Law is given by:

$A = ε b c$

Beer-Lambert Law in Experiments

In most experiments, molar absorptivity (ε) and the length (b) are constant, therefore, Absorbance (A) is proportional just to the concentration of molecules or ions present in the sample
This mathematical relation can be used to build a calibration curve
A calibration curve is a method used to calculate the concentration of an unknown sample, by comparing its absorbance with the absorbance of standards
Standards are solutions with known concentration

How to build a calibration curve?

Prepare a series of standard solutions
Measure the absorbance at the best possible wavelength
Plot an Absorbance vs Concentration curve
Draw a line of best fit (it must have a linear positive correlation)

Example of Calibration Curve

graph-showing-a-calibration-curve-absorbance-vs-concentration

Graph showing a calibration curve Absorbance vs Concentration

Exam Tip

There is a high probability that you will be assessed in Beer-Lambert Law either in Section I or II. In most scenarios, they will give you the calibration curve and the absorbance of an unknown sample. Therefore, you will need to calculate the concentration of the sample using the line equation for the calibration curve

Worked example

A student has prepared an experiment to determine the concentration of X (aq) in an unknown sample. The absorbance at different concentrations is shown below:

calibration-curve-built-from-samples-of-x-with-known-concentration

Calibration curve built using standard samples of X

If the absorbance of the unknown sample is 0.275 at 420 nm, what is the concentration of X in the unknown sample?

Answer:

Step 1: Set up the equation of the line to show the relation between absorbance and concentration

$A = mc + b$

Step 2: Calculate the gradient (m) for the equation of the line of the calibration curve, using the data for two nearest standard solutions

$Data point 1 (0.002, 0.10)$

$Data point 2 (0.004, 0.22)$

$m = \frac{A_{2} - A_{1}}{c_{2} - c_{1}}$

$m = \frac{0.22 - 0.1}{0.004 - 0.002}$

m = 60

Step 3: Calculate the y axis intercept (b) for the calibration curve by replacing A and c with one of the data points used in Step 1

$Data point 1 (0.002, 0.10)$

$A = 60 c + b$

$0.10 = 60 (0.002) + b$

$0.10 - 60 (0.002) = b$

$b = - 0.02$

Step 4: Complete the equation of the line for the calibration curve using the calculated values of m and b

$A = 60 c - 0.02$

Step 5: Rearrange the equation of the line in terms of the concentration (c)

$A = 60 c - 0.02$

$A + 0.02 = 60 c$

$c = \frac{A + 0.02}{60}$

Step 4: Calculate the concentration of X in the unknown sample, using the absorbance given in the problem statement by replacing its value in the equation obtained in st

$c = \frac{A + 0.02}{60}$

$c = \frac{0.275 + 0.02}{60}$

$c = 4.92 \times 10^{- 3} M$

Beer-Lambert Law (College Board AP Chemistry)

Revision Note

Beer-Lambert Law

Principles of the Beer-Lambert Law

Beer-Lambert Law in Experiments

How to build a calibration curve?

Example of Calibration Curve

Exam Tip

Worked example

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Author: Martín