This screencast is going to cover the ideal gas equation of state. I will give you a quick
refresher on it what it is and provide an example at the end to test your abilities
to use it. So an equation of state is just a relationship between the molar quantity
and volume of a gas to its temperature and pressure. The ideal gas equation of state
is the simplest form. We write that out as the pressure times the volume of the gas,
is going to be related to the moles of the gas times some gas constant we can write out
as R, and the temperature T. Make sure you use the absolute pressure and typically the
units on that will be pascals, bars, atmospheres, mmHg, and ect. The V stands for the volume of the gas the units
on that will typically be L, meters cubed, mL, or feet cubed. Now no the other side of
the equation n is going to be the moles of the gas typically is going to be written as
moles. You might see kmol or some other unit of moles. So make sure that you do the proper
conversions when using that. Now R is the gas constant and it is important to use the
appropriate gas constant depending on the units of your other variables. The form the
gas constant therefore is going to have a pressure-volume units over moles-temperature
units. So make sure that that is consistent and that your units are correct when using
the gas constant. Typically the gas constant can be found in any kind of properties handbook.
and also at the back of some of the major textbooks, and the last variable is T, is
the absolute temperature. So it is always going to be kelvin or degree rankin make sure
that is correct when using that. Now while everybody hopefully is familiar with the PV=nRT
form there are 2 other forms you may see or encounter in the near future. The first is
if you have some kind of flow system. You may see something of the follow form where
the variables for V and n have a dot above them. This stands for some kind of flow. So
on the left you are going to have a volumetric flow and on the right you are going to have
some kind of molar flow. Now of course there may be another form where instead of moles it is related to
mass and molecular weight. So just something to keep in mind when we see this dots over
the variables. The other form is where you might see this hat over the V. Basically what
that is doing is using the specific molar volume, V-hat, therefore, an example of units
for the specific volume may be something like meter cubed per mole. Now there are a couple
of assumptions that allow us to use the ideal gas law. The first assumption is that the
gas molecules have a negligible volume. The second assumption is that molecules exert
no force on each other. Thus that means that as molecule A is traveling along molecule
B will not exert any interaction with that path of molecule A. Now if they crash into
each other or if molecule A crashes into a wall of the container these collisions will occur
elastically, and those are the assumptions. The basic assumptions that we use to make
the ideal gas law. STP or standard temperature and pressure are the conditions were standard
temperature is 273 kelvin and standard pressure is 1 atm. The thing about ideal gases is
that at STP conditions 1 mole of an ideal gas occupies 22.414 liters of space, and we
get this by setting up our ideal gas law. and plugging in the values for pressure, and
1 atm, unknown volume, and this is going to be equal to 1 mole of gas again doesn't matter
what kind of gas it is times our temperature of 273 kelvin times our gas constant, which
in this case is going to be 0.08206 that is going to have units of atm*L/mol*K. So when
we do this calculation we get a volume of 22.414 L. So all ideal gases 1 mole takes
up 22.414 L. Probably a good number to remember.
So let's use the ideal gas law to take a quick look at say breathing. We are going to simplify a lot of things here, but let's just say we
have air coming into the lung and that is made up of just noncondensable gases and all
those gases are going to behave ideally. So what I want to propose that if we breathe
in air at room temperature. You know room temperature typically being around
20 degree Celsius, and that is at 1 atm. We let it equilibrate in our lungs. What
is the pressure of the air going to be inside of the lungs. Once it reaches body temperature,
which is about 37 degree Celsius. So at this point I would say go ahead and
give it a shot. Let me know what the pressure inside the lungs is going to end up being,
and you are going to write out the ideal gas law.You are going to say we have
a temperature going in and we know the pressure going in and we can look up a gas constant,
but we don't know what the volume or the amount of moles. True. So in this case and let me
go ahead and give you the volume of the lungs as being 4 liters, and we are going to go
through this calculation and I will show you why you don't even need that, but assuming
that you have now a volume of 4 L. We can plug in for the first step to figure the amount
of moles that we breathe in. 1 atm for pressure, volume of 4 liters of air. Some unknown amount
of moles, a gas constant and we are going to use that same one as we did before, which
is atm*L/mol*K, and this is going to be times an absolute temperature. So 273 plus 20 degrees
Celsius, and that is going to be Kelvin. When we do this calculation you should get the
amount of moles of air that you breathe in as 0.16695. We are going to go ahead and round
that up to 0.17 moles. So on the second case we will label that outlet as 2. We don't know
the pressure. We know that we have the same amount of volume. We are going to go ahead
and make the assumption that the lung capacity does not change. So we still have 4 liters
of air, and we know that we have 0.17 moles. Using the same gas constant I am not going
to write the units this time. You should always practice that you use them right. At this
point now the temperature has gone up to 37 degree Celsius. So 273 kelvin plus the 37
degree Celsius. When we do it this way we see that the pressure inside our lungs reaches
1.06174 atm or in other words 1.06. Now because we made the assumption that the volume does
not change and we know that the moles don't change and the gas constant doesn't change
we can simply write out the following relationship. P1 times V equals nRT1, and in the second
case we do the same thing, and we can divide these two equations by each other and we get
a relationship P1 over P2 equals T1 over T2. So of we go this route we can see that P2
is going to be equal to T2 over T1 times P1, and this comes out to 310K over 293K times
1 atm, and that gives use the same thing we solved before 1.06 atm. So that is the pressure
inside the lungs. So a question that came up recently actually was at lower temperatures,
say freezing 0 degree Celsius how is this going to affect how we hold our breath. Well
let's do these same calculations, but instead of the outside air temperature being 20 degree
Celsius let's change this to 0 degree Celsius. So let's use that exact relationship that we
just set up before P1 over P2 equals T1 over T2. So our P2 is going to be equal to T2 over
T1 times P1. Using the new values that we have this time. We have 273 K times the 1
atm, What we are going to see this time is that the pressure is going to be 1.135 atm.
So at colder temperatures it actually increases the pressure in our lungs once it reaches
equilibrium in our body. So it is harder to hold your breath at colder temperatures arguably.
Of course now we are making a lot of assumptions of the body and that the lungs are not actually
changing its volume, but this gives you a quick easy relationship using the ideal gas
law. Hopefully this screencast has shown you how to use the ideal gas law to calculate
some of the properties of gases given other conditions.