A patient is breathing air at sea level. PAO₂ is 100 mmHg, PaO₂ is 80 mmHg, and PaCO₂ is 40 mmHg. Using the alveolar gas equation (FiO₂ = 0.21, PB = 760, PH₂O = 47, RQ = 0.8), what is the A-a gradient and what does elevation suggest?

• A A-a gradient = 0 mmHg; normal gas exchange
• B A-a gradient = 40 mmHg; consistent with hypoventilation alone
• C A-a gradient = 10 mmHg; normal for age > 40 years
• D A-a gradient = 20 mmHg; elevated, suggesting V/Q mismatch or diffusion impairment ✓

Explanation

Alveolar gas equation: PAO₂ = FiO₂(PB − PH₂O) − PaCO₂/RQ = 0.21(713) − 40/0.8 = 149.7 − 50 ≈ 100 mmHg. A-a gradient = PAO₂ − PaO₂ = 100 − 80 = 20 mmHg. Normal A-a gradient is < 10–15 mmHg in young adults (up to ~2.5 mmHg per decade of age). An elevated A-a gradient indicates V/Q mismatch, intrapulmonary shunt, or diffusion impairment—not pure hypoventilation, which preserves the gradient.

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

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