Alveolar gas equation

The main job of the lungs is gas exchange, pulling oxygen into the body and getting rid of carbon dioxide. Normally, during an inhale - the diaphragm and chest muscles contract to pull open the chest and that sucks in air like a vacuum cleaner, and then during an exhale - the muscles relax, allowing the lungs to spring back to their normal size pushing that air out.

When we breathe in, oxygen-filled air from the environment enters through the nostrils, goes through the airways, and finally reaches the alveoli, the tiny air-filled sacs in the lungs where oxygen finally moves into the blood.

The amount of oxygen in the alveolus equals whatever enters from the airways minus whatever moves into the blood, and that relationship is the alveolar gas equation.

The total pressure of the air in the alveoli is equal to the atmospheric pressure outside, Patm. But unlike atmospheric air, the air inside the alveoli gets saturated with water vapor after travelling through the moist airways.

The partial pressure of water vapor is Pvapor. So in the alveoli, the total pressure, which is equal to the atmospheric pressure, is equal to the pressure of water vapor plus the pressure of the mixture of gases.

So, rearranging,i the total alveolar pressure exerted from all of the gases except water vapor is equal to (Patm- Pvapor).

Now, let's take this mixture of gas particles, red being oxygen and blue being CO2.i the partial pressure of one of the gases is proportional to the fractional concentration of the gas in that mixture, which is a fancy way of saying the fraction of that gas molecule to all the gas molecules, so in this case CO2 would have a fractional concentration of 0.3, since it accounts for 30% of the gas molecules, and O2 would be .7, since it accounts for the remaining 70%.

The reason these are proportional to the partial pressure is that more molecules are more likely to bounce around and hit the container.

With our example, we see way more O2 balls bouncing off the container as CO2 balls, simply because there are more of them, every time one of these bounces, they exert pressure!

So, based on that, you’d expect the O2 to exert more pressure than the CO2—proportional to their fractional concentrations!

How much? Well, let’s say the total pressure in the box was 20 mmHg, then the partial pressure of oxygen would be 0.7 x 20 = 14 mmHg, and carbon dioxide would be 0.3 x 20 = 6 mmHg!

Where we’re just multiplying the total pressure by the fractional concentration. So basically this equation is the fractional concentration of oxygen in air FO2 times the total pressure of the mixture of gases Pgases, and since we’re looking at inspired air, let’s say the partial pressure of inspired air PiO2 and the fractional concentation of oxygen in inspired air, FiO2.i and remembering our equation we found from before that takes water vapor into account, the partial pressure PiO2 will be: PiO2 = FiO2 X (Patm- Pvapor) Ok so back to our alveoli, we’ve got an equation for partial pressure of air coming into the alveoli, but what about the other side, the partial pressure of oxygen in the arterioles, with little ‘a’ for arteriolar, where you have oxygen dissolving into blood.

In calculating how much oxygen is consumed by the body, we make use of the respiratory quotient, abbreviated as R. Put simply, it is the ratio of carbon dioxide molecules produced by the body to oxygen molecules consumed by the body.

The value of R depends on our diet, and for a person consuming a healthy mix of carbohydrates, proteins, and fats, R is around 0.8.

In other words, for every 10 molecules of oxygen that we consume from the blood, we produce 8 molecules of carbon dioxide.

So going back to the alveoli, 10 molecules of oxygen move from the alveoli and into the blood and get replaced by 8 molecules of carbon dioxide.

So, if we know how much carbon dioxide is in the alveoli and we know the respiratory quotient R, we can figure out how much oxygen moved into the blood by rearranging this equation.

Also, remember that partial pressure is proportional to the fractional concentration, so essentially this becomes partial pressure of oxygen dissolved in the blood, or little a for arteriole, equals partial pressure of CO2 dissolved in the blood, divided by R.

Now, these 8 molecules in the alveoli actually represent the partial pressure of CO2 in the alveolus, or PACO2, where PaCO2 from our equation would be the CO2 dissolved in the blood down here, but it turns out that carbon dioxide is so highly soluble in water or blood that its partial pressure in the alveoli is equal to its partial pressure in the blood.

So the partial pressure of oxygen that’s dissolved in the blood equals the partial pressure of CO2 in the alveoli divided by R.

PaO2 = (PACO2) / R So going back to the beginning - remember how we said the amount of oxygen in the alveolus equals the amount in airways minus the amount taken into the blood?

Well, since again partial pressure’s proportional to the concentrations, then the partial pressure of oxygen inside the alveolus, PAO2, equals the partial pressure of inspired oxygen, PiO2, minus the partial pressure of oxygen going into the blood, PaO2.

And now we’ve got all the pieces we need, so plugging in Partial pressure of inspired O2 and partial pressure of O2 in the arterioles, we get: PAO2 = [FiO2 X (Patm- Pvapor)] - [(PACO2) / R] This is the alveolar gas equation.

This might look daunting at first but if you plug in some real-life numbers it becomes quite simple. Normal air has about 21% oxygen, so FiO2 is 0.21.

Atmospheric pressure is 760 mmHg. Water vapor pressure is 47 mmHg.

And R is 0.8. So the equation becomes PAO2 = 150 - (1.25 X PACO2) All right, as a quick recap… the alveolar gas equation describes the relationship between the partial pressure of oxygen inside the alveolus to the partial pressure of carbon dioxide in the alveolus which is equal to the partial pressure of carbon dioxide in the arterioles, P little a O2.