The alveolar air equation
If we wish to determine the alveolar concentration of a gas X, it is
clear that:
alveolar concentration
_{X} = Fi
_{X} 
uptake
_{X}/
_{A}
In other words, the final alveolar concentration depends on the
inspired concentration less the change in concentration due to removal
of the gas. As the alveolar ventilation (
_{A}) increases, so
will the change in concentration due to removal decrease, because more
of the gas is being provided in the inhaled air. Similarly, if a gas
(such as CO2) is being added, the above version of the alveolar air
equation will allow us to calculate the alveolar concentration, given
inspired concentration, output of the gas, and
_{A}.
(We must of course change the sign to "+" as the amount will be greater
than the inspired concentration).

An alternative, convenient but inaccurate
way of estimating P_{A}O2 is
to assume that the amount of oxygen absorbed is almost the same
as the amount of CO_{2} produced! If we do this, then we
can estimate that:
P_{A}O2 ~ PiO2  P_{A}CO2
 Using the knowledge that carbon dioxide rapidly diffuses across
the membranes of the alveolus into the blood, we can say that
P_{A}O2 ~ PiO2  P_{a}CO2
In other words, we can substitute arterial PCO2 (PaCO2) for
the moredifficulttomeasure P_{A}CO2, without much loss
of accuracy. This is more than a trifle inaccurate, as in most
people the ratio of CO2 production to oxygen consumption
(respiratory quotient or RQ) is about
0.8 to one. We can compensate for this by:

P_{A}O2 ~
PiO2  PaCO2 / RQ
 This is still not quite right, because the volume
of inspired gas will also change if the RQ is not one. We can
compensate for this by:
P_{A}O2 ~
PiO2  PaCO2 / RQ * (1  FiO2(1RQ) )