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In today’s lecture, we continue our discussion on vapor liquid equilibrium. If you recall
we talked about degree of freedom, if you have binary component and then if you fixed
pressure and temperature then the mole fraction of two components in liquid and vapor phase
will be fixed, so we apply this rule degree of freedom f equal to c minus p plus 2, which
means if T and pressure are known mole fraction of A and B in V and l two phases will be fixed.
Of course, we can applied Raoult's Law and equate with the total pressure or the partial
pressure to calculate x and y. In today’s lecture, we do this, we prepare T x y diagram,
if you recall in absorption also we started with the thermodynamics. First thing is that
we must establish the equilibrium conditions between the two phases so in other words given
mole fractions of y given mole fractions of A in vapor phase what is the mole fraction
in the liquid phase for one component or for both the components.
The first thing we have to do in this distillation the second unit operation is to establish
this T x y diagram. For this one has to do the experiment so in batch experiment you
start with the system of liquid A plus B heat the liquid and monitor it composition and
monitor the amounts of liquid and vapor formed in that closed system and then plot this T
x y diagram. We one has to do this experiment and one has to; one can also apply this Raoult’s
Law to corroborate is in a finding or observation, so we will do this exercise here in plotting
this T x y diagram, which is the first thing one has to do before we get into this distillation
column.
Let us start with this T x y diagram, which will look like this, so essentially this is
what we want to plot here or we want to establish here, we have temperature here, and we have
mole fraction of A in liquid and vapor. What we are looking here at a batch system, suppose
we take a batch system here of liquid say l A plus B, there be some amount of vapor
in contact with liquid here also containing A plus B. And if we heat this liquid slowly,
if you have say pure component of you know A or B it says zero here, and if it is one
at this end, so if you take pure component of B and heated you will expect that at boiling
temperature T b corresponding to the total pressure P t, the system will boil or this
component B will boil. Similarly, if we have A if your component
A mole fraction one, and heat this liquid then at a certain temperature corresponding
to the boiling temperature of A write the component A will boil here, and will be vaporize
and entire liquid will converted into vapor. When we have component - the binary component
of A plus B then start with certain mole fractions and heat this system here, one can do this
experiment, one can monitor the amount amounts of l and vapor, and mole fractions and or
compositions mole fractions of A or B in two phases. Essentially, we one can monitor x
A and y A, so 1 minus x A will be the mole fraction of B and one minus y A will be mole
fraction of B in vapor and the liquid phase. If you do this experiment, what we observed
here that as we increase the temperature. A certain temperature is reached, at which
the first bubble is found. This is very important that we understand the difference between
the boiling of a binary components, and boiling of a pure components A and B here. When we
take this cold fluid liquid and we increase a temperature, a temperature is reached here
at which the first bubble is formed. If you chose another mole fraction here, let
us say some mole fraction is smaller than this and heat this liquid, we will get another
boiling temperature here, at which the first bubble will be found. Essentially, we will
have a locus of all boiling temperature like this; if you take the mole fraction here and
heat it we have another boiling temperature. Essentially, we have a locus of bubble points
curve, so we call it bubble points curve. What are the bubble points curves. It is a
locus of the temperature depending upon the mole fractions of A in the liquid phase, at
which the first bubble is formed. This is the temperature, at which the boiling just
starts taking place. If further heated, then we will see this where
significant amount of vapor is formed, in other words now we will have two phases one
vapor containing A plus B and another phase we have the liquid containing A plus B also,
in this case the amount of liquid and vapor will be different one can measure this amount
of liquid and vapor one can also measure the composition of A in vapor phase and the liquid
phase. We have now two phases here, so this is the liquid, now we have l plus P a liquid
phase and the vapor phase, if we take another mixture here let us say we have heated here
reach this bubble point if further heat then again there is a separations observe, we have
some amount of liquid form, some amount of vapor form.
We will talk about this later what is the total amount. Essentially, we have now another
locus curve like this, in which for different compositions there will be a separation of
two phases in vapor phase and the liquid phase, in which the amount of liquid and vapor is
different and amount of vapor compositions and amount of liquid compositions are different.
