Langmuir isotherm and Freundlich isotherm, Adsorption Phenomenon (Part2) and MCQs for GPAT, NIPER, Pharmacist and Drug Inspector exam

Many attempts have been made to develop a mathematical expression that relates the amount of the adsorbate per unit weight of adsorbent to a function of the solute concentration remaining in the solution at a fixed temperature. The most frequently used equations to fit the experimentally observed isotherm are Langmuir, Freundlich, and Brunner, Emmett and Teller (BET).

Langmuir isotherm: Langmuir tried to explain adsorption in terms of dynamic equilibrium between the rates of adsorption and desorption. He derived an equation based on the following facts:

1. Every active site of the adsorbent acts in the same way
2. Adsorbate is adsorbed on the surface of the solid (adsorbent) to form a monolayer
3. The rate of adsorption is proportional to the concentration of the adsorbate [A] and the number of unoccupied sites available (1 – α)

Rate of adsorption of solute = k_a [A] (1 – α)

where ka is the adsorption rate constant.

4. The adsorbed substances tend to escape from the surface and therefore the rate of desorption is proportional to the number of occupied sites (α)

Rate of desorption of solute =  k_d α

where kd is the desorption rate constant.

5. At equilibrium, the rates of adsorption and desorption are equal

k_a [A] (1 – α) = k_d α

or

α = k_a [A] / k_a [A] + k_d

If a monolayer of the solute covers the surface of the adsorbent, the amount of solute, adsorbed per unit weight of adsorbent, is directly proportional to the fraction D of the surface occupied with the solute:

q_e = k’ α

where k’ is a constant. Substituting above equations and dividing the resulting equation by kd yields the following:

q_e = (k_a k’/ k_d) [A] / 1 + (k_a/k_d) [A] = k₁A/1+k₂A

where, k_{1 =} k_a k’/ k_d and k₂ = k_a/k_d

In a double reciprocal form, the equation is rearranged as follows:

1/ q_e = k₁/ k₂ + 1/ k₁ (1/[A])

Hence the plot of 1/qe versus 1/[A] gives a slope of 1/K1 and an intercept of K1/K2.

Freundlich isotherm: There are two special cases of the Langmuir isotherm.

For very low concentrations (i.e. K2[A] << 1) the specific adsorption is proportional to the concentration of the adsorbate:

q_e = k₁/[A]

For very high concentrations (i.e. K2[A] >> 1) the specific adsorption is independent of the concentration of the adsorbate:

q_e = k₁/k₂

For intermediate concentration, the Freundlich equation for adsorption at a given temperature is

q_e = k[A]ⁿ

where k and n are constants and the value of n ranges from 0 to 1.

When n = 1, the Freundlich equation is identical to the very low concentration case of the Langmuir isotherm.

When n = 0, the Freundlich equation is identical to the very high concentration case of the Langmuir isotherm.

The logarithmic form of Freundlich equation is

log qe = log k + n log [A]

Plotting qe against log [A] gives a straight line with a slope n and intercept log k

Multiple choice questions (MCQs)

1.BET stands for

a)Brunner, Emmett and Teller

b)Burner, Emmett and Teller

c)Brunner, Emet and Teller

d)Brunner, Emmett and Tailor

2.Langmuir tried to explain adsorption in terms of _____ between the rates of adsorption and desorption. 

a)Dynamic equilibrium

b)Static equilibrium

c)Both of these

d)None of these

3.Langmuir derived an equation based on which of the following facts?

a)Every active site of the adsorbent acts in the same way

b)Adsorbate is adsorbed on the surface of the solid (adsorbent) to form a monolayer

c)The rate of adsorption is proportional to the concentration of the adsorbate [A] and the number of unoccupied sites available (1 – α)

d)All of these

4.In adsorption at liquid interface, when the added molecules move on their own according to the interface, this process is called

a)Negative adsorption

b)Positive absorption

c)Positive desorption

d)Positive adsorption

5.The Freundlich equation is identical to the very low concentration case of the Langmuir isotherm when

a)n = 1

b)n = 0

c)n>1

d)n=2

6.The Freundlich equation is identical to the very high concentration case of the Langmuir isotherm when

a)n = 1

b)n = 0

c)n>1

d)n=2

7.According to Freundlich adsorption isotherm, which of the following is correct?

a)x/m α p^1/n

b)x/m α p¹

c)x/m α pº

d)all are correct at different ranges of pressure

8.According to Langmuir isotherm the adsorbed substances tend to escape from the surface and therefore the rate of desorption is proportional to the number of occupied sites (α).

a)True

b)False

9.A plot of log x/m versus log p for the adsorption of a gas on a solid gives a straight line with slope equal to

a)N

b)1/n

c)Log k

d)–log k

10.According to Langmuir isotherm at equilibrium, the rates of adsorption and desorption are equal.

a)True

b)False

11.For very high concentrations (i.e. K2[A] << 1) the specific adsorption is proportional to the concentration of the adsorbate.

a)True

b)False

12.For very high concentrations (i.e. K2[A] >> 1) the specific adsorption is ____ of the concentration of the adsorbate.

a)Dependent

b)Independent

c)More

d)Less

13.For very low concentrations (i.e. K2[A] << 1) the specific adsorption is _____ to the concentration of the adsorbate.

a)Proportional

b)Inversely proportional

c)Independent

d)Higher

14.For intermediate concentration, the Freundlich equation for adsorption at a given temperature is

a)q_e = k₁/[A]

b)q_e = k[A]ⁿ

c)q_e = k₁/k₂

d)log qe = log k + n log [A]

15.The logarithmic form of Freundlich equation is

a)q_e = k₁/[A]

b)q_e = k[A]ⁿ

c)q_e = k₁/k₂

d)log qe = log k + n log [A]

Solutions:

1. a)Brunner, Emmett and Teller
2. a)Dynamic equilibrium
3. d)All of these
4. d)Positive adsorption
5. a)n = 1
6. b)n = 0
7. d)all are correct at different ranges of pressure
8. a)True
9. b)1/n
10. a)True
11. b)False
12. b)Independent
13. a)Proportional
14. b)q_e = k[A]ⁿ
15. d)log qe = log k + n log [A]

References:

1. GAURAV KUMAR JAIN – THEORY & PRACTICE OF PHYSICAL PHARMACY, 1st edition 2012 Elsevier, page no. 128-136.

2. Martins Physical Pharmacy, 6th edition 2011, page no. 669-696.

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