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The partial pressure of oxygen in alveoli is about 104 mmHg, after gas exchange it becomes 40mmHg. I understand that during gas exchange, the pressure gradient drives oxygen into the blood and Co2 out. My issue is that: since the partial pressure of oxygen in the alveolus is 104 mmHg and that of blood in the pulmonary capillary is 40mmHg, why would the partial pressure of oxygen in the blood after gas exchange also equal 104 mmHg and not 72mmHg since as oxygen leaves the alveolus the partial pressure drops and and increases by the same amount in the pulmonary capillary. At equilibrium shouldn't they both be at 72mmHg? Mathematically speaking:
104-X(Alveolar PO2)=40+X(blood PO2)

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There are three unfounded assumptions in your equation that I can see.

  1. You're treating partial pressure as a concentration. Partial pressures are not concentrations, though they're convenient representations of concentration for gases because the behaviors of gases, especially with respect to diffusion between gases and liquids, behave according to partial pressure via Henry's law. For oxygen in blood, partial pressures are even more distinct from the "amount of oxygen per volume", because most of the oxygen carried in blood is bound to hemoglobin rather than floating freely/dissolved in the liquid.

  2. You're assuming there is a finite amount of oxygen present in the alveoli, as if 104 mmHg of oxygen is present in the alveoli, and then blood comes and takes some of it away. That isn't the case; blood is constantly coming in through the capillaries, and there is constant diffusion and bulk flow of gases throughout the lungs (resupplied with external inspired air).

  3. Following (1) and (2), it seems you're assuming the blood and gas are the same volume. This need not be the case.

Instead, to understand why the partial pressure of oxygen in blood leaving the lungs is the same as the partial pressure of oxygen in the alveoli themselves, it's important to realize that the surface area of the alveoli is absolutely massive, and that gases diffuse quite freely across distances the sizes of capillaries. They're the same for the same reason that if you put some water soluble dye in a glass of water and shake it up vigorously for a few seconds, you're going to find the dye evenly distributed. If it weren't evenly distributed to start, it's going to be very close when you're done. Same with blood through the lungs. If you put a little more oxygen into the alveoli, then a little more would flow into the blood; both concentrations would be higher, but they'd still be the same.

So, that tells you why the number is the same, but why is this number about 104 mmHg? Well, that exact number is going to vary by specific conditions, but you can be certain that the number will be an equilibrium somewhere between the atmospheric concentration of oxygen and the oxygen of blood entering the lungs. That averaging has already happened and is happening constantly all the time.

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  • $\begingroup$ @ Bryan Krause; if the pressure in the alveolus is constant, then why is it that after the diffusion of O2 into the capillaries( in external respiration) the PO2 of Alveolar air reduces to 40 mmHg. Also, in internal respiration, the PO2 of blood reduces to 40 after Oxygen diffuses into the tissues, if pressure was constant there should be no reduction. BTW, I would appreciate if you could give me another analogy, the "dye" one was difficult to imagine. $\endgroup$
    – Taofeek
    Commented Nov 24, 2021 at 6:32
  • $\begingroup$ I read somewhere that the difference between the vol of air in the alveoli and the vol of blood in the capillaries also plays a role in why the partial pressures are the same. And you also said it in your explanation, so I was wondering how they could be related $\endgroup$
    – Taofeek
    Commented Nov 24, 2021 at 6:49
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    $\begingroup$ @Taofeek "the PO2 of Alveolar air reduces to 40 mmHg" - it doesn't. If you stopped breathing for a long time perhaps it eventually would, but not for normal breathing. "the PO2 of blood reduces to 40 after Oxygen diffuses into the tissues, if pressure was constant there should be no reduction" - I never said pressure was constant everywhere. There is low oxygen in tissues due to cellular respiration. Blood leaving the tissues has lower oxygen than blood entering the tissues, but blood leaving the tissues has about the same pressure of oxygen as the tissues themselves. $\endgroup$
    – Bryan Krause ♦
    Commented Nov 24, 2021 at 14:27
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    $\begingroup$ Another factor to consider is that oxygen is not (primarily) dissolved in the blood, it's chemically bound to hemoglobin. So partial pressure may not be all that relevant. $\endgroup$
    – jamesqf
    Commented Nov 24, 2021 at 18:36
  • $\begingroup$ @jamesqf Added that as an additional point under (1). It still remains that you can't treat partial pressures as concentrations for any solution, but it's particularly true for blood and oxygen (or CO2) as these are primarily carried by hemoglobin, so even if you used the partition coefficients for water or plasma you'd come up with some very wrong numbers. $\endgroup$
    – Bryan Krause ♦
    Commented Nov 24, 2021 at 19:03

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