Now, you further heated continue with this heating then temperature is reached, at which
the entire liquid is now converted into vapor. So, similar to all this bubble point curves
we have a locus of what we call dew points curve. This is dew points curve.
Now, what we have here is the when we reach this temperature for this binary components
of A plus B depending upon what mole fraction, we has starting here is a temperature at which
the entire liquid is now converted into vapor phase. Essentially for this binary phase,
there is a temperature range right one is T B for a pure component B and we have this
boiling temperature for a pure component A and if you choose any binary components of
A plus B, a mixture of A plus B, then there is a temperature range between here and here.
There is a temperature range, at which the boiling takes place. First boiling or first
bubble is observed at certain temperature you call it bubble point. If further heated
there is separations liquid plus vapor the vapor phase contain so much mole fraction
of y A given by this curve here and the liquid phase will contains so much mole fraction
of x A given by this curve. If you further heated boiling continues till we reach this
point and entire liquid is now converted into vapor phase, this temperature we call it dew
point curve. So, we make three very important points here, one there is a bubble point this
corresponds to x A in liquid phase. This is the temperature, at which the first
bubble is formed or the liquid just starts boiling, after that there is a phase separation.
There is a phase separation or we have liquid plus vapor mixture, in which you can see the
vapor phase composition is greater than feed compositions, if you call it Z f, which is
in turn is greater than x A. Let us see what we trying to say here, suppose we start with
certain mole fraction here, this is you call it Z f. We start with a composition of feed
with Z f mole fractions say sixty percent of A and we start heating it, first we will
reach a bubble point, so this is the temperature at which the first bubble will be formed if
further heated, now there is a separation l plus B you call this as a tie line.
Now, there is liquid and vapor form vapor phase composition is given by this y A and
the liquid phase composition will be given by x A, you can see y A is greater than Z
f and Z f is greater than x A, which means there is a enrichment, we starting with sixty
percent mole fraction of A now, we have been able to achieve eighty percent of A in the
vapor phase and forty percent for example, lesser than the feed composition in this liquid
phase. This is essentially we have y A greater than Z f greater than x A and here also once
should note that with the boiling temperature of B is higher than the boiling temperature
of a because vapor pressure of A is greater than the vapor pressure of B at any temperature.
We have the boiling temperature A smaller than the boiling temperature at means there
is a temperature range, there is a del T, which is in between the boiling temperature
of a pure component B and the boiling temperature of A over which the boiling takes place and
as a consequence similar to this bubble point there is a dew point, so dew point is a temperature
or is a locus of a different temperatures, at which entire liquid is now converted into
vapor pressure, so starting with liquid you have now liquid plus vapor and then we have
this vapor phase. We start with a certain compositions Z f at
any instance liquid has x A vapor has y mole fractions and now entire liquid has been converted
into vapor, which means the final composition will be same as the starting composition,
which we have Z F. The same experiment one can also do starting with a vapor, which means
here we start with a liquid in an close container fix the pressure, composition is 40 percent
A, 60 percent B heated with the temperature is raise from room temperature for example,
30 degree centigrade to 80 degree centigrade, when the temperature reaches 80 degree centigrade
one can physically observe that there is now the liquid has started boiling or just above
to boil that point is your dew point. And this dew point will depend up on what
is your mixture composition, if you start with some other composition higher compositions
then if you increase the temperature now the dew point will be form or dew will be form
at a temperature lower than the previous temperature so just follow this curve qualitatively to
understand this physical meaning of this. Now, we have in the in case of binary mixtures,
there is a temperature range, at which over which the liquid boils before it converted
into vapor phase. We start with A plus B pure liquid first bubble
point further heated now there is a vapor phase and the liquid phase one can calculate
the amount one can also measure the amount to make a to ensure that it is a consistent
with our material balance, so we have certain amount of vapor form certain amount of liquid
form vapor is now enriched in A that means the vapor composition an given by y A is not
greater than the Z F initial mixture concentrations, which in turn as greater than your mole fraction,
you further heat it liquid is still the mixture is still boiling more amount of vapor is formed
less amount of liquid is now left in the container till you reach a temperature, which you call
it dew point at which the entire liquid is now converted into vapor phase.
