Partial pressure and the alveolar air equation made simple

Partial pressures made simple. Read this short Clinical Guide article about the fundamentals of alveolar air equations.
Last update30th Sep 2021

Gases are in constant motion, colliding with each other and any surfaces they bump into. And the number of collisions determines the pressure of the gas—the more collisions, the higher the pressure.

In a mixture of gases, the total pressure of the gas mixture equals the sum of the partial pressures of the individual gases. This is Dalton’s Law.

Figure 1. Dalton’s law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of the individual gases.

And, the partial pressure of each gas is proportional to the number of molecules of the gas in the mixture. So the partial pressure of any gas in the mixture can be calculated by multiplying the fractional concentration (or proportion) of the gas by the total pressure of the gas mixture.

Figure 2. Partial pressures of a gas (A) in a mixture (M) can be calculated from the fractional concentration of the gas and the total pressure of the gas mixture.

The same is true for the air around us. The kinetic energy of the mixture of gases that constitutes the atmosphere creates atmospheric or barometric pressure, Pbarometric.

An important determinant of barometric pressure is the height above sea level at which the measurement is made. At sea level, barometric pressure is 760 mmHg; it declines with the ascent to higher altitudes.

Figure 3. Barometric pressure is created by the kinetic energy of atmospheric gases, and an important determinant of barometric pressure is the height above the sea level.

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As it is inhaled, dry atmospheric air is warmed to body temperature and fully humidified. The resulting humidification adds a component, water vapor, to the gas mixture which has a partial pressure of 47 mmHg. However, by convention, fractional concentrations of inspired gases are calculated after water vapor pressure has been subtracted (i.e., as dry gases).

Therefore, the partial pressure of each inspired gas, including oxygen, is calculated as the fractional concentration of the gas in the mixture times the difference between atmospheric pressure (e.g., 760 mmHg at sea level) and water vapor pressure (47 mmHg).

Figure 4. The partial pressure of an inspired gas is calculated from the fractional concentration of the gas and the difference between atmospheric pressure and water vapor pressure, to account for the humidification of inspired gases in the airway.

But when calculating the partial pressure of a gas in the alveoli, we also need to consider the concentration of carbon dioxide evolved into the alveoli from the mixed venous blood returning to the lungs.

So the partial pressure of oxygen in the alveoli (PAO2) is determined by the partial pressure of oxygen in inhaled gas, minus water vapor pressure, minus the concentration of carbon dioxide evolved into the alveoli from mixed venous blood returning to the lungs. This is expressed in the alveolar air equation.

Figure 5. The expanded and simplified alveolar air equation calculates the partial pressure of oxygen in the alveoli by accounting for water vapor pressure and the concentration of carbon dioxide being returned to the lungs from the venous blood.

The factor of 1.25 reflects the fact that metabolizing tissues generate slightly less carbon dioxide than oxygen consumed.

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Recommended reading

  • Grippi, MA. 1995. “Gas exchange in the lung”. In: Lippincott's Pathophysiology Series: Pulmonary Pathophysiology. 1st edition. Philadelphia: Lippincott Williams & Wilkins. (Grippi 1995, 137–149)
  • Grippi, MA. 1995. “Clinical presentations: gas exchange and transport”. In: Lippincott's Pathophysiology Series: Pulmonary Pathophysiology. 1st edition. Philadelphia: Lippincott Williams & Wilkins. (Grippi 1995, 171–176)
  • Grippi, MA and Tino, G. 2015. “Pulmonary function testing”. In: Fishman's Pulmonary Diseases and Disorders, edited by MA, Grippi (editor-in-chief), JA, Elias, JA, Fishman, RM, Kotloff, AI, Pack, RM, Senior (editors). 5th edition. New York: McGraw-Hill Education. (Grippi and Tino 2015, 502–536)
  • Tino, G and Grippi, MA. 1995. “Gas transport to and from peripheral tissues”. In: Lippincott's Pathophysiology Series: Pulmonary Pathophysiology. 1st edition. Philadelphia: Lippincott Williams & Wilkins. (Tino and Grippi 1995, 151–170)
  • Wagner, PD. 2015. The physiologic basis of pulmonary gas exchange: implications for clinical interpretation of arterial blood gases. Eur Respir J45: 227–243. PMID: 25323225

About the author

Michael A. Grippi, MD
Vice Chairman, Department of Medicine | Pulmonary, Allergy, and Critical Care Division, Perelman School of Medicine, University of Pennsylvania, USA.
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