Liquid/Liquid and Solid/Liquid Equilibria Video Lecture - Biotechnology Engineering (BT)

welcome in the last class we had looked
at vapour liquid equilibrium as a
special case of equilibrium and we had
worked out the special condition for
vapor liquid equilibrium based on
original conditions of equilibrium the
five equations that we had seen very
early in this module and we had also
worked out an example problem to better
understand how the equilibrium comes
about and how we can use the various
parameters that we have developed or
defined to come about with useful
relationships at equilibrium in the case
of vapor liquid equilibrium what we are
going to do in this class essentially is
to develop the governing equations for
liquid liquid and solid liquid
equilibria and there could be various
different kinds of equilibria we're just
going to take these two and develop the
governing equations because these occur
quite often in the case of biological
systems especially by a process related
activities as well as some activities
that deal with analysis of biological
molecules and so on and what are you
going to do how we are going to develop
these governing equations is as
exercises which means you're going to
develop it that way it builds up your
confidence of addressing and developing
equations in hitherto unknown situations
and a complete appreciation of the
principles that are involved also comes
about as a part of doing such exercises
so we will do these as exercises I am
going to start you out and then I will
give time and of course I will present
the equations the governing equations
the way I have done it we can
cross-check after some time what
I would like you to remember when you
are developing these governing equations
for liquid liquid and solid liquid
equilibria are is the fact that
equations five point one to five point
five and further you know we had stopped
at five point five essentially equation
five point one is T alpha equals T beta
equals T gamma the sameness of
temperature the equality of temperature
across the various phases at equilibrium
the equation five point two was the
equation of pressures or equality of
pressures across the various phases P
alpha P beta P comma and so on and then
equations five three two five five we
had written for three components one two
and three and what we had written there
was that the chemical potential of each
component was equal across the various
phases in which it is present of course
we are assuming that all the all the
components are presented all the phases
therefore mu one alpha equals P one beta
equals mu and gamma and so on was
equation five point three mu 2 alpha
equals mu two beta equals mu 2 gamma
equation five point four mu 3 alpha
equals mu 3 beta equals mu 3 gamma and
so on was equation five point five these
these are the five fundamental equations
that are necessary for the thermodynamic
equilibrium in any system need to keep
this in mind and we need to develop it
let me start you out for the case of
liquid liquid equilibrium which means
there are two liquid phases distinctly
separate and you know there could be of
many different kinds one could be a
hydrophilic phase the other could be a
hydrophobic phase this is easy to
imagine a hydrophilic phase hydrophobic
phase let us say a mixture of oil and
water they are not going to mix
each other you can clearly demarcate
these two phases and one such system may
be tahleen water system and so on so
forth it's actually used in the
antibiotic extraction process one
hydrophilic phase which is the water
phase in which the antibiotic is present
after it is produced by the organisms
after the bioreactor phase and what is
added may be hydrophobic liquid is added
to extract most of the antibiotic into
the hydrophobic phase because at
equilibrium the concentration of the
antibiotic in the hydrophobic phase is
many-fold the concentration of the
antibiotic in the hydrophilic or the
water phase that's the basic reason for
using this to liquid process for
extraction and purification of certain
biomolecules such as antibiotics so this
is one example of a liquid liquid or of
the occurrence of two liquid phases and
equilibrium conditions are the limiting
conditions and more interestingly they
could be even two aqueous phases two
water-based phases but which are
distinct phases one sits on top of the
other an example is different mixtures
of let us say polyethylene glycol and
ammonium sulfate salt polyethylene
glycol and ammonium sulfate if we mix
them together then depending on the
composition they could form two
different distinct phases in fact such a
two aqueous phase systems are or equals
two phase systems as they called are
actually used in the industry for
extraction and purification of proteins
why do we need to do that you know that
proteins get their activity because of
the way the amino acid chain is folded
and the way the amino acid chain is
folded
makes or has relevance only in an
ecosystem because as you all recall from
your early classes maybe an initial life
sciences course or molecular biology
course biochemistry course for that
matter that a protein folds itself
according to the forces between them as
well as the forces between the various
constituents of the proteins that amino
acids their side chain and so on and the
environment that is present and if the
environment that is present in and water
it it forms a certain conformation which
is active they put the same protein
molecule in a non aqueous phase then the
forces are completely different and the
way it gets folded may result in a
molecule that is not active at all
because it's only the three-dimensional
folding of the protein molecule that
gives it its activity therefore what is
done is two aqueous phases are used and
based that is based on the fact that the
solubility of protein and one of the
aqueous phases is higher may not be a
ten hundred fold higher but maybe about
a few for three to five volt higher then
the other phase and this is used to