Now, the vapor phase composition will be is natural that will be same as what we have
studied you just follow this vertical line here and every point in between del T dew
point and the bubble point there is a tie line, the tie line decides how much is your
mole fractions of a in the vapor phase ? How much the mole fraction of a in the liquid
phase? And also decides how much is the amount of liquid and vapor formed? We will talk about
this later. Why it is called dew point because I was talking about this earlier that the
state of doing this experiment from liquid to vapor one can start with the vapor phase
so super heated vapor. A vapor temperature is greater than the boiling temperature of
less boiling less volatile component, which is B here that is why it is as higher temperature.
We have T b and we T a here and you take a temperature higher than this T B and start
now cooling it, just do it reversible, if you cool it then you reach a temperature,
which we call it dew point curve, at which the first dew is formed, that means the first
drop of the liquid is formed. Further cool it there is separation vapor liquid it follow
the same exactly for and till you reach a further cool it, till you reach a bubble point
curve at which the entire now this liquid and entire vapor has been converted into liquid.
Now, I start with the vapor l plus V and you have l e to this what we have this T x y diagram
one can observe experimentally, if we can measure the amount of liquid vapor form we
can do some chemical analysis to find the composition of vapor and liquid to obtain,
but you must not forget that this curve can also be obtain analytically by applying this
Raoult’s law. Let us redraw this curve and make you know similar observations what we
had in case of heating the vapor, so heating the liquid now let us start with the vapor
and let us follow the locus of this line.
Now, we have T x y diagram. So, here are we trying to understand the change in the compositions,
if we have condenses in other words we are starting with the pure vapor, so let us say
we have this general T x y diagram like this we have fixed total pressure, if you write
T B and T A like this that means we are saying that vapor pressure of a is greater than vapor
pressure of B it is more volatile compounds and as you consequence boiling temperature
of a is smaller than the boiling temperature of B here. Now, let us see if you start with
a pure vapor say the compositions of this pure vapor is Z f and start cooling it. When
you start cooling it what will happened the first bubble; first dew will occur right here
and if so we call it dew point curve, which is nothing but the locus of all such dews
here. If you start with different compositions the
first you will appear if you start with different compositions that first you will appear right
here, so we have this locus which we call it dew point curve. Now, if you further cool
from here then we will get a liquid and vapor mixtures here, so we can call this as x A,
we can denote this as y A the idea here is that the amount of the liquid form will be
in the ratios of this by this. It is all tie line and we can apply the lever rule, which
we discuss in the previous slide here if further cool it cool it the amount of liquid will
be more and all the time the amount ratios of the liquid amount and this vapor amount
will be given by this ratio by this ratio, if you keep on further cooling it till we
heat this point we can say that we have heat what do we call bubble point curve and we
further cool it we have now this pure liquid so starting with pure vapor we have l plus
V then we have this liquid, the idea is that either we start from the pure vapor to reach
there is own up your liquid through this l plus V by condensations or we start like in
the previous class with the pure liquid and heat it till we reach l plus V and then we
have this pure vapor, both of them will trace the same T x y diagram in a general curve
like this, so either you go from here or you starts from here it will give the same results.
We can make a note that all the time vapor is rich in A, it is a more volatile compound
we said the vapor pressure of A is more greater than vapor pressure of the B or the boiling
temperature of A is a smaller than boiling temperature of B or and all the time liquid
fraction is rich in B. We have this T x y diagram either way you
starting from the pure vapor or heating of this pure liquid.
We will like to redraw this again, so let us redraw this T x y diagram. We are plotting
x A and y A 0 to 1 we have T b we have T a, this is a bubble point curve and this is dew
point curve. If you take any compositions of Z f and we reach this zone of liquid plus
vapor we have compositions given by this bubble points curve given as x and we have this composition
y given by dew points curve. This is you calling it is tie line, because
we are going to apply what do we call tie rule and of course, we know that if further
heated then we will reach this dew point curve then the entire vapor liquid will be converted
into this vapor phase. There is a boiling temperature range for binary compound. For
a pure component entire liquid gets converted into vapor at one temperature for pure a entire
liquid gets converted into vapor at one temperature above A for binary mixture there is a temperature
range between T b and T a, at which the entire liquid boils. This composition for Z f is
composition can say that this is del T range of temperature at which the boiling takes
place. First boiling starts from here and ends here. Similarly, if we condense first
condensation takes place this temperature then entire vapor is converted into liquid
at this temperature. This is a temperature range for these binary component mixtures.
