We are going to run through reading binary vapor liquid equilibrium phase diagrams so
that we can use them in binary flash and column-based distillation column calculations like those
used in the McCabe-Thiele method. so the place to start is either using the thermodynamic
model such as the modified Rouault's law or the Peng-Robinson EOS or the unit fact method
or you are going to look up experimental data collected and published in the handbooks like
Perry's Engineering Handbook or in scholarly articles. So we want to collect phase equilibrium
data. Now we are going to use this data to generate our plots. I have collected phase
equilibrium data for water and ethylene-glycol at a pressure of 30.4 kPa, I got this from
Perry's Chemical Engineering Handbook. So this gives us the mole fraction of water in
the liquid phase and our y is our mole fraction of our water in the vapor phase. So outside
of these two temperatures, 69.5 an 160.7 we won't have vapor liquid equilibrium. Now that
we have this information we can create a Txy phase diagram. Basically what we do is we
are going to plot our mole fractions on the x-axis and we are going to plot our temperature
on the y axis. And when we do we get the following diagram. So I will highlight our two axes.
So we get these two lines- one that represents the mole fraction of the liquid and one that
represents the mole fraction of the vapor. So everything we need to know about this two
phase system is set on this plot because it must follow Gibbs' Phase Rule. So a couple
things to point out. The plot is for water and ethylene-glycol. Typically our axis will
be for the more volatile component, so is it here? Since we have pure water when we
have a value of 1 then indeed this is for water. Is this the more volatile component?
Well when we have pure water we have a lower saturation temperature which is around 70
degrees compared with no water we have a composition of zero, we have all ethylene-glycol which
has a higher saturation temperature which is around 161. So for binary mixtures where
we don't have azeotropes or some non-ideal behavior we should expect this downward trend
for the more volatile species. Alright. So let's look at the composition of 50% water
and 50% ethylene glycol. At a low enough temperature we will be below this bottom line and we will
have one phase. This phase will be liquid. So we will have some liquid mixture that as
we increase the temperature will eventually come to this first line. Now this is our bubble
point line. So it is at this temperature we will have our first bubble that will form
which will be enriched in the more volatile component- in this case water. The opposite
line is called the dew point line. This is going from a vapor downward as we decrease
temperature we will form our first liquid droplet. So these are also known as the saturated
liquid line and the saturated vapor line. Anytime we are between these two lines we
have both vapor and liquid at equilibrium and we call this VLE. So anytime we are within
this envelope or on these lines we can draw horizontal lines to determine the composition
in each phase. These horizontal lines are known as tie lines and we can draw them because
both phases, both the liquid and vapor are at the same temperature. In this case when
we go from one phase of liquid we hit our saturated liquid line around 87 degrees. You
draw a horizontal line to our vapor line to determine the composition of that first droplet
of vapor. And in this case, enriched in water with a mole fraction of 0.97. So let's say
we keep increasing the temperature for our mixture. The composition of both phases will
change with the vapor becoming less enriched in our more volatile component. This means
that the mole fraction of water in the vapor phase is decreasing with increasing temperature.
Let's say we move up to 105 and we draw our tie line at 105. Now our vapor will have a
mole fraction of 0.93, which is less. And you can see the trend of our saturated vapor
line will continue to decrease the mole fraction of our more volatile component, water, as
we increase in temperature. Now this part is important. Most people think that the less
volatile component, in this case, ethylene-glycol, is evaporating and the vapor is becoming less
enriched in water, the liquid must be doing the opposite. Some will say that the liquid
mole fraction must therefore be increasing if it is decreasing the in the vapor phase.
Just a material balance 101. However that is completely wrong. Now as we increase the
temperature, the more volatile component, water, will preferentially vaporize and this
will decrease in the liquid composition as well. And we can see that on the plot as well.
As we increase in temperature our point on our saturated liquid line will continue to
decrease. Say we increase from 105-135 you can see now that our mole fraction of water
in the vapor phase is less than 0.7 and our mole fraction of water in the liquid phase
is less than 0.1. Both decrease. Ok so the last thing, if we keep increasing, we will
eventually get to our saturated vapor line, in this case just above 145 decrees C. Now
we have all vapor at its dew point. Any further increases will get us back into one phase,
which in this case is vapor. And this vapor will have a composition the same as what we
started in the liquid, in this case a 50/50 mixture except now it's all vapor. So these
changes in composition with temperature can be plotted. And it is a good exercise to examine
your understanding of a binary vapor liquid equilibrium. You can see the screen cast labeled
phase equilibrium Txy diagram for a test yourself question and explanation. The last thing to
point out is we can determine the relative amounts of each phase at a given temperature
using what is known as the inverse lever rule. Let's go back to say, 105 degrees C. We draw
an equilibrium tie line at 105 degrees C connecting both their saturated liquid and their saturated
vapor lines. Now if we were at 50% composition we would draw a point on the line as such.
So do we expect more liquid or more vapor at this temperature. We are closer to the
saturated liquid line so we would expect more liquid. And to determine the amount of liquid
we could take the ratio of the line from the mixture composition, I will call M, to our
saturated vapor line.Let's just call it B and a point on the saturated liquid line,
point A. So this means that the amount of liquid compared to the amount of mixture is
just the distance MB/Total distance AB. this will give us fraction that is now liquid.
We could do the same thing if we wanted to compare L/V. Liquid to vapor. In this case
it would just be the distance MB over the distance AM. So the ratio of each individual
length can give you relative amounts of vapor and liquid. So in this case we don't need
to get a ruler out we could just take the distance using our x axis. So let's say our
MB is 0.93- M, 0.5 over 0.5- our point at A, which we will call 0.26. This gives us
a value of 1.8 telling us that there are 1.8 times more liquid than there is vapor. So
this diagram is nice for determining phase states, determining the transition temperatures
between phases, compositions and the relative amounts of each phase however once we start
doing separations problems like those in McCabe-Thiele method we want to use what is known as an
xy diagram. If we draw our equilibrium tie lines and record both the x and y compositions
and we do this for a number of temperatures now we will generate a plot that looks like
the following. So on the left we have our Txy diagram and on the right is our xy diagram.
On the x diagram is the mole fraction of water in the liquid and y axis is the mole fraction
in the vapor. And again we get this because at any given temperature, 125, we get a point
for our mole fraction in the liquid phase just above 0.1. So that puts us right around
here. Our vapor mole fraction is about 0.8. If I didn't draw my point so large you would
see it is above 0.8 which is where we are at. So drawing those equilibrium tie lines
converts to the xy diagram. Notice this is a constant pressure equilibrium phase diagram.
This type of plot is convenient because the equilibrium points are plotted and can be
placed on the same graph as material balance lines which we will see in other separations
calculations. So we also want to put a y=x line for reference. This will help us identify
azeotropes, when the compositions of vapor and liquid are the same. Check out our other
screen casts on the flash and column distillation calculations so you can see how we apply these
plots in practice.