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Langmuir Adsorption Isotherm
1
KP
KP
“Adsorption”!
“Isotherm”?
Surface
Consider gas molecules striking a surface
In this case, molecules do not adsorb or “stick” to the surface
Now, consider the following scenario…
In this case, molecules do adsorb to the surface
Surface
Isotherm- it means…Constant Temperature
That is, adsorption at a fixed temperature
What about…
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…
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
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…
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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