If you are doing this batch experiments and start with some feed of A plus B at any time
we can write that f equals l plus V, at any instance between here and here feed is now
converted or feed has two components, so initially we have hundred moles now we are saying that
spot of this hundred moles is as the liquid phase and part of this as the vapor phase
and part of this as a liquid phase so we can make a material balance to say that f equal
to l plus V. We are looking at starting with now we have
vapor phase and we have liquid phase is started with a pure say one liquid phase F which is
consisted of A plus B and we have heated it to bring it two phases l and V, each l each
phase A l and vapor will contain A plus B. Now, we are made this, we have written this
total material balance, you can now make the balance for A alone. If you have f and starting
composition was Z F so f dot Z F, this would be the moles in this moles of a in this feeds
and now this is distributed in liquid and vapor.
This is y this is x this is z, now you should be able to understand the meaning of this
tie line and this horizontal tie line, which we have drawn here was point this Z F anywhere
in between, this gives you Y 1 X 1, Y 2 X 2, Y 3 X 3 over this temperature, so essentially
this A is distributed now between the liquid phase and the vapor phase with these two equations
one can write l over V as y minus Z F over Z F minus x. If we chose say this o in between
and we call this as v vapor which is a point, which is a coordinate on this dew points and
we call this for corresponding to this o or v if a l on this bubble points nothing but
y minus Z F is nothing but O V and Z F minus l is nothing but O L.
This what we have so we have this T x y diagram at a given pressure we have fix the pressure
we have this T x y diagram T b, T a and let us do this calculation for Z F, so this mixture
had brought to this temperature, now we have o this point here, this is v, this is l, this
is y, this is x, so y minus Z F, y minus Z F is nothing , but O V and Z F minus x is
nothing but O L, so l by v amount of liquid form reduces of amount of liquid form to that
of vapor is given by this time line O V by O L this what it says.
If we know the compositions y and x the vapor phase, we know the feed composition Z F and
Z F one can obtain the ratios of l and v form since we know the amount of f one can calculate
out of 100 moles may be 40 moles are liquid 60 moles are vapor depending upon what temperature
the feed mixtures and follow this locus the way it moves, we further heated now we are
here Z F is fixed, but now, we have v reach be here and reach l here now look at his ratios
now, o has reached here now we have new y, y minus Z F and we have new x, Z F minus x,
so every time the amount of liquid and vapor the change as between as you increase the
temperature between the first bubble point and the dew point and how does the liquid
of vapor amount change ? This quite expected that in the beginning you have pure liquid
l is almost equal to f when the temperature reaches bubble points and just you further
heat more amount of vapor is formed so the tie lines can be we can look at this l by
v right ? Now you have the small segments becoming a larger here.
We will one can let us redraw this and follow how does the segments of tie lines in the
change? So you have tie line here suppose you are starting with this Z F you have just
very small amount very small increment the temperature now we have this so this is a
tie line Z F is fixed here this v this is one further increase, now we have another
v another one further increase now we have this, so follow the segments. This segment,
this segment, this segment it decreases this segment, this segment, this segment increases,
so this what we wrote here l by v equals O V over O L or we can write l into O L equals
v into O V or l into Z F minus x equals v into y minus Z F so what we have here l this
is l and this is v l into this so we are applying essentially a lever rule or this also known
as tie rule. The amount of liquid and vapor form it varies
along this, initially we have very small amount of vapor form then the vapor amount increases
till it reaches here and everything is now the vapor, so starting with pure liquid we
have reach now the vapor the amount will be just inverse of the segment, l by v is now
O V if this all this locus is of course, Z F is o then l by v is O V over O L, so you
should monitor this one can do this experiment, one can also apply this material balance and
you know to determine how much is the amount of liquid? And how much amount of vapor is
form? What is the mole fraction of x? And what is the mole fraction of y? You should
also note that this is consistent with our you know we talked about this degree of freedom.
