A person in a closed room at sea level has an alveolar $pC{O}_2$ of $35mmHg$. If the atmospheric pressure is $760mmHg$, water vapor pressure in alveoli is $47mmHg$, $FI{O}_2$ is $0.21$, and the respiratory exchange ratio $R$ is $0.8$, calculate the alveolar oxygen partial pressure $P_{AO2}$ using the alveolar gas equation.

Step-by-step solution

1. 1. Write alveolar gas equation: $P_{AO2}=P_{IO2}-\frac{P_{aCO2}}{R}$ where $P_{IO2}=(P_B-P_{H2O})F_{IO2}$.
2. 2. Compute $P_{IO2}=(760-47)\times 0.21=713\times 0.21=149.73mmHg$.
3. 3. Calculate $\frac{P_{aCO2}}{R}=\frac{35}{0.8}=43.75mmHg$.
4. 4. Subtract: $P_{AO2}=149.73-43.75=105.98mmHg$.
5. 5. Round to nearest integer: $106mmHg$.
6. 6. This is the alveolar oxygen partial pressure.

Concept tested: Alveolar gas equation

Published 16 October 2026 · How this solution was prepared and checked