Beer Lambert Law

Beer-Lambert law describes the relationship between the attenuation of light through a substance with the properties of that substance. It asserts that the length of a sample route and the concentration of a solution are proportional to the light’s absorbance. This law is dependent on the properties of the solution in question. It elaborates on the linear relationship between the concentration and absorbance of a solution.

Beer-Lambert Law Statement

The Beer-Lambert law states that: for a given material sample path length and concentration of the sample are directly proportional to the absorbance of the light.

A ∝ L

A ∝ c

where L is the path length and c is the concentration of the sample.

Beer-Lambert Formula

According to Beer-Lambert law, the absorption capacity of light is equal to the product of its molar absorption coefficient, molar concentration, and optical path length.

Since, A ∝ Lc

A = εLc

ε = A/LC

where,

A is the absorbed light for a wavelength by the solution,
ε is the molar absorption coefficient,
L is the distance travelled by light through the solution,
c is the solution concentration.

Beer-Lambert Law Equation

The Beer-Lambert law can also be expressed in terms of relative intensity, the path length of a solution, and molar absorption coefficient as:

I = I_o e^–εL

where,

I_o is the initial intensity,
I is the final intensity,
ε is the molar absorption coefficient,
L is the path length of travelling light.

Beer-Lambert Law Derivation

The Beer’s law states that there exists a direct relation between the concentration and absorbance of a solution.

A ∝ c   …… (1)

The Lambert’s law states that there exists a direct relation between the absorbance and path length of a solution.

A ∝ L  …… (2)

Now we know that if a quantity is proportional to two different quantities, it means that it is directly proportional to their product also. Using this principle we have,

A ∝ c L

Replacing the proportionality symbol with constant, which in this case is the molar absorption coefficient, we get

A = εLc

This derives the formula for Beer Lambert law.

What Is Beer’s Law?

Beer’s law was stated by August Beer states that concentration and absorbance are directly proportional to each other.

What Is Lambert Law?

Johann Heinrich Lambert stated Lambert law. It states that absorbance and path length are directly proportional.

Beer-Lambert Law Applications

This law finds applications in various fields such as:

Analytical Chemistry

In analytical chemistry, Beer-Lambert law has got its application in the quantitative analysis of matter by spectrophotometer. For Example, the pathology lab studies the Bilirubin count for a given blood sample using a spectrophotometer which is based on Beer-Lambert Law. 

In Atmosphere

The dust particles and gases in the atmosphere result in the scattering and absorption of the sunlight coming into the earth’s atmosphere. Hence, this absorption can be calculated using the formula mentioned below:

T = e^-m(T_a ^{+ T}_g ^{+ T}_RS ^{+ T}_NO2 ^{+ T}_w ^{+ T}_O3 ^{+ T}_r^..)

Where,

a is the aerosols

g is the mixed gases

RS is the Raman scattering effect.

NO₂ is Nitrogen dioxide

w is the water vapour absorption

O₃ is Ozone

r is Rayleigh scattering

Beer-Lambert Law Limitation

Beer-Lambert Law can be successfully used to study absorption when the concentration of the sample is less than 10 millimoles, above it the law is not applicable successfully due to the increased electrostatic interaction between the particles of the sample.

Read More,

• Diffraction of Light
• Tyndall Effect

Solved Examples on Beer-Lambert Law

Example 1: Find the absorbance of a solution if its concentration is 1 mole/litre, the molar absorption coefficient is 6240 M/cm and the path length is 0.002 m.

Solution:

We have, 

c = 1, ε = 6240 and L = 0.002

Using Beer Lambert law, we have

A = εLc

= 6240 (0.002) (1)

= 124.8

Example 2: Find the absorbance of a solution if its concentration is 1000 millimoles/litre, the molar absorption coefficient is 5342 mM/cm and the path length is 0.00001 mm.

Solution:

We have,

c = 1000, ε = 5342 and L = 0.00001

Using Beer Lambert law, we have

A = εLc

= 5342 (0.00001) (1000)

= 5.342

Example 3: Find the concentration of a solution if its absorbance is 6.85, the molar absorption coefficient is 2371 mM/cm and the path length is 321 nm.

Solution:

We have,

A = 6.85, ε = 2371 and L = 321

Using Beer Lambert law, we have

A = εLc

6.85 = 2371 (321) c

c = 6.85/761091

c = 90 nM

Example 4: Find the path length of a solution if its absorbance is 0.37, the molar absorption coefficient is 3298 mM/cm and the concentration is 75 μM.

Solution:

We have,

A = 0.37, ε = 3298 and c = 75

Using Beer Lambert law, we have

A = εLc

0.37 = (3298) (75) L

L = 0.37/247350

L = 15.23 μM

Example 5: Find the relative intensity of light absorbed by the solution if it has an absorbance of 2.

Solution:

We have, A = 2.

Using Beer Lambert law, we have

A = log₁₀ (I₀/I)

I₀/I = 10 A

Putting A = 2, we have

I₀/I = 20

I/I₀ = 1/20

1 – I/I_o = 1 – 1/20

(I_o – I)/I_o = 19/20

[(I_o – I)/I_o] × 100 = (19/20) × 100

R = 95%

Example 6: Find the relative intensity of light absorbed by the solution if it has an absorbance of 5.

Solution:

We have, A = 5.

Using Beer Lambert law, we have

A = log₁₀ (I₀/I)

I₀/I = 10 A

Putting A = 5, we have

I₀/I = 50

I/I₀ = 1/50

1 – I/I_o = 1 – 1/50

(I_o – I)/I_o = 49/50

[(I_o – I)/I_o] × 100 = (49/50) × 100

R = 98%

Example 7: Find the relative intensity of light absorbed by the solution if it has an absorbance of 1.5.

Solution:

We have, A = 1.5.

Using Beer Lambert law, we have

A = log₁₀ (I₀/I)

I₀/I = 10 A

Putting A = 1.5, we have

I₀/I = 15

I/I₀ = 1/15

1 – I/I_o = 1 – 1/15

(I_o – I)/I_o = 14/15

[(I_o – I)/I_o] × 100 = (14/15) × 100

R = 93.33%

FAQs on Beer-Lambert law

Q1: Define Beer-Lambert Law

Answer:

Beer-Lambert law state that for any material the sample path length and the sample’s concentration are directly proportional to the absorbance of the light.

Q2: What are the limitations of Beer-Lambert Law?

Answer:

Various limitations of the Beer-Lambert law are,

• It only works for the diluted solution.
• It fails when the scattering of the light beam occurs.
• It only works with Monochromatic Electromagnetic Radiation.

Q3: Why does Beer-Lambert Law fail at higher concentrations?

Answer:

Beer-Lambert law fails at higher concentrations because higher concentration changes the refractive index of the solution and at higher concentrations, the molecule of the concentration are very close to each other which decreases the absorptivity of the solution.

Q4: Who discovered the Beer-Lambert Law?

Answer:

The base of Beer-Lambert law was provided by Pierre Bouger in 1729.

Q5: What is the Beer-Lambert law Equation used for?

Answer:

Beer-Lambert law is used to relate the movement of light with the properties of the material in which it is travelling which is very helpful in spectrophotometry and other activities.

Q6: Why is Beer-Lambert Law important?

Answer:

Beer’s law is one of the most important laws of science. It finds its uses in various fields such as Physics, Chemistry and Meteorology. The law helps us to measure the concentration of chemical solutions, measure the degradation of polymers and analyze oxidation reactions.

Q7: When does the Beer-Lambert Law fail?

Answer:

Beer-Lambert law fails for the solution containing a higher solution i.e. the concentration greater than 10^-2 M.