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# Alveolar gas equation - part 1

Find out how to calculate exactly how much oxygen is deep down inside your lungs! Rishi is a pediatric infectious disease physician and works at Khan Academy.
These videos do not provide medical advice and are for informational purposes only. The videos are not intended to be a substitute for professional medical advice, diagnosis or treatment. Always seek the advice of a qualified health provider with any questions you may have regarding a medical condition. Never disregard professional medical advice or delay in seeking it because of something you have read or seen in any Khan Academy video. Created by Rishi Desai.

Video transcript

Let's say this person is
lying here in front of me. And I'm thinking
about how the air is passing through their
nose and their mouth and entering their lungs. And specifically I'm interested
this time in how much oxygen is actually getting
to their alveolar sacs. So, deep inside their lungs
they have these branches, they're conducting in
respiratory bronchials. But at the end, of course,
they have these alveolar sacs that we've talked about. And I'm interested in thinking
about how much oxygen is really down there at the very ends. And you have to excuse
this alveolar sac. It really is that. It looks a little bit like a
three-leaf clover, I guess. But that's the issue. How much oxygen is deep
down in here where the x is? So how do we figure this out? I want to first
think about the air this gentleman is breathing in. He's breathing in air
from the atmosphere. So this is atmospheric
pressure air. And we say ATM for short. And we know that atmospheric
pressure at sea level is 760 millimeters of mercury. It's going to be lower
at higher altitudes. So, if you're at the
top of a mountain, it would be less than that. And this pressure is made up of
many, many different molecules bouncing around. So, I've got some
molecules of oxygen. Let's say this is about 21%. This is my oxygen. And before I move on,
I should mention FiO2. You might come across this. And FiO2 stands for the
fraction-- which in this case was 21% or 0.21--
fraction of inspired, meaning how much oxygen
you took in or air you took in-- fraction
of inspired oxygen. And the fraction happens to be
21%, which is, of course, much, much lower than the nitrogen. Now nitrogen-- when
I draw it this way-- it's pretty impressive. All the purple is nitrogen. This is about 78% of
what you're breathing in. And the last little
tiny little bit, I'm going to draw
the green line. This is mostly argon. And argon is-- in
Greek, it actually comes from the term lazy. But it basically reminds
me when I think of that, that argon is not
going to do much. It's not going to react with
anything that is in our body. And of course, you have other. You have less than 1%. And this would be things
like carbon dioxide. So, this is a
breakdown of the air that my friend is breathing in. This is my friend breathing. And if I want to now think
about how much oxygen they're taking in,
all I have to do is a little tiny bit of math. I can say OK, pO2-- this is the
partial pressure of oxygen-- is just 0.21, or 21%, times
760 millimeters of mercury. And this turns out to be
160 millimeters of mercury. Now, that oxygen kind of
goes down in his lungs. And it goes through his
trachea and into his-- all the little bronchials and
down into the alveolar sac. And when it gets there--
on the way over there, an interesting thing happens. The body temperature here
is 37 degrees Celsius. He's got a normal
body temperature. And what that does
is-- the air is going through these
bronchials and trachea. And as it does, there's
a lot of moisture in the respiratory tree. There's moisture there. And that moisture,
when it starts heating up-- and of
course, 37 degrees is pretty warm-- It's going to
start leaving the liquid phase and going into the gas phase. So all of a sudden you
have now little molecules. I'm going to draw them
as little dots of water. That's here. And it's going to start
entering and mingling with the gas that's
going through. So, the gas that got
taken in, that he inhaled is now mingling. And what happens as a
result, is that water has what we call
a vapor pressure. And that vapor pressure
is going to change depending on the temperature. But at 37 degrees,
that vapor pressure ends up being 47
millimeters of mercury. In other words, if the
temperature is 37 degrees, then we can expect that some
of those water molecules will leave the liquid
and enter the gas phase. And it turns out that
the amount of molecules-- or the number of
molecules-- that leave are going to generate
a pressure that is 47 millimeters of mercury. And this is pretty standard. This is known off of a table. And in fact, if
you think about it, if you just generated
lots of heat-- let's say you actually were
boiling water-- that would be 100
degrees Celsius. And the vapor pressure
there would be very high, because it's boiling. And it would be 760. So boiling is actually 760. So just keep that in mind. Boiling water has a
vapor pressure of-- And what do you think
760 reminds you of? That is atmospheric pressure. So it's interesting. Vapor pressure is going to
equal atmospheric pressure when you are boiling water. And that's actually exactly
what's happening as you boil. But I don't want to
get too distracted. We're not boiling water inside
of our bodies or our lungs. We're actually much
cooler than that. But we are warm. We're at 37 degrees. And so you do have some of these
little water molecules that have entered the gas phase. And so if overall it's got
to be-- this whole thing has got to be 760. So, on average,
our lung pressures are going to be the same
as atmospheric pressure. But now you've got
water taking up 47. So if water's taking up 47,
the rest of those little gas molecules have got to be 713. So this is the rest. What was in that rest? It's going to be
the same as before. It's going to be-- and I'm
going to try to sketch it as best as possible--
this is going to be my oxygen right here. This is 21% of 713. And then we have lots and
lots of nitrogen still. Same kind of break
down as before. And remember this is all
air that is being inhaled. So we're not talking
about breathing out. We're just talking
about breathing in. And this purple right
here-- and this is 78%. Again, this is 78%
percent of 713. And we still have a
little bit of that argon, and those other gases--
I won't write it all out, but you get the idea. That basically now
because water is taking up some of the overall pressure,
all of the other gases are going to have a
lower partial pressure. So what is the partial
pressure of the air that's entering into that alveolar sac? It's going to be basically
FiO2, which is 21%. I'll write that here. And then we have the
atmospheric pressure. This is atmospheric
pressure over here. And we said that was 760. We can draw a little arrow so
we know what's pointing to what. 760 millimeters of mercury. And then, from that to account
for the partial pressure of water. Because now we have some
water vapor in there. We have to subtract out 47. So, so far, if you've
kept up with this math, you see that we have-- what
does that work out to be? About 150 millimeters
of mercury. Now this is the partial pressure
of oxygen, at this spot. Let me just make it very
clear with my arrow, not at this orange x. So far, we've
figured out that we have a partial pressure that's
a little bit lower than when we started. And that was because of the
partial pressure of water. Let's pick up there
in our next video.