concentrate and purify the protein
molecules therefore liquid liquid
systems are used quite extensively in
biological systems and we are going to
look at one or we are going to look at
liquid liquid systems in general what
I'd like you to do is take about twenty
minutes from now because you need to
think about various things and so on and
the question is this if L 1 and L 2 are
the two liquid phases in equilibrium for
each component I in the two phases
develop the expression that can be
written as simple as that to give you a
hint the first five equations equations
five one two five five are valid
also take a look at how we went about
doing pretty much the same thing but for
a component I that is distributing
between the vapor and liquid phases in
the case of vapor liquid equilibrium
those are the hints that are that I am
going to leave you with take about 20
minutes and then we look at what the
solution is go ahead
okay you would have found it easy to
write the condition for equilibrium
which is nothing but the Equality of
chemical potentials we are of course
going to take the conditions of
temperature equality and pressure
equality as a given so we do not have to
write them explicitly here as mentioned
some time earlier and that is considered
as a given thing here mu I in the l1
phase must equal mu I in the l2 phase I
is a component which is distributing
between the two liquid phases l1 and l2
as mentioned earlier l1 could be a
hydrophilic phase and l2 could be a
hydrophobic phase or l1 could be one
aqueous phase in l2 could be another
aqueous phase as in the case of aqueous
two phase extraction now let us call
this equation 539 now if we expand
equation 539 in terms of you gas ities
we can write mu I naught plus RT lon if
I in l1 hat I hope you recall this fi
hat equals mu I naught plus RT lon if I
in l2 hat this is the fugacity of the
component I in l1 in a multi-phase and
multi-component system and similarly
this is Fi l 2 hat is the fugacity of
component I in L 2 in a multi-component
system therefore
it's quite easy to see me why not is
going to cancel with me why not Artie
cancels with this side this side and
then lon fil one hat equals non fil two
hat and therefore if I L one hat equals
fi L 2 hat now if you go back and look
at expressions for this you could write
it is essentially equation for 8 in the
previous module you could express f I ll
1 hat in terms of the pure component
fugacity which is easier to estimate
this is written as mu I l1 f I l1 X I L
1 where X is the mole fraction and gamma
sorry this is not mu this is gamma gamma
I l1 fil 1 x IL 1 gamma I is the
activity coefficient X I is the mole
fraction and F I is the pure component
fugacity in the L 1 phase must equal
gamma il-2 f il-2 X il-2 this becomes
the condition for equilibrium let us
call this equation 541 to get a little
more comfortable with this let us work
out an example for the liquid liquid
extraction of ampicillin at equilibrium
express the ratio of the activity
coefficients of ampicillin that ratio is
missing here the ratio of activity
coefficients of ampicillin in the two
liquid phases in terms of fugacities and
mole fractions okay take about 15
minutes and go ahead and do this please
this is on the same lines as the
derivation we could directly use the
final relationship that we got just a
while ago we know if we employ equation
539 directly see this is the case of
liquid liquid equilibrium and ampicillin
as the component I that is distributing
between the two liquid phases we know
that from equation 539 that mu I of
ampicillin in the L 1 phase must equal
mu sorry mu of ampicillin in the L 1
phase must equal mu of the ampicillin in
the L 2 phase and writing this in terms
of gamma I bringing this down to free
gas ities and then writing it either way
it's okay
gamma of ampicillin in the L 1 phase
times fugacity of pure component
ampicillin and the mole fraction of
ampicillin in the L 1 phase must equal
gamma of ampicillin in the L 2 phase
velocity of ampicillin interphase and
the mole fraction of ampicillin in the L
2 phase and therefore what is required
is the ratio of the activity
coefficients of ampicillin gamma
ampicillin in the L 1 phase divided by
gamma of ampicillin in the L 2 phase is
nothing but the product of fugacity and
mole fraction in the L 2 phase divided
by the product of fugacity and mole
fraction of ampicillin in the L 1 phase
this is the
equation that we were looking for or the
relationship that we are looking for in
this example so for completeness I would
okay let us actually present the since
we are almost out of time in this
particular lecture let me just present
this it's quite straightforward this is
an example of solid liquid equilibrium
there are many different examples of
solid liquid equilibrium in biological
systems they arise in situations is as
bios option which is the removal of
let's say toxic trace metals using a
biological agent such as cells and so on
bio leaching which is taking the metals
or useful components out by using
biological means and even in some
analytical steps you come across solid
liquid equilibrium in biological systems
and we know that equations 5 1 to 5 5
are valid and therefore using similar
arguments as for the liquid liquid
liquid equilibrium we can start with the
governing equation that mu I in the
solid phase must equal mu I in the
liquid phase equation 542 and therefore
the fugacity of I in the liquid phase
this a solid phase must equal the
fugacity of I in the liquid phase and in
times of in terms of the activity
coefficient the gamma I in the solid
phase times fi in the solid phase times
the mole fraction in the solid phase
given as Zi equals gamma I in the liquid
phase times fugacity coefficient in the
liquid phase times mole fraction in the
liquid phase this is the governing
equation for solid liquid equilibrium
when we come back in the next class we
will review whatever we have done in
this particular module on phase
equilibrium see you then