Using the alveolar gas equation, PAO2 for a patient at sea level with FiO2 0.21 and PaCO2 40 mmHg; Pb 760 mmHg; PH2O 47 mmHg; and R = 0.8, PAO2 is approximately what value?

Using the alveolar gas equation, PAO2 for a patient at sea level with FiO2 0.21 and PaCO2 40 mmHg; Pb 760 mmHg; PH2O 47 mmHg; and R = 0.8, PAO2 is approximately what value?

• A. 68 mmHg
• B. 75 mmHg
• C. 99 mmHg
• D. 120 mmHg

Answer: (C)

The calculation centers on the alveolar gas equation, which links inspired oxygen, humidified air pressures, and CO2 to the alveolar oxygen pressure: PAO2 = FiO2 × (Pb − PH2O) − (PaCO2 / R). First, find the effective inspired O2 pressure: Pb − PH2O = 760 − 47 = 713 mmHg. Multiply by FiO2: 0.21 × 713 ≈ 150 mmHg. Next, account for the CO2 term: PaCO2 / R = 40 / 0.8 = 50 mmHg. Subtract the CO2 term from the inspired O2 term: 150 − 50 ≈ 100 mmHg. With rounding, PAO2 ≈ 99–100 mmHg, so the closest value is about 99 mmHg.

The calculation centers on the alveolar gas equation, which links inspired oxygen, humidified air pressures, and CO2 to the alveolar oxygen pressure: PAO2 = FiO2 × (Pb − PH2O) − (PaCO2 / R).

First, find the effective inspired O2 pressure: Pb − PH2O = 760 − 47 = 713 mmHg. Multiply by FiO2: 0.21 × 713 ≈ 150 mmHg.

Next, account for the CO2 term: PaCO2 / R = 40 / 0.8 = 50 mmHg.

Subtract the CO2 term from the inspired O2 term: 150 − 50 ≈ 100 mmHg. With rounding, PAO2 ≈ 99–100 mmHg, so the closest value is about 99 mmHg.