Alveolar gas equation

Equation

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

If F_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:

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

Doubling F_iO₂ will double p_iO₂.

Other possible equations exist to calculate the alveolar air.

$${\displaystyle \begin{array}{cc}{p}_A{\text{O}}_2^{}& =F_I{\text{O}}_2^{}\left(PB-p{\text{H}}_2^{}\text{O}\right)-p_A{\text{CO}}_2^{}\left(F_I{\text{O}}_2^{}+\frac{1-F_I{\text{O}}_2^{}}{R}\right)\\ & =p_I{\text{O}}_2^{}-p_A{\text{CO}}_2^{}\left(F_I{\text{O}}_2^{}+\frac{1-F_I{\text{O}}_2^{}}{R}\right)\\ & =p_I{\text{O}}_2^{}-\frac{V_T}{V_T-V_D}\left(p_I{\text{O}}_2^{}-p_E{\text{O}}_2^{}\right)\\ & =\frac{p_E{\text{O}}_2^{}-p_I{\text{O}}_2^{}\left(\frac{V_D}{V_T}\right)}{1-\frac{V_D}{V_T}}\end{array}}$$

Abbreviated alveolar air equation

$${\displaystyle p_A{\text{O}}_2^{}=\frac{p_E{\text{O}}_2^{}-p_i{\text{O}}_2^{}\frac{V_D}{V_T}}{1-\frac{V_D}{V_T}}}$$ p_AO₂, p_EO₂, and p_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.

Respiratory quotient (R)

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

Physiologic dead space over tidal volume (VD/VT)

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