If fix the pressure say one atmosphere and any temperature between the boiling temperature
of A and the boiling temperature of B, we assume that A is more volatile than B that
means the vapor pressure of A is larger than B and the boiling temperature of A will be
smaller than B. If you chose any temperature in between right for a given pressure then
y and x is fixed given by the tile and once y and x are fixed we know the initial amount
of mixture the compositions or amounts of liquid and vapor there also fixed this all
consistent with your degree of freedom fix P and t, x and y are fixed degree of freedom
is two here. The idea of this small exercise is to generate
this T x y diagrams they we want to distill acetone from methanol water from benzoic acid
acetic acid from formic acid so they are two binary component one can create this T x y
diagram by batch experiments. If you know some chemical analytical tools to measure
the composition of vapor and liquid for example, gas chromatography, liquid chromatography
one can also find the amount of liquid and vapor one can generate this T x y, , but T
x y diagram can also be generate by Raoult’s Law, which we will do in a minute. This is
also very important to note that instead of this batch experiment, which we are doing
in a close system suppose you do this experiment in open vessel that means as soon as you start
with a liquid. And you heat it once the vapor is formed you
remove the vapor again heat it again you remove the vapor or alternatively you start with
the vapor phase of A plus B and load the temperature till it reaches this dew point that time as
soon as the liquid amount is formed you remove it essentially one can do this experiment
in open vessel if you do this experiment in open vessel what T x y will obtain that is
very interesting and you should must understand that this is consistent with your experiment.
If we do this experiment in open vessel where you remove liquid or vapor as soon as it is formed so
if you do this it is not difficult to understand that now we have this T x y diagram if you
start with the vapor suppose it condenses here that is your first dew point and remove
the liquid, now further cool it, now you have the locus, which will go like this, because
you are removing the liquid as soon as this form so there is no liquid here of course,
there is phase separation there will be vapor and the liquid like in the previous case,
but you are just moving all the dew similarly, if you start with the vapor with a liquid
phase a same compositions and as soon as the vapor is formed you remove it you will reach
follow this path like this, which is same as T B and same as T A.
This is very similar to what we have to the previous case except you are removing the
liquid form or the vapor form here as soon as you know you reach dew point of the bubble
point curves, Now what will do next is we will show that this T x y diagram one can
also calculate from or obtain from Raoult’s Law.
So experimental observation is one thing for most of the binary components you know you
look at the Perris hand book or you look at the Treybals or McCabe Smith they have given
this T x y diagram. If you have new systems A plus B new type of liquid mixture of course,
one has to do this experiment, otherwise one has to rely on this vapor pressure curve and
to an equation which you must have to done in thermodynamics to calculate this vapor
pressure at a given temperature, but it still one can calculate the T x y diagram by calculation
so let us see how we can do it. These are the governing equations we are fixing
temperature that means we are fixing vapor pressure and of A vapor pressure of B, so
for example, we have this Antoine’s equation or you have some hand out tables to calculate
or estimate the vapor pressure of A and B, so total pressure is P t is fixed that means
the partial pressure of P t will equal to partial pressure of A and partial pressure
of B. What is the partial pressure of A? The Raoult’s Law now assuming ideal gas law,
ideal systems you have x A, P a 0 T and similarly for P v we can write x B as vapor into vapor
pressure of T so we are assuming the ideal component, they behave as a ideal solutions
and x A, P a 0 T is a partial pressure it can also be equated as y A into , so essentially
partial pressure in the liquid phase we have equated with the partial pressure in the vapor
pressure this will also equal to y B into P.
So, P is fixed and P t is fixed to and what are the unknowns here, unknowns are x A and
y A because x B is nothing but one minus x A and y B is nothing but one minus y A, so
we have two equations so these are the two equations we have and we have two unknowns
to solve for x A and y A, one can solve for x A and y A for different temperature to obtain
this T x y diagram. Essentially, we have this T x y diagram generated for a binary component
of A and B at a given pressure P t, at chose P is one atmosphere, two atmospheres and chose
a temperature I have y and x given from two point in the bubble. This small x exercise,
we have done small calculation; we have done to calculate x and y for a given pressure
and temperature of course, we need to know the vapor pressure of A and B given by some
correlations or Antoine’s equation so out are from some hand out.
