In the alveolar gas equation, the alveolar O2 tension (PAO2) is calculated as: PAO2 = FIO2 × (Patm − PH2O) − (PaCO2/R). At sea level breathing room air (FIO2 = 0.21, Patm = 760 mmHg, PH2O = 47 mmHg, PaCO2 = 40 mmHg, R = 0.8), what is the PAO2, and what is the normal A-a gradient?

• A PAO2 = 120 mmHg; A-a gradient = 25 mmHg; normal up to 30 mmHg
• B PAO2 = 100 mmHg; A-a gradient = 5–15 mmHg with PaO2 ~ 95 mmHg; normal A-a gradient for age <30 is < 10 mmHg ✓
• C PAO2 = 80 mmHg; A-a gradient = 0 mmHg because alveolar and arterial O2 are equal
• D PAO2 = 100 mmHg; A-a gradient = 30–40 mmHg due to normal shunt fraction

Explanation

PAO2 = 0.21 × (760 − 47) − (40/0.8) = 0.21 × 713 − 50 = 149.7 − 50 = 99.7 ≈ 100 mmHg. Normal PaO2 is approximately 95 mmHg, giving an A-a gradient of ~5 mmHg. The normal A-a gradient is 5–15 mmHg in young adults (< 10 mmHg for age < 30) and increases with age (approximately 2.5 mmHg per decade, with upper limit ~ age/4 mmHg). An elevated A-a gradient in the setting of hypoxemia suggests V/Q mismatch, shunt, or diffusion limitation (not pure hypoventilation, which raises PaCO2 but keeps A-a gradient normal).

Reference: Guyton & Hall, Textbook of Medical Physiology, 14th ed.

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