Thealveolar gas equation is the method for calculatingpartial pressure ofalveolar oxygen (p_AO₂). The equation is used in assessing if thelungs are properly transferringoxygen into theblood. The alveolar air equation is not widely used in clinical medicine, probably because of the complicated appearance of its classic forms.The partial pressure of oxygen (pO₂) in thepulmonary alveoli is required to calculate both thealveolar-arterial gradient of oxygen and the amount of right-to-leftcardiac shunt, which are both clinically useful quantities. However, it is not practical to take a sample of gas from the alveoli in order to directly measure the partial pressure of oxygen. The alveolar gas equation allows the calculation of the alveolar partial pressure of oxygen from data that is practically measurable. It was first characterized in 1946.^[1]

The equation relies on the following assumptions:

• Inspired gas contains no carbon dioxide (CO₂)
• Nitrogen (and any other gases except oxygen) in the inspired gas are in equilibrium with their dissolved states in the blood
• Inspired and alveolar gases obey theideal gas law
• Carbon dioxide (CO₂) in the alveolar gas is in equilibrium with the arterial blood i.e. that the alveolar and arterial partial pressures are equal
• The alveolar gas is saturated with water

$${\displaystyle p_A{\text{O}}_2^{}=F_I{\text{O}}_2^{}(P_{\text{ATM}}-p{\text{H}}_2^{}\text{O})-\frac{p_a{\text{CO}}_2^{}(1-F_I{\text{O}}_2^{}(1-\text{RER}))}{\text{RER}}}$$

IfF_iO₂ is small, or more specifically if${\displaystyle F_I{\text{O}}_2^{}(1-\text{RER})\ll 1}$ then the equation can be simplified to:

$${\displaystyle p_A{\text{O}}_2^{}\approx F_I{\text{O}}_2^{}(P_{\text{ATM}}-p{\text{H}}_2^{}\text{O})-\frac{p_a{\text{CO}}_2^{}}{\text{RER}}}$$

where:

Quantity	Description	Sample value
${\displaystyle p_A{\text{O}}_2^{}}$	The alveolar partial pressure of oxygen (${\displaystyle p{\text{O}}_2^{}}$)	107 mmHg (14.2 kPa)
${\displaystyle F_I{\text{O}}_2^{}}$	The fraction of inspired gas that is oxygen (expressed as a decimal).	0.21
${\displaystyle P_{ATM}}$	The prevailing atmospheric pressure	760 mmHg (101 kPa)
${\displaystyle p{\text{H}}_2^{}\text{O}}$	The saturated vapour pressure of water at body temperature and the prevailing atmospheric pressure	47 mmHg (6.25 kPa)
${\displaystyle p_a{\text{CO}}_2^{}}$	The arterial partial pressure of carbon dioxide (${\displaystyle p{\text{CO}}_2^{}}$ )	40 mmHg (5.33 kPa)
${\displaystyle \text{RER}}$	Therespiratory exchange ratio	0.8

Sample Values given for air at sea level at 37 °C.

DoublingF_iO₂ will doublep_iO₂.

Other possible equations exist to calculate the alveolar air.^{[2][3][4][5][6][7][8]}

$${\displaystyle p_A{\text{O}}_2^{}=\frac{p_E{\text{O}}_2^{}-p_i{\text{O}}_2^{}\frac{V_D}{V_T}}{1-\frac{V_D}{V_T}}}$$p_AO₂,p_EO₂, andp_iO₂ are the partial pressures of oxygen in alveolar, expired, and inspired gas, respectively, and VD/VT is the ratio of physiologic dead space over tidal volume.^[9]

$${\displaystyle R=\frac{p_E{\text{CO}}_2^{}(1-F_I{\text{O}}_2^{})}{p_i{\text{O}}_2^{}-p_E{\text{O}}_2^{}-(p_E{\text{CO}}_2^{}\ast F_i{\text{O}}_2^{})}}$$

$${\displaystyle \frac{V_D}{V_T}=\frac{p_A{\text{CO}}_2^{}-p_E{\text{CO}}_2^{}}{p_A{\text{CO}}_2^{}}}$$

As it is not practical to take a sample of gas from the alveoli in order to directly measure the partial pressure of oxygen, the alveolar gas equation allows the calculation of the alveolar partial pressure of oxygen from data that is practically measurable.

Firstly, the partial pressure of inhaled oxygen is simply the fraction of inhaled oxygen multiplied by the atmospheric pressure${\displaystyle F_I{\text{O}}_2^{}\ast P_{\text{ATM}}}$. Once oxygen enters the airways, we must account for the partial pressure of water vapor which is assumed to reach 100% saturation, hence${\displaystyle F_I{\text{O}}_2^{}(P_{\text{ATM}}-p{\text{H}}_2^{}\text{O})}$. Once the humidified atmospheric air reaches the alveoli, gas exchange takes place so we need to consider the amount of${\displaystyle {\text{O}}_2^{}}$ that enters the blood and${\displaystyle {\text{CO}}_2^{}}$ that leaves the blood. Conveniently, the arterial blood${\displaystyle p_a{\text{CO}}_2^{}}$ equals the alveolar blood${\displaystyle p_A{\text{CO}}_2^{}}$ and so this is a value we know. It would also be convenient if the same number of${\displaystyle {\text{CO}}_2^{}}$ and${\displaystyle {\text{O}}_2^{}}$ molecules were exchanged, in which case the alveolar gas equation would simply be${\displaystyle p_A{\text{O}}_2^{}\approx F_I{\text{O}}_2^{}(P_{\text{ATM}}-p{\text{H}}_2^{}\text{O})-p_a{\text{CO}}_2^{}}$. However in reality the number of${\displaystyle {\text{CO}}_2^{}}$ molecules exchanged differs slightly from the number of${\displaystyle {\text{O}}_2^{}}$ molecules, according to therespiratory exchange ratio. Hence the alveolar gas equation becomes:

$${\displaystyle p_A{\text{O}}_2^{}\approx F_I{\text{O}}_2^{}(P_{\text{ATM}}-p{\text{H}}_2^{}\text{O})-\frac{p_a{\text{CO}}_2^{}}{\text{RER}}}$$

• Pulmonary gas pressures

• Free interactive model of the simplified and complete versions of the alveolar gas equation (AGE)
• Formula at ucsf.edu
• S. Cruickshank, N. Hirschauer:The alveolar gas equation in Continuing Education in Anaesthesia, Critical Care & Pain, Volume 4 Number 1 2004
• Online Alveolar Gas Equation and iPhone application by Medfixation.
• A computationally functional Alveolar Gas Equation by vCalc.

• Respiratory physiology

• Articles with short description
• Short description is different from Wikidata