We are going to look at Langmuir isotherms for binary mixtures.
So the ideas we have two components in the gas phase.
We want to see how much is absorbed on the surface of each component and how this changes
with change of temperature.
We change the heats of adsorption or are we change the relative pressures for a fixed
total pressure, and we are going to do this by looking at a mathematica simulation that
is available on the wolfram demonstration project website.
The location is given here.
So I am going to bring up that demonstration for you.
So what we are plotting here is the number of molecules that are per site.
Versus the total pressure.
So the sum of the partial pressures of A and B. For the conditions we are showing here.
The heats of adsorption are the same for A and B, and the pressure for B is twice the
pressure of A. Since the pressure of B is higher, and of course more of B adsorbs then
A. Note as we increase the total pressure we start to saturate the surface because we
cannot put more then 1 molecule per site for the module we are looking at.
So lets look at what exactly the Langmuir isotherm model is.
It says the fractional coverage.
Fraction of sites covered with molecule A are related to the adsorption equilibrium
constant for A, partial pressure of A, over 1 plus the adsorption equilibrium constant
times the pressure of A. If we also have a second component present.
Then we have additional terms for B, and this assumes A and B each occupy one site of the
surface.
So now lets go back to the simulation.
So we are looking at Langmuir isotherms.
The number of molecules to adsorb per site at a function of total pressure.
Now the heats of adsorption are the same.
There is more B molecules adsorbed then A molecules because the pressure for B is twice
the pressure of A. If we were to raise the temperature.
We see that the coverage goes down significantly.
If we lower the temperature we notice that we meet saturation.
So the higher total pressure makes no difference on the amounts adsorbed and in this case the
amounts adsorbed sum together.
Correspond to 1 molecule per site.
So that is effect of temperatures.
So lets go back to intermediate temperature.
We will get changing heat of adsorption.
So if I increase the heat of adsorption of A, and I can increase the amount of A adsorbed
relative to B. Even though the pressure of B is higher.
Notice this is a small change in the heat of adsorption because the heat of adsorption
is exponential, and its adsorption equilibrium constant.
So I can have dramatically different amounts of adsorption.
So you can imagine for separations processes you can preferentially adsorb one molecule
and say pressure swing or temperature swing adsorption in process.
We can occupy the surface preferentially with the strongly adsorbing molecule.
Like wise if I lowered the adsorption we can reverse it rather dramatically in the other
direction.
Now lets go back to the same heats of adsorption.
If we look at the effect of the relative pressures.
So I make the pressures the same.
The heats of absorption the same.
We have the same amount of each component absorbed.
But as I raise the pressure of B relative to A. Then I can preferentially occupy the
surface with components B. So the Langmuir isotherms are important in separations.
They have a lot of simplifying assumptions.
We have to keep that in mind, but they often fit experimental observations pretty well.
And so you can on your own use this wolfram, mathematica simulation.
That is available you do not need mathematica, and here again is the location of the simulation
for the Langmuir isotherms.