Chemical Potential (Multi-Component Systems) Video Lecture | Mass Transfer - Chemical Engineering

In this screencast, we'll discuss chemical
potential for multi-component systems and
the importance of chemical potential is that
it tells us the direction of mass transfer
because molecules will move from high chemical
potential to low chemical potential.
We'll look at an example to make this clearer.
We start off with a beaker that contains water
and iodine.
So we've dissolved iodine in water.
This mixture is now brown.
What we're going to do is add ether to this
mixture.
Ether is less dense so it'll be on the top
phase.
Ether and water do not mix and so we have
a two phase system.
Water on the bottom and ether on the top.
And then what we see is the ether becomes
brown because the iodine dissolves in the
ether and leaves the water and the water becomes
clear again and so we have mass transfer that's
against the concentration gradient.
As the iodine is depleted from the water and
goes into ether, we'll have a lower concentration
of iodine in the water but the chemical potential
will still be higher so the iodine will continue
to move until the chemical potential in the
water is equal to the chemical potential in
the ether.
So this is the chemical potential for the
iodine.
That's then our criteria for equilibrium and
we can move against the concentration gradient.
So I've written equations for chemical potential.
This is the chemical potential of component
i in the mixture.
This is the single component chemical potential
for that component and then the activity,
and this is for the liquid phase and we typically
end up using activity, it's a mole fraction
of the component and the activity coefficient
which depends on what other species are present.
If instead we're in gas phase, we typically
use fugacity where our standard state is pure
component ideal gas at 1 bar so this units
for fugacity must be in bar for this equation
to be meaningful.
And if it were an ideal gas mixture, we could
replace the fugacity by the partial pressure.
So this is the partial pressure of species
i and you can see the chemical potential depends
on the log of the pressure.
Now it's worth writing down the definition
of chemical potential and that's partial derivative
of the total Gibbs free energy of a mixture
with respect to the number of moles of component
i, constant temperature, constant pressure
and constant moles of all the other species.
This also is equal to the partial of the total
internal energy with respect to number of
moles of component i, but now at constant
entropy, volume, and moles of all the other
species.
So let's look at chemical reactions.
We're going to define chemical potential as
zero for the stable form of the element.
Chemical potential scale is arbitrary so this
is, if you like, our reference state.
The idea is if we had hydrogen gas standard
conditions or if we had carbon solid, its
chemical potential would be zero.
And then we could look at a chemical reaction.
So what I've done is list the reaction from
this reference at the beginning of the screencast
and listed from the table they have for the
chemical potentials of each of these components.
So the first thing to note is that these values
are all negative and that's because the species
formed, so the elements have chemical potential
of zero, we go to lower chemical potentials
meaning that we expect the compound to have
a lower chemical potential than the pure components.
And if we had these together, the left side
is -1291 kJ/mol.
And the right side is -1366 kJ/mol.
This is for one mole of each species at standard
conditions.
And what this says is we expect reaction in
this direction to get to equilibrium, namely
we go to lower chemical potential.
The idea is at lower chemical potential, the
driving force is chemical potential and so
just like for the phase change we can look
at reactions and determine which direction
equilibrium reaction will take place.
It doesn't tell us anything about the speed
but it tells us the direction.