Now, in principle it is also possible that we plot P x y in other words. We say that
temperature is fixed and if you vary pressure there also we have a same degree of freedom
two, if you apply you know the rule of degree of freedom f P equal to c minus P plus two.
So, if you fix temperature and vary p one can also obtain P x y and generally P x y
is not very popular or not very convenient to calculate the calculus in distillation
one extensively relays on p a and x y, but theoretically one can also P x y and if you
plot P x y you will get this equilibrium curve P x y like this.
Now, we have same x A y A 0 1 now if we vary the mole fraction of x A then it is not difficult
to so that partial pressure of A will vary like this and the partial pressure of B will
vary like this, so what we have plotted here is partial pressure of A so P a one can write
as x A vapor pressure of a at any temperature, so it is linear similarly, 0 x 0 that means
of vapor pressure of pure component B, which would be A B would be one minus x A into vapor
pressure of B. With this one can then plot P t versus x and P t versus y and leave as
an exercise to plot this, we have this P t versus x and we a have P t versus y. This
is also equilibrium curve for the binary mixture of A and B, P x y instead of P x y, but generally
as I said earlier that P x y is more convenient to use and widely used is most popular.
In distillation, there is one more variable called relative volatility, which is widely
used in several calculations if you recall we said that if you have a binary components
of A and B and we plot T x y diagram, A is more volatile it has a larger vapor pressure
than B so it has a smaller boiling point than A than B. Larger the volatility you will see
that larger the separations, so we like to plot this T x y diagram for different volatility
as per. Let us define this relative volatility, which is use nomenclatures use alpha A B,
so relative volatility of a with respect to B is defined as Y star over one minus Y star,
so star means it is an equilibrium with x and one minus in other words for a and b this
would be y A over y B over x A over x B or which would be same as P a over P b.
Volatility must be larger than one in fact much larger than one, one much larger than
one, if A is more volatile than B and 1 can also that if alpha equal to 1 that means Y
star equal to x and there is no separation is possible. This alpha relative volatility
signifies what extent A is more volatile than B or from the practical point of view to what
extent separation is possible right. This T x y diagram, which we have plotted for temperature
n x and y can also be plotted as y versus x and we will do this by taking the projections
of x and y for T x y plot.
Let us again redraw this T x y diagram, so we have T x y diagram like this, which is
T b here and we have t a, now just underneath this. Let us plot y versus x right where y
and x they are in equilibrium phase, so we are talking of vapor phase l phase liquid
y and x in equilibrium, so liquid and vapor they are in equilibrium phase so very often
we use y or y star here, now in T x y diagram as you said earlier if you chose any temperature
between T a and T b at this temperature here, then we have vapor phase this is v, this is
l we have l plus v, now all it means that they will be two phases vapor in the liquid
and the vapor will have this mole fraction and this liquid will have mole fraction of
A and the liquid phase and here we have this y and this x and if you want to plot y versus
x the best would be first to draw this 45 degree line here.
