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# Beer Lambert Law

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Beer Lambert law is one of the popular topics in analytical chemistry. It relates the weakening of the intensity of the light to the characteristics of the medium through which it is traveling.

Let’s say, we have a clear sample of a drug with a polished surface around its container.

Now, passing electromagnetic radiation (incident radiation or we may use UV rays) to the drug sample, some of the light may get absorbed, and the rest of it gets transmitted.

Here, the intensity of incident radiation = Io, and

The intensity of transmitted radiation = It

So, the absorbance A = log $(\frac{Io}{It})$

∴ It is a unitless quantity.

### What we will study in the Beer Lambert Law?

Here, we will focus on the factors which influence the absorption. So, the factors are:

• The concentration of the sample.

• The thickness of the medium.

• The temperature at which we will measure the absorbance.

• The wavelength of the EM radiation.

Point to Remember:

Here, the absorbance of the material will be measured at the wavelength at which we would observe the maximum absorption, and the temperature will be kept at the uniform level.

This is how we will use Beer Lambert law to determine the absorbance of any number of samples.

This article will explain Beer Lambert law most simply.  So, let’s get started.

### Beer Lambert Law Definition

Beer Lambert law consists of the following two laws:

• Lambert’s Law

This law is concerned with the thickness of the medium.

• Beer’s Law

This law is concerned with the concentration of the solution via which monochromatic radiation passes.

Lambert’s Law

When monochromatic radiation (it can be UV rays) is passed through a medium, the intensity of the transmitted radiation decreases with the increase in the thickness of the absorbing medium, and it varies directly with the incident radiation.

Mathematically, we can express this statement as:

$-\frac{dIo}{db}$= k’Io  (Here, the negative sign indicates the decrease in the intensity of the transmitted radiations)...(1)

Equation (1) says that the rate of decrease in the intensity to the thickness is directly proportional to the incident radiation.

Now, equation  (1) can be rewritten as:

It = Io 10-k'b….(2)

Here,  It = Intensity of transmitted radiation

k’ = Proportionality constant

We can write the equation (1) in the following way as well:

A = log $(\frac{Io}{It})$ α b

This expression says that the absorbance of light in a homogenous material/medium is directly proportional to the thickness of the material/medium.

So, A = εb….(p)

### Beer’s Law

When monochromatic light passes through a ‘transparent medium’, the rate of decrease of transmitted radiation with the increase in the concentration of the medium is directly proportional to the intensity of the incident light.

We can express this statement mathematically as;

$-\frac{dIo}{dc}$ = kIo….(3)

We can rewrite this equation as:

It = Io 10- k''c….(4)

Another form of writing equation (3) is:

A = log$(\frac{Io}{It})$ α b

This expression says that the absorbance of light in a homogenous material/medium is directly proportional to the concentration of the sample.

Now, we get our simplified expression as:

A =  εb….(q)

### Beer Lambert Law Derivation

For determining the Beer Lambert law equation, let’s combine equation (2) & (4), and take the log of these, we get:

log$(\frac{Io}{It})$ = k’k’’bc….(5)

We can express equation (5) as:

A = εbc…(6)

Equation (6) is the required Beer Lambert Law Formula.

Where,

A = Absorption

ε = Molar absorption coefficient or molar absorptivity in m-1cm-1= k’ x k’’

b = Thickness of the medium in cm

c = Molar concentration in M

So, the final Beer Lambert law statement is:

When monochromatic radiation passes through a homogeneous medium, then the rate of decrease in the intensity of the transmitted radiation with the increase in the thickness of the medium and the concentration of the solution varies directly with the intensity of incident radiation.

### Beer Lambert Law Applications

The important use of the Beer Lambert law is found in the electromagnetic spectroscopy.

Now, let’s understand the applications of Beer Lambert law:

• To analyze the drugs, for that, let’s take an example of a tablet:

Let’s suppose we have a tablet and we don’t know which drug is present in it. Though we may know the drug, then the question arises about what its molar concentration is.

In electromagnetic spectroscopy, we use electromagnetic radiation (we may take UV rays), which scans the tablet and determines the qualitative (drug present) and the quantitative (concentration) property of the tablet.

• The same method can be used in determining the molar absorbance of bilirubin in blood plasma samples.

• We use Beer Lambert Law to conduct a qualitative and quantitative analysis of biological and dosimetric materials that may contain organic or inorganic materials.

• We can determine the concentration of various substances in cell structures by measuring their absorbing spectra in the cell.

Question 1: How do you calculate the Absorbance?

Answer: We calculate the absorbance by using the following formula:

Ay = - log (Io/It) of a light with the wavelength ‘y’.

Here, Io/It = Transmittance of the testing material/sample. We need to understand that  absorbance is a pure number having no unit.

Question 2: How the Absorbance helps determine the concentration of a solution?

Answer: The value of the absorbance lies between 0.1 and 1. If the absorbance of material is greater than or equal to 1.0 (too high), then we can say that the solution has a higher concentration.

Question 3: What is the slope of Beer’s Law Graph?

Answer: We can determine the absorbance of a chemical or biological molecule in a given sample by using Beer-Lambert’s law. Below is the graph of the absorbance versus concentration of the solution: