How do I calculate the fractional concentration of gases in a mixture?

New to blood gas analyses? Check out this article on calculating the fractional concentrations of gases in a mixture.
Last update24th Nov 2020

What is the fractional concentration of a gas?

The concentration of a single gas, A, in the mixture, M, can be represented in terms of its fractional concentration: the number of molecules of gas A divided by the number of all the molecules in the gas mixture (the amount of gas A plus the amount of gas B plus the amount of gas C).

Figure 1. The concentration of a gas (A) in a mixture can be represented as its fractional concentration (FMA) which is calculated from the concentrations of all the gases in a mixture.

The atmosphere is a mixture of gases, including nitrogen, oxygen, carbon dioxide, argon, and water vapor. The amounts of argon and carbon dioxide are minimal. Under normal ambient (dry) conditions, there is also little water vapor.

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Calculating the fractional concentrations of the gases in our atmosphere

Just as we did for the generic gas mixture above, the concentrations of gases in the atmosphere can be expressed as fractional concentrations. But for these purposes, we can ignore the concentrations of all gases but oxygen and nitrogen. And, since this is the air we breathe in, we can express them as fractional concentrations of inspired gas, X (FIX).

Figure 2. Concentrations of gases in the atmosphere can be expressed as fractional concentrations of inspired gases (FIX) in the atmosphere.

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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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