Which expression correctly represents the alveolar (PAO2) equation?

• A. PAO2 = FiO2 × (Pb − PH2O) − (PaCO2 / R)
• B. PAO2 = FiO2 × (Pb − PH2O) + (PaCO2 / R)
• C. PAO2 = FiO2 × Pb − (PaCO2 / R)
• D. PAO2 = PaO2 × 0.8

Answer: (A)

The main idea is to estimate the oxygen tension in the alveoli by accounting for the oxygen you actually inspired, the water vapor that humidifies that air, and the CO2 that must be exhaled. The correct expression combines these factors as PAO2 = FiO2 × (Pb − PH2O) − (PaCO2 / R).

Why this form is best: FiO2 tells you how much oxygen is in the inspired air. Subtracting PH2O from Pb gives the pressure available for dry inspired gas after humidification. Multiplying by FiO2 scales that available pressure to the alveolar oxygen contribution. Then you subtract PaCO2 divided by the respiratory quotient R because CO2 production and clearance effectively reduce the amount of oxygen available in the alveoli for metabolic use; the ratio R (approximately 0.8 in healthy adults) reflects the amount of CO2 produced per O2 consumed. Putting it together gives PAO2 in mmHg, and with standard sea-level values you get a typical alveolar O2 around 100 mmHg on room air.

For context, at sea level Pb ≈ 760 mmHg and PH2O ≈ 47 mmHg, so PAO2 ≈ FiO2 × (760 − 47) − (PaCO2 / R). If PaCO2 is about 40 mmHg and R ≈ 0.8, PAO2 ≈ 0.21 × 713 − 50 ≈ 150 − 50 ≈ 100 mmHg, which matches normal physiology.

Other forms miss important pieces: adding the CO2 term would overcount its effect; omitting PH2O ignores humidification of inspired air; and a simple PAO2 = PaO2 × 0.8 misuses arterial oxygen to estimate alveolar oxygen and ignores the inspiratory and humidification factors.