Net CO2 production:
CO2 Production(1)
Net O2 consumption:
O2 Consumption(2)
Respiratory quotient:
Respiratory quotient(3)
Inspired & expired gas composition:
Inspired gas composition(4)
Inspired gas composition(5)
X represents gases that are neither produced nor excreted.
Therefore, at steady state:
Inert gas equivalency(6)
Solving for Vexp
Vexp solved(7)
Using (7) to restate (1) and (2) as f(Vinsp)
VCO2 solved for Vinsp(8)
VO2 solved for Vinsp(9)
Substituting (8) and (9) into (3):
solved for FeO2(10)
The same result can be obtained by solving for Vinsp
Vinsp equation(7a)
VCO2 as f(Ve)(8a)
VO2 as f(Ve)(9a)
solved for FeO2(10a)
Under normal physiologic circumstances, FiCO2 approx 0
Therefore, (10) reduces to:
solved for FeO2 (approx)(11)
By Dalton's law of partial pressures, the full humidification of alveolar air and the high diffusibility of CO2:
PAO2 equation(12)
Cruickshank S, Hirschauer N. The alveolar gas equation Contin Educ Anaesth Crit Care Pain (2004) 4(1):24-27. doi: 10.1093/bjaceaccp/mkh008 Web.

Fenn WO, Rahn H, Otis AB. A theoretical study of the composition of the alveolar air at altitude. Am J Physiol. 1946 Aug;146:637-53. PubMed PMID: 20996488. Web