In this screencast we will look at water as a condensable species. In many systems water
is present in a gas stream, and can be condensed out. So let's make our system. Let's say we
have a dehumidifier and coming in we have a stream of water and air coming out we have
a stream of water and air, but we have condensed out some of the water from the air. So let's
say that for the sake of this dehumidifier that the water and air comes in at 30 degree
C, and it is saturated with water. The dehumidifier operates at 15 degree C on the inside, and
we can thing of the dehumidifier as basically having a water phase of condensed water, and
a gas phase. We also know that our system is going to be at 1 atm. So what we are interested
in calculating is the mole fraction of water in the air coming in versus the mole fraction
of the water and the air coming out, and the equation we are going to use to solve this
is the a limiting case of Raoult's law. Raoult's law is used to relate the composition of the
gas to its saturation pressure. So what Raoult's law tells us is that yi the molar composition
of component i in the gas phase times the total pressure of this system, equals the
saturation pressure at a certain temperature. of component i. So in the case of this system
we are interested in calculating yi coming in and out of the system. So we can solve
for the fact that yi equals Pi saturation at a certain temperature, divided by the total
pressure of the system. So now we can find what the composition is coming into and out
of the dehumidifier. So first let's calculate the molar composition of the water and air
coming in to the system. So to do this we are going to need to look up the saturation
pressure of water at 30 degree C. So to do this we are going to use the table B.3 from
Felder and Rousseau, Elementary Principles of Chemical Processes, 3rd edition, and when we go to this table we can see that for 30
degree, come down to 30, and then 0 in the decimal place. That the saturation pressure
of water at 30 degrees is 31.824 mmHg. So now that we have the saturation pressure of
water. We can use it to calculate the mole fraction of water in the incoming stream.
So yi is going to equal 31.824 mmHg, divided by our atmospheric pressure, that we were
told was 1 atm, which is equivalent to 760 mmHg, and from this calculation we can see
that we have 0.041 moles of water per total moles. Next let's calculate the composition
of water in the gas coming out of the dehumidifier. So now we can see that our temperature is
decreased and Pi sat, we need to find out what it is at 15 degree Celsius, because the
dehumidifier has cooled off our system. So again we go to table B.3 from
Felder and Rousseau, and here in table B.3 we can find that at 15 degrees the saturation pressure of water
is 12.788 mmHg. So using the same equation for our input water stream. We can see now that
yi is going to equal 12.788 mmHg divided by again our total 760 mmHg of total pressure,
and this is going to give us now that the mole fraction of water in air is 0.0168 moles
of water per total moles. So as we can see the dehumidifier has successfully decreased
the mole fraction of water in air from our input to our output, and we can also see that
Raoult's law is a useful way to turn partial pressure into mole fractions. When we have
water in a system.