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## Health and medicine

# Alveolar gas equation - part 2

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.

## Want to join the conversation?

- Around3:45, Rishi talks about the Respiratory Quotient and how it is related to a person's diet. Instead of using what the person eats to compute the RQ, could a doctor measure the RQ to figure out what a person is eating?(2 votes)
- While the RQ can be directly measured using very cumbersome equipment (i.e. it's very rarely done in practice), doing so would provide almost no information about someone's diet since only the most extreme of diets result in a RQ that differs measurably from a value of 0.8. In the event the value was very different than 0.8, it would only tell you that the person's diet was extreme, but wouldn't necessarily inform you in what way.(7 votes)

- I am curious about using the alveolar gas equation at high altitude; but I got some funny numbers. For example, if I take the pressure of say Long's Peak (a popular hike near here in Denver) then it's around 450 mm Hg. So PAO2 = 0.20(450 - 47) - (40/0.8) = 30.6 mm Hg. But this just doesn't seem right -- it's way too low. I tried to think about it about and I am wondering if perhaps the vapor pressure of water changes at altitude and is no longer 47? Or if perhaps the PaCO2 is not 40? Or what is going on?(3 votes)
- The PaCO2 will be lower than 40mmHg because respiratory rate is going to increase at that altitude until acclimatization occurs. The pressure of water vapor will not change. If the altitude of Long's Peak is around 14,000 feet, PaO2 is going to fall dramatically. An unacclimatized person will show signs of hypoxia at around 11-20 thousand feet. Of course its different if a person lives in Denver and climbs the peak; they are already acclimatized to a higher altitude and will have compensatory mechanism in place to deal with low FiO2. I live at sea level and if I were to climb to the tip I would certainly be hypoxic.(3 votes)

- What is Respiratory Quotient?!(1 vote)
- The ratio of the volume of carbon dioxide evolved to that of oxygen consumed by an organism, tissue, or cell in a given time.(4 votes)

- At4:02, is the amount of CO2 the body produces only dependant on diet?(1 vote)
- Co2 is produced by the body as a byproduct of metabolism, or in simpler terms CO2 is waste. It is removed from the body via respiration, or the entire breathing process, more specifically exhalation.

The production of CO2 is dependent on the activity of the body. For example, during exercise, there is high activity within your cells, and as we saw above, CO2 is a byproduct of cellular activity, waste. The more activity, the more waste.

With that said, THEORETICALLY, diet may have some effect if you eat a HUGE meal, but the effect would not be notable. Doing things like exercise would have a more marked effect on CO2 production.(3 votes)

- Could you help edit this equation to demonstrate what happens with diffusion hypoxia as a result of turning off a patients nitrous oxide flow? i.e. the massive diffusion of n2o back into the alveolar space?(1 vote)
- When the speaker refers to R/Q, is this the same as V/Q ratio. Ventilation/ Perfusion (Q) ratio?(1 vote)
- Why is the RQ for a person lower if they do not eat sugars? Is this based on which stage in cellular respiration that the fuel enters? For example, proteins or lipids bypassing glycolysis and jumping straight into TCA.

The second question related to that is why would a diet composed of fats or protein be more efficient than sugar? Shouldn't the body have to consume more fats or protein to produce the same amount of ATP? Glucose should yield more ATP as a more energy dense resource and should therefore be consumed at a slower rate to maintain ATP levels in the body. In that case wouldn't the body produce the same amount of CO2 regardless of the fuel source because it needs a certain amount of ATP?(1 vote) - Leaving off at7:58explains PaO2 fine. It would be interesting to address PvO2, or venous oxygen content, to understand if it would work in the formula. The PAO2 equation is the basis for many related respiratory equations and I ask if this equation can be used with venous blood gas results.(1 vote)
- What exactly is the formula for gas equation?(1 vote)
- For the alveolar equation, why aren't we also considering the O2 that is leaving the pulmonary capillaries and re entering the alveli after being gone through the systemic circuit?(1 vote)
- This video describes just part of the formula. In the last video of "Advanced Respiratory System Physiology", oxygen in the reverse direction is considered.(1 vote)

## 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.