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Langmuir Adsorption Isotherm - Assumptions, Mathematical and Graphical Representations, Practice Problems and FAQ

Adsorption isotherms have been used extensively in research on environmental protection and adsorption strategies. Two of the most common approaches for forecasting a material's adsorption capacity are the Freundlich and Langmuir isotherms.

Adsorption is of two types: physisorption and chemisorption. Because the mechanisms of both types of adsorption differ, we require different isotherms to describe them. This concept page will go into detail about the Langmuir Adsorption isotherm and the type of adsorption it deals with.

• Langmuir Adsorption Isotherm and its Assumptions
• Mathematical Representation
• Graphical Representation
• Practice Problems
• Frequently Asked Questions - FAQ

Langmuir Adsorption Isotherm and its Assumptions

Based on the theoretical considerations of the kinetic theory, Langmuir derived an adsorption isotherm. This isotherm is termed the Langmuir adsorption isotherm. Langmuir considered two opposite processes taking place during adsorption namely, adsorption of the gas molecules on the surface of the solid and desorption of the adsorbed gas molecules from the surface of the solid.

1. Adsorbed gas is considered to behave ideally.

2. A solid surface is considered homogenous but contains a fixed number of adsorption sites on the surface.

3. Each site adsorbs a single molecule i.e. adsorption is unimolecular. As unimolecular adsorption occurs in the case of chemisorption, Langmuir adsorption isotherm works better for chemisorption.

4. Rate of adsorption is equal to the rate of desorption.

5. There is no lateral overlapping between adsorbed molecules.

Mathematical Representation

∝

Fraction of surface covered =

Pressure of the gas = P

For a reversible physisorption process,

… … … … …

Case 2: For desorption

… … … … …

Where is the desorption rate constant.

We know,

Rate of adsorption = Rate of desorption

On equating equations and ,

On rearranging,

Dividing the numerator and the denominator by

Let

According to Langmuir, the extent of adsorption is proportional to

Where is a proportionality constant.

= … … … … …

Where are Langmuir parameters

At high pressure,

Using equation

becomes independent of pressure i.e. the surface is fully covered and change in pressure has no effect on further adsorption.

At low pressure,

Using equation

increases linearly with pressure.

Graphical Representation

At low pressure,

At high pressure,

Hence, Langmuir isotherm could explain the variation of the extent of adsorption with pressure for wider ranges of pressure.

Determination of Values of a and b

Taking the reciprocal of equation

… … … … …

On comparing equation with the equation of a straight line,

Slope ( =

Intercept ( =

Values of a and b can be determined using the slope and intercept of the vs curve.

Practice Problems

Q. 1. Langmuir isotherm is valid for which kind of adsorption?

a. Monolayer
b. Multilayer
c. Both A and B
d. None of the above

So, option (A) is the correct answer.

Q. 2. is a form of Langmuir isotherm obtained under which condition? a. At low pressure
b. At high pressure
c. Both A and B
d. None of the above

Answer: The general equation of Langmuir isotherm is given by the equation,

Where are Langmuir parameters

At low pressure,

So, option A) is the correct answer.

Q. 3. The plot of vs is:
a. Straight line plot
b. Exponential plot
c. Hyperbolic plot
d. Gaussian plot

Answer: is the required equation for plotting vs graph.

On comparing with the equation of a straight line,

Slope ( =

Intercept ( =

Thus, its a straight-line plot

So, option A) is the correct answer.

Q. 4. The true statements regarding Langmuir isotherm are

a. Surface is fully covered in case of high pressure.
b. Surface is fully covered in case of low pressure.
c. Both A and B\
d. None of the above

From the equation, =

= =

becomes independent of pressure i.e. the surface is fully covered and change in pressure has no effect on further adsorption.

So, option A) is the correct answer.

Q 1. How is Langmuir isotherm different from Freundlich isotherm?

Q 2. What is adsorption isotherm in general?
The variation in the amount of gas adsorbed by the adsorbent with pressure at constant temperature can be expressed by a curve termed an adsorption isotherm.