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respiration - Why is the partial pressure of oxygen in blood same as that in alveoli - Biology Stack Exchange

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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