This is the 45 degree line and we take this projection here x and corresponding to this
x this liquid phase vapor is in equilibrium, this y we can extend here to 45 degree line
and move in this directions to obtain this coordinate, suppose I chose this temperature
and this tie line we have x mole fraction of A in the liquid phase mole fraction of
A in the vapor phase, I extend this, so this is x here corresponding to this x now i have
this y here, which as take to the 45 degree line I come to this direction I have another
coordinates. Similarly, we can plot different x and y to
obtain this what do we call x y diagram, so this is also an equilibrium curve y versus
x, the more important here to notice that at every coordinate y and x the temperature
is different. It is very important that you understand this all the we do not specified
temperature here and temperature is different for every y and x, so T x y diagram is one
type of equilibrium curve and more simplified version if you call it is y versus x, which
is also very more widely used here. We were talking about the relative volatility,
A is more volatile than B, you will expect that alpha will be greater than 1 and larger
is volatile than B alpha will be larger than 1 from here we can show that or one can see
that, now if you want to plot this liquid vapor equilibrium curve for a larger volatility
and there will be a separations more separations, in other words if you plot it here this will
be now wider liquid and vapor curve oval point curve and the dew point curves will be wider
here that means for the same temperature you go this way now you look at the this difference
between y and x will be larger, so that means it is more separation here. This phase is
much richer in A and here. And similarly, for this if you want to plot
y or x versus diagram by the same technique while taking the projection here one can show
that this 45 degree line now y versus x curve will also be y versus x curve be x curve will
also be away from this forty five degree line. For the same curve same plot if you want to
plot for different relative volatility it is easy to show that there what we have done
is increasing relative volatility, it is 45 degree line and away you are from 45 degree
lines you have y much larger than y one greater than y two greater than y three for the same
x, so we have plotted y x diagram for different relative volatility.
These are the things, which we have to understand from both physically and also from mathematically.
We can write down all these Raoult’s Law equations, we can also write down this relative
volatile expressions alpha to convince our self the shape of T x y diagram wider it is
that means more separations y is much larger than Z f, Z f is much larger than x and we
have very small relative volatility this curves take one side or they come closer we have
very separations you can do these equations for Raoult’s Law and one can do this kind
of exercise as I leave this an exercise you must try to convince yourself.
Similarly, if you plot y versus x diagram and draw this forty five degree line if you
are very small relative volatility this curve will be very close to this y this forty five
degree line and your larger relative volatility that means A is more volatility than B it
has more vapor pressure than B then the curve will be away from this x y diagram this what
we have done here. Now, these are all for ideal system and we said that we are fixing
the pressure here now if you change the pressure T x y diagram will also change. Now we are
saying that T x y diagram we want to plot for different pressures P 1, P 2, P 3 etcetera.
There also qualitatively you will an you should try to understand that increase the pressure
then there is a possibility of that means we are trying to approach critical pressure
of A or B since A is more volatile than B then at the certain pressure there is risk
of pressure reaching the critical pressure of A, in that case there is no phase separations
right if you recall from thermodynamics one is you reach a critical pressure, then you
essentially you have reach a stage where there is no l and v separations so if you want to
plot T x y diagram for different pressure one can plot qualitatively like this.
Let us plot this pressure effects so we have T x y diagram what we did earlier x y we have
T x y, so let us say that we have plotted this, T x y for certain pressure, we have
T b T a and this at corresponding to some pressures P, now if increase the pressure
then you will expect that this now we have the new T x y diagram, which will be slightly
more compact, in other words now the separation between two phases as gone the smaller, if
further increase the pressure there is a possibility that we will might reach the critical pressure
of A in that case this curve will shrink it will come like this, so that means now there
is no separation corresponding to this zone here. We have liquid plus vapor, we have vapor
again for the system only this region where we have liquid and vapor if you further increase
this curve will further become narrower till we reach a pressure where we have exceeded
the critical pressure of B components. This is like increasing pressure we have plotted
T x y diagram, corresponding to this T x y diagram if you just underneath this, if you
plot y versus x again qualitatively you should be able to just that if this is the curve
for the lower part right for A pressure and then if increase a pressure then this will
become flatter and flatter, it will approach y this forty five degree lines till you will
have situations like this where there is no liquid and vapor separations, it has heat
the forty five degrees like this and like this, so this is now increasing pressure.
Again T x y diagram, which we have plotted from this y x diagram, which we have plotted
from here one can take the projections of y and x take x here take y here go to the
forty five degree line connect with this etcetera, so one can do this.
The idea is that here we have plotted this T x y diagram or x y diagram or y x diagram
for change of the pressure at higher pressures in general most of the ideal solutions they
behave like this the separation is less the curve becomes narrower and narrower. Now,
these are all for your ideal solutions. Right now, there are some non-ideal solutions, where
we have very typical you know things what do you call as azeotropic mixtures, in which
case the total pressure is actually more than what we predicted by the Raoult’s Law, so
we call it positive deviations from ideality. Similarly, you can have different types of
A plus B binary components whether deviation is negative that means the pressure total
pressure is exerted is smaller than theoretical calculation.
