# Alveolar gas equation - part 2

## Video transcript

In our last video, we were
kind of getting to the idea that there's a partial
pressure of oxygen that is a little bit lower
in the bronchial tree than you would expect by
just comparing it to the air that you breathe in. And the reason is
because we said, well, of course you have a
little bit of water vapor. And that's what this
little pH2O represents. This is the partial pressure
of water in your lungs, because, of course, it's
pretty warm in there. This is the 37 degrees
that I had drawn up here. So I had said, well, of
course this works out to 150. And just to go over
that math very quickly, it was because
this FIO2 is 0.21. And we multiply by 760
millimeters of mercury. That's this
atmospheric pressure. And subtract off 47, because
that was the partial pressure of some of that water vapor
that we get in our lungs. And that's how we
got our 150 answer. But I had said in the last
video that actually, that's not the alveolar oxygen. This is the partial
pressure of oxygen. But that's not this. Watch this And there's
a subtle difference. And the difference
is this capital A. This A means the alveolar,
because it's capitalized just like this A over
here is capitalized. So how do we calculate the
alveolar oxygen concentration? Let's start where we left
off, and I'll wrap things up. I'll show you how you do it. You basically have
to think about it from a person's point of view. Let's imagine that
you're a little person, and you're standing here inside
of this little alveolar sac. You can see on the
one hand, you've got some oxygen coming in. That's what I circled
at the red arrow. And that's all this stuff. This is all the stuff coming in. But you also can
see that, of course, alveoli are going to
be releasing oxygen to a little blood vessel nearby. So of course if there's an
alveolar sac right here, you must also have
some blood rushing by. And there might be
some gas exchange. Of course, there probably
will be some gas exchange. So you have some stuff
coming in oxygen-wise, but you also have
some oxygen going out. And so if you have
some oxygen going out, you have to subtract
from this formula the oxygen that's leaving. And that would be the second
part of this equation. We have to figure out
how much is leaving. Because again, if you
keep your eye on that x, you really want to know what
is the steady state of oxygen in the alveolar sac. How much is coming, but
also how much is going? So at any point in
time during inhalation, what is the actual alveolar
partial pressure of oxygen? So we have to
remember in and out. So how do we figure out
how much oxygen is leaving? Well, the first
trick is remembering that you have some carbon
dioxide in here as well. So here you have
some carbon dioxide. And I'll refer to that as PACO2. And you also have
carbon dioxide in here. And I'm going to refer
to this one as PaCO2. And it turns out that in the
blood vessel in the alveolar sac, the concentration of carbon
dioxide is basically the same. Because it equilibrates
really well. In that number
turns out to be 40. So the partial pressure
of arterial-- and I could just as easily
say alveolar here-- but arterial CO2, because
that's what we measure is 40. So that's the first
clue as to how we're going to figure out
how much oxygen is leaving. Now, how do we use the
carbon dioxide number to calculate how much oxygen
is leaving the alveolar sac? Here's where things get fun. It turns out that
there's a relationship, and we call it the
respiratory quotient. And respiratory quotient--
actually sometimes they end up shorthanding
it to just RQ. So sometimes you'll see RQ. And what RQ is, is
it's a relationship between oxygen and
carbon dioxide. It's a relationship
between those two things. So for example, let's say
my diet is all sugars. Let's say that's all I ever eat. For every 10 molecules of oxygen
that I breathe in and use, my body cells are going to make
10 molecules of carbon dioxide. So my ratio-- and this is
my ratio of CO2 to O2-- my ratio is going to be what? It's going to be one. That's 10 versus 10 is a ratio
of 1 if you divide the 2. Now let's say instead of
sugars, my diet consists of, I don't know, let's say fats
and lipids and things like that. So a slightly different diet. It turns out that now
my body is actually a little bit more efficient. And by that what I mean is that
with 10 molecules of oxygen used, your body only makes seven
molecules of carbon dioxide. So it's actually a lot
better than before. Less waste. And so the ratio ends
up being better-- 0.7. So the ratio is actually
lower with lipids. And of course, we have diets
that are probably mixed. Most people have a mixed diet,
not just one thing or another. So if you have a mixed diet,
they've estimated something in between, and
said, OK, well maybe a ratio of oxygen to carbon
dioxide is something like 0.8. So if I know, going back
to our formula then, if I know that carbon
dioxide, the partial pressure in the alveolus or the
arterial is 40-- so let me show you that
on this picture. That basically means that
if we have then-- let me do it in a different color. Carbon dioxide is going
from the blood vessel-- 40 millimeters of mercury--
that's the partial pressure. But that's of
course a reflection of how many molecules
there are, then I can just divide by the
respiratory quotient, which is 0.8-- that gives me
a ratio to think about. And I can say,
ah, then that must mean that this is going
to be 40 divided by 0.8 which is 50 millimeters
of mercury of oxygen, O2, that must have left. So if I want to figure out
how much has gone out-- that's what these purple
arrows were-- I could say, ah, it must be
basically 50 millimeters of mercury worth of oxygen left. And I base that
on the fact that I know 40 millimeters of mercury
of carbon dioxide came in. So because of that
relationship-- see this ratio is really
cool, because you can say, ah, well if you know that
there's this relationship between the two, I can just
measure this thing, this guy. And I immediately
can get a good sense for how much oxygen
left my alveolar sac. And so then just plugging into
the formula you could say, OK, 150 millimeters
of mercury is where we're left here,
and then subtract off 50, because that's about how
much oxygen is leaving. And the net amount--
my PaO2 is going to be 100 millimeters
of mercury, like that.