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# How can alveolar gas contain water vapor and less oxygen if the breathing loop is isobaric?

I was wondering why the partial pressure of oxygen is lower in the alveoli than in the air we inspire. From this related question I found the answer that the water inside the lung saturates the air and lowers the partial pressure of oxygen.

Here is the associated equation :
$$p_{A}^{O2}=F_{I}^{O2}(P_{ATM}-p_{H2O})-\frac{p_{a}^{CO2}(1-F_{I}^{O2}(1-RER))}{RER}$$

On the other hand, from other sources I found that breathing is isobaric, that is there is the same total pressure of 1 atm whether it is outside our body, in the airways or in the alveoli.

So if you add water vapor in the inhaled gas, that is 47 mmHg as depicted here, how could the total pressure stay 760 mmHg ? For the partial pressure of oxygen to be reduced, there is only two ways from my point of view: either you reduce the total pressure (excluded) or you remove some oxygen molecules. So this would mean that during the trajectory of air through our airways, oxygen molecules are replaced or left outside by water molecules ? How is that possible ?