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Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

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Page 1: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?
Page 2: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Langmuir Adsorption Isotherm

1

KP

KP

Page 3: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

“Adsorption”!

“Isotherm”?

Page 4: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Surface

Consider gas molecules striking a surface

In this case, molecules do not adsorb or “stick” to the surface

Page 5: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Now, consider the following scenario…

In this case, molecules do adsorb to the surface

Surface

Page 6: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Isotherm- it means…Constant Temperature

That is, adsorption at a fixed temperature

What about…

Page 7: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

molecules in the gas phase

molecules adsorbed at the surface

…To describe the equilibrium between the molecules in the gas phase and the molecules

bound to the surface

The objective of Langmuir Equation…

Page 8: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

The Experiment…

We will:

1. Introduce molecules in this chamber

2. Wait for an equilibrium to reach

3. Plot number of molecules adsorbed versus the equilibrium pressure

Page 9: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Pressure, P

Amount Adsorbed

Nadsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1

2345

6789

10

11

12

No Gas Molecule The Experiment…

Page 10: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Pressure, P

Amount Adsorbed

Nadsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1

2345

6789

10

11

12

The Experiment…Now, Let’s introduce 4 Molecules

Page 11: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

3 adsorbed

1 in gas phase

Pressure, P

Amount Adsorbed

Nadsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1

2345

6789

10

11

12

The Experiment…Now, Let’s introduce 4 Molecules

Page 12: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Pressure, P

Amount Adsorbed

Nadsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1

2345

6789

10

11

12

The Experiment…Now, Let’s introduce 8 Molecules

6 adsorbed

2 in gas phase

Page 13: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Pressure, P

Amount Adsorbed

Nadsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1

2345

6789

10

11

12

Now, Let’s introduce 12 MoleculesThe Experiment…

8 adsorbed

4 in gas phase

Page 14: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Pressure, P

Amount Adsorbed

Nadsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1

2345

6789

10

11

12

Now, Let’s introduce 15 MoleculesThe Experiment…

9 adsorbed

7 in gas phase

Page 15: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Pressure, P

Amount Adsorbed

Nadsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1

2345

6789

10

11

12

Now, Let’s introduce 21 MoleculesThe Experiment…

10 adsorbed

11 in gas phase

Page 16: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Pressure, P

Amount Adsorbed

Nadsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1

2345

6789

10

11

12

Finally, Let’s introduce 24 MoleculesThe Experiment…

10 adsorbed

14 in gas phase

Page 17: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Pressure, P

Fraction Adsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

We can plot this data as a fraction of molecules

adsorbed

max

N

N

.vs P

Fraction Adsorbed

Maximum Available sites

Number Adsorbed

Page 18: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

3. Only a monolayer coverage is possible

Irving Langmuir1881 -1957

In 1916, Langmuir proposed a simple model…

So, how to describe this behavior?Basic Assumptions…1.Adsorption sites are homogeneous and equivalent

2. The adsorbed molecules are immobile and they do not interact

Page 19: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Irving Langmuir1881 -1957

In 1916, Langmuir proposed a simple model…

So, how to describe this behavior?

1

KP

KP

Based on these assumptions, Langmuir derived the following equation…

Fraction Adsorbed

Equilibrium constant

Equilibrium Pressure

Page 20: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

The Langmuir Equation

Based on these assumptions, Langmuir derived the following equation…

Pressure, P

Fraction Adsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1

KP

KP

Fraction Adsorbed

Equilibrium constant

Equilibrium Pressure

This is the Langmuir Equation describing (fitting) the Data

Recall, the data we collected

Page 21: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

The Langmuir Equation

Pressure, P

Fraction Adsorbed

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1

KP

KP

Notice…

when 0, 0P

when , 1P

And at low concentration, adsorption is linearly proportional to P

i.e. reaches a monolayer

This is the Langmuir Equation describing (fitting) the Data

Recall, the data we collected

Page 22: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

The Langmuir Equation1

KP

KP

What about the Equilibrium Constant, K…

• Larger the value of K, stronger the binding

1.0

0.8

0.6

0.4

0.2

0.0Fra

ctio

n A

dsor

bed,

2.5x10-4

2.01.51.00.50.0

Equilibrium Pressure (atm.)

Keq = 0.5 x 104

• Equilibrium constant can be used to calculate Gibb’s free energy of adsorption using the following equation…

1.0

0.8

0.6

0.4

0.2

0.0Fra

ctio

n A

dsor

bed,

2.5x10-4

2.01.51.00.50.0

Equilibrium Pressure (atm.)

Keq = 1 x 105

Keq = 0.5 x 105

1.0

0.8

0.6

0.4

0.2

0.0Fra

ctio

n A

dsor

bed,

2.5x10-4

2.01.51.00.50.0

Equilibrium Pressure (atm.)

Keq = 5 x 105

Keq = 1 x 105

Keq = 0.5 x 104

lnG RT K

Now, that’s an equation for another video!

Stronger binding affinity

Page 23: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Langmuir Equation - Application• Kinetics of Catalytic Reactions

• Pollution Remediationadsorption of contaminants to colloids

• Material Sciencee.g. adsorption on DSSCs

AB

A B C

ProductSurface Reaction

Adsorption

Page 24: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Historical• Was nearly blind for the first eleven years of his life

Irving Langmuir1881 -1957

Tidbits about Langmuir

• Graduated from Columbia’s School of Mines, NYC in 1903

• Post graduate work at Univ. of Gottingen in Germany in Physical Chemistry under Walther Nernst

lno RTE E Q

nF

• 3rd Law of Thermodynamics• Nernst Equation

Page 25: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Historical

Irving Langmuir1881 -1957

Tidbits about Langmuir

• Graduated from Columbia’s School of Mines, NYC in 1903

• Post graduate work at Univ. of Gottingen in Germany in Physical Chemistry under Walther Nernst

lno RTE E Q

nF

• 3rd Law of Thermodynamics• Nernst Equation

• Worked at the General Electric Labs

• Was nearly blind for the first eleven years of his life

Page 26: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

Historical

Irving Langmuir1881 -1957

Tidbits about Langmuir

• Graduated from Columbia’s School of Mines, NYC in 1903

• Post graduate work at Univ. of Gottingen in Germany in Physical Chemistry under Walther Nernst

• Worked at the General Electric Labs

• 1932 – First Industrial Chemist to receive Nobel Prize in Chemistry

• “for his discoveries and investigations in surface chemistry “

• This is the same year Schrodinger won the prize in Physics

• Was nearly blind for the first eleven years of his life

Page 27: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

1

KP

KP

http://www.britannica.com/biography/Irving-Langmuir

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1932/langmuir-bio.html

http://www.aip.org/history/newsletter/spring2007/photos.htm

http://www.nndb.com/people/776/000079539/

Music: “Mouton Swing” by Robert R. Putnam – https://archive.org/details/MoutonSwing

The End

Resources

Page 28: Langmuir Adsorption Isotherm “Adsorption”! “Isotherm”?

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