In this screencast we are going to look at how to draw a q-line on a yx phase diagram,
because this is useful in helping to visualize the behavior in separations. And this line
basically corresponds to a mass balance. So let's look at the system whose behavior we
are interested in. And that is if we have a flash where we have some feed, and its mole
fraction of component A, we are looking at a binary mixture, is zA. And what we are going
to do is we are going to flash to get vapor which has a mole fraction yA. And liquid.
A mole fraction of xA. So xA and yA, those two phases, those compositions are in equilibrium,
or in vapor liquid equilibrium (VLE) and so that means they are going to appear on this
green line on the left. They have to be on the green line if they are in equilibrium.
Let's look at a case where zA is 0.4 and we want to vaporize 60% of the feed. If V, F
and L represent molar flow rates, V/F is 0.6, you are vaporizing 60%, 40% remains as a liquid.
So we are going to feed in a liquid and separating into a vapor and a liquid. So to draw the
Q line what we are going to do is, write down mass balances. One is pretty simple- the vapor
plus the liquid must equal the feed, however much we are feeding in must come out as either
the vapor or the liquid. That is an overall mass balance. We will then write a mass balance
for component A. It's arbitrary but let's do it for component A, which says, F times
zA, this is the number of moles of A per time being fed, and it is leaving as vapor, mole
fraction yA, or as liquid, mole fraction xA. So number of moles of liquid for example,
per time, times the mole faction of A in that liquid tells us how many moles of A per time
are leaving as a liquid. Well we can combine these two equations and eliminate L. And so
the algebra is pretty simple so I am just going to write down the answer. And I have
written it in this form because we are interested in a certain fraction that is being evaporated,
in this case 0.6. So in the equation that V/F appears because we know that value. And
so what we are going to do is draw this mass balance. This is a line, it's linear. zA is
fixed. Since I know the value for zA and I know the value for V/F, I can actually write
the equation for this line. So let me write this equation again here, that yA is minus
2/3 xA plus 2/3. So that is the line that we want to plot on our yx diagram and it is
easy to see if we look at this equation, for example. If xA equals yA, equals zA, the value
we are using, 0.4, then of course we get back to this equation. Which we know is satisfied.
So that means that one point on this line is 0.4, 0.4. Now another point when xA is
zero, yA is 2/3 so that's about here. This is the q line. It corresponds to the mass
balance. This point then, since this is where vapor and liquid are in equilibrium, corresponds
to the values for yA and xA leaving this flash unit. So we use the graphical representation
we are plotting the mole fraction of the vapor verses the mole fraction of the liquid, the
green line. And then drawing the q line, the purple line, which corresponds to mass balance,
taking advantage of the xA equals yA line to locate one point and then essentially using
the slope or the intersection to draw the q line and determine what the composition.
And of course this composition corresponds to a certain temperature. We can go back and
look at a Txy diagram, determine what that temperature is. So if we have a given feed
composition and we fix what fraction is going to be in the vapor phase in order for it to
satisfy the mass balances and to satisfy phase equilibrium we have to be at a specific temperature.
That is something then that we can go back and read off of a Txy diagram.