there is a complication, this is not all about solution chemistry, this is a biological system that uses molecular affinities to transport O2 and CO2. A propertiy of any transport chain is lowest affinity at source of substance, highest affinity at destination. the overall efect is that small variences in atmospheric O2 have a large effect at the lung surface where the lowest O2 affinity occurs. This also is sensative to the promiscuity of haemoglobin, having affinity for BOTH O2 and CO2kneejerk link below V
http://bio1520.biology.gatech.edu/nutrition-transport-and-ho...
https://en.wikipedia.org/wiki/Oxygen%E2%80%93hemoglobin_diss...
www2.hawaii.edu/~moeng/Web_Zoo142/Lecture Notes/Zoo142ch23.pdf [PDF]
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