The air we breathe in has the same amount of oxygen (about 21 percent or just 0.21) at all altitudes. This is referred to as the Fraction of Inspired Oxygen or FiO2. However, the atmospheric air pressure, or Patm, decreases with altitude from about 760 mmHg at sea level to about 500 mmHg at the top of a 3000 meter mountain. So the problem is not that there’s proportionally less oxygen at high altitudes, but rather the problem is that the lower air pressure means that the same oxygen proportion will result in a lower partial pressure of oxygen in the alveoli, or PAO2 for short. So when there’s an increase in altitude, the amount of oxygen getting to the alveoli reduces. But luckily, the body makes physiological changes to keep the tissues well oxygenated even at low atmospheric pressures. Now if that fails, it can lead to altitude sickness.
OK, so normally, the respiratory mucosa is a bit moist, and at 37 degree Celsius (a normal body temperature), some water molecules exist as water vapor. These molecules create a pressure of their own known as the vapor pressure or pH2O, which is about 47 mm Hg. So the air we breathe in mixes up with these vapors and becomes humidified.
Now, at the end of inspiration, the air pressure within the alveoli becomes equal to the Patm, or the air pressure outside the body, but the composition is a bit different due to the humidification that takes place in the respiratory tract and alveoli. So if we want to know how much of the dry air remains within the alveoli, we have to subtract this vapor pressure from the mixture and then, multiply the dry air pressure with FiO2, to get the amount of oxygen that gets into the alveoli.
OK, now, across the alveolo-capillary membrane, gas exchange is happening all the time. Some oxygen molecules are diffusing across the membrane and binding to the hemoglobin within red blood cells. At the same time, red blood cells are dropping off carbon dioxide which diffuses from the blood, through the membrane, and into the alveoli so that it can be released in exhalation.
OK, let's check the amount of each of the gas crossing the wall. If we assume that there is no carbon dioxide in the inspired air, then that means that all of the carbon dioxide that is in the alveoli must have come from deoxygenated blood in the capillaries. The partial pressure of carbon dioxide in capillaries, or PaCO2, varies between 35 to 45 mm Hg, but let’s take the average, 40 mm Hg, and say that it’s the amount of CO2 that’s diffusing from the blood into the alveolar sacs. Now while this is happening, oxygen is also diffusing in the other direction, from the alveoli to the blood. So we have to determine the amount of oxygen that’s leaving and subtract it from the amount that’s in the alveoli. That gives us the steady state amount of oxygen partial pressure available in the alveoli, or PAO2. The amount of oxygen going into the blood, gets delivered to the body cells where it is used to oxidize substrates. Now, it turns out that there’s a pretty reliable ratio of carbon dioxide entering the alveoli to oxygen entering the blood represented by PaO2, with a little a for arteriole. This ratio is called the respiratory quotient or RQ. Rearranging a bit, that means that the amount of oxygen entering the blood is equal to the amount of carbon dioxide entering the alveoli divided by RQ. RQ varies a bit, but for someone eating a mixed diet, RQ is about 0.8. So, if the amount of carbon dioxide entering the alveoli is 40 mm hg, the amount of oxygen that’s being exchanged would be PaCO2/RQ, or 40 mm hg/0.8 or 50 mm Hg.
To tie things up, the partial pressure of oxygen available in alveoli at the end of every inspiration is the partial pressure of oxygen in the inspired dry air, minus the partial pressure of oxygen that has already left the alveoli to the capillaries. That’s the alveolar gas equation.