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# Alveolar gas equation - part 2

## Video transcript

in our last video we were kind of getting to the the idea that there's a partial pressure of oxygen that is a little bit lower in the in the bronchial tree than you would expect you know 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 P h2o represents this is the partial pressure of water in your lungs because of course it's pretty warm in there right this is the 37 degrees that I had drawn up here so you know I had said well of course you know 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 out 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 right this is the partial pressure of oxygen but that's not this watch this and there's a subtle difference right and the difference is this capital a what is 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 well let's start where we left off and I'll kind of 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 well you can see on the one hand you've got some oxygen coming in right that's what I circled with the red arrow and that's all this stuff this is all the stuff kind of 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 kind of rushing by and there might be some gas exchange of course there probably will be some gas exchange right so you have some stuff coming in oxygen wise but also some oxygen going out and so if you have some going out you have to subtract from this formula the oxygen that's leaving that would be that 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 you know 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 oxide now refer to that as P big a co2 and you also have carbon dioxide in here and this is I'm going to refer to this one is P little a co2 and it turns out that in the blood vessel in the alveolar sac the concentration of carbon dioxide is basically the same because it equilibrate s' really well and 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 kind of 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 well here's where things get kind of fun so it turns out that there's a relationship and we call it the respiratory quotient respiratory respiratory quotient and rest for a quotient actually sometimes they end up short handing it to just RQ so sometimes LCR Q and what our Q is is it's a relationship between oxygen 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 well 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 my ratio this is my ratio of co2 - OH - my ratio is going to be what it's going to be one right that's a ten versus ten is a ratio of one if you divide the two right 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 well it turns out that now my body is actually a little bit more efficient and by that what I mean is that with ten molecules of oxygen used your body only makes seven molecules of carbon dioxide so it's actually a lot better than then before less waste right and so the ratio ends up being better point seven so the ratio is actually lower with lipids and you know of course we have diets that are probably mixed right you most people have a mixed diet not just one thing or another so if you have a mixed diet they've kind of estimated something in between and said okay well maybe a ratio of oxygen to carbon dioxide is something like point eight 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 forty so let me show you that on this picture that basically means that if we have then let me do it a different color carbon dioxide is going from their blood vessel forty millimeters of mercury that's a partial pressure but that's of course a reflection of how many molecules there are then I can just divide by the rest Troy quotient which is 0.8 that kind of 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 can say ah it must be basically 50 50 millimeters of mercury worth of oxygen left and I base that on the fact that I know 40 millimeters of mercury of carbon oxide came in so because of that relationship see this ratio is really cool right 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 okay well 150 millimeters of mercury is where we are 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 a hundred millimeters of mercury like that