Alveolar Gas Equation
The alveolar gas equation calculates oxygen pressure in the lungs.
Learn the PAO₂ formula with clinical examples and applications.
The Formula
The alveolar gas equation calculates the partial pressure of oxygen in the alveoli (tiny air sacs in the lungs where gas exchange occurs). This value, called PAO₂, represents the maximum oxygen pressure available for diffusion into the blood.
The equation accounts for the fact that inhaled air is humidified (water vapor takes up space) and that oxygen is consumed as carbon dioxide is produced. The respiratory quotient (RQ) relates these two processes.
Clinicians use this equation to calculate the A-a gradient (PAO₂ - PaO₂), which measures the efficiency of gas exchange. A normal A-a gradient is about 5-15 mmHg in young adults and increases with age. An elevated A-a gradient suggests problems like pneumonia, pulmonary embolism, or interstitial lung disease. This makes the alveolar gas equation one of the most important formulas in pulmonary medicine.
Variables
| Symbol | Meaning |
|---|---|
| PAO₂ | Alveolar partial pressure of oxygen (mmHg) |
| FiO₂ | Fraction of inspired oxygen (0.21 for room air) |
| P_atm | Atmospheric pressure (760 mmHg at sea level) |
| P_H₂O | Water vapor pressure (47 mmHg at body temperature, 37°C) |
| PaCO₂ | Arterial partial pressure of CO₂ (normally 40 mmHg) |
| RQ | Respiratory quotient (typically 0.8 on a mixed diet) |
Example 1
Calculate PAO₂ for a healthy person breathing room air at sea level with PaCO₂ = 40 mmHg.
Identify values: FiO₂ = 0.21, P_atm = 760, P_H₂O = 47, PaCO₂ = 40, RQ = 0.8
PAO₂ = 0.21 × (760 - 47) - (40 / 0.8)
PAO₂ = 0.21 × 713 - 50 = 149.7 - 50
PAO₂ ≈ 99.7 mmHg
Example 2
A mountaineer at 5,500 m altitude (P_atm ≈ 380 mmHg) breathes room air. PaCO₂ drops to 25 mmHg due to hyperventilation. What is PAO₂?
Identify values: FiO₂ = 0.21, P_atm = 380, P_H₂O = 47, PaCO₂ = 25, RQ = 0.8
PAO₂ = 0.21 × (380 - 47) - (25 / 0.8)
PAO₂ = 0.21 × 333 - 31.25 = 69.93 - 31.25
PAO₂ ≈ 38.7 mmHg (significantly reduced — supplemental oxygen may be needed)
When to Use It
The alveolar gas equation is essential in pulmonary and critical care medicine.
- Calculating the A-a gradient to diagnose lung disease
- Assessing oxygenation at high altitudes
- Adjusting supplemental oxygen in hospitalized patients
- Understanding the physiological effects of changes in ventilation