Now, when we have this type of situation as azeotropic compositions, a very peculiar thing
happens that at certain temperature in between the boiling temperature of pure component
B and A there is a azeotropic compositions, at which entire liquid will be converted vapor
pressure without any phase separations. Now, if that happens you can imagine that in distillation
column at that trey wherever it happens the distillation will stop there is no enrichment,
remember if you started with A plus B for a liquid phase you had Z f we heated we reach
a bubble points we further heat it the liquid mixture is now boiling we have vapor phase
composition y which is greater than Z F and Z F is greater than x.
So, there is a separation here we are reaching we are doing enrichment, we are purifying
it we have vapor, which is richer in A and liquid which is richer in B, so this is the
way we have achieved this separations or if you have this azeotropic mixture or what do
we call constant boiling mixture then at that compositions you will see that entire liquid
is converted into vapor phase, that means there is no separation there and one has to
avoid this azeotropic boiling mixture. For this course, most of the discussion will be
confined to this ideal system, , but now we should must make a note of this non-ideal
mixture. So today’s lecture, we complete with this qualitative description or this
non-ideality in binary component mixtures.
We have non-ideality gave say let us take P t is greater than P t ideal so what we call
is positive deviation from Raoult’s Law. What Raoult’s Law predicts? Now, we have
pressure greater than this, for that such type of system as we said earlier that if
we plot T x y diagram then what we obtain is something like this qualitatively. Now,
we have T b and we have T a and the bubble point curve reaches the minimum and before
it increases to this T a and we plot the dew point then we have curve like this.
Notice here, if we have this composition mixture of Z F as a feed and if heat it then entire
liquid will be converted into vapor without any separations. There will be a separations,
if we take a mixture smaller than Z F, if increase it we have the bubble point curve
here bubble point, first bubble is form, liquid is starts boiling, there is a separation here,
this y is greater than Z F further heated y is greater than Z F till we reached this
dew point. So any region any composition smaller than
this Z F or we call it isotropic composition, we should notice that y is greater than x
alright and if you are here and draw a tie line is not difficult to show that now we
have a just reverse situations this is also dew point curve and this is also a bubble
point curve here. Now, we have x greater than y and if you have a mixture here that means
there is no separation at all, entire liquid is converted into this azeotropic composition
that was it also known as constant boiling temperature.
So only in this reason as long as feed composition is smaller than Z F we have vapor in rich
and richer than your feed composition and the liquid is linear in A and richer in B,
on the other hand if the feed composition is greater than isotropic composition and
we just have a reverse conditions x is greater than y, A is richer in the liquid phase rather
than in this vapor phase except non-ideality situations it raises because total pressure
exhausted by such component is greater than you know what is predict by the Raoult’s
Law. Corresponding to this T x y diagram, if it plot y x diagram and if we have this
45 degree line here when you take the projections from the top to the bottom you should be able
to convince yourself that you will get a curve like this here, now this is the isotropic
composition and notice here y is greater than x it is above 45 degree line.
This range y is greater than x and this range here is curve is below this forty five degree
line x is greater than y, so this is a non-ideality situation, non-ideal components, which view
main counter depending upon type of binary components we have, for example, water with
most of the alcohols right it is a kind of immiscible fluids and there is certain isotropic
compositions at a given pressure at which if you have that compositions then entire
liquid will converted into vapor and they will not be in a separation. If you want to
separate this type of mixture one of course, the feed composition should be smaller than
this isotropic composition or if you increase the pressure there is a possibility of removing
this isotropic composition, just now in the case of ideal mixtures we plotted the effect
of pressure and the curve of T x y diagram changes.
Similarly, one can show that we take a increase the pressure they will be locus of isotropic
mixture and this point will move away to you know one or pure component of A in which case
is a possible to increase our feed compositions at which the distillation or the separation
is possible. As, we said earlier that for this course distillations we confine our discussion,
calculations, or the design of a distillation column for an ideal binary component system.
We can apply Raoult’s Law without bring in this activity coefficient etcetera, which
accounts for non-ideality.