Alveolar gas equation
The alveolar gas equation is used to estimate the partial pressure of oxygen in the alveoli. It connects inspired oxygen, atmospheric pressure, water vapor pressure, carbon dioxide, and the respiratory quotient into one compact model. This makes it one of the most useful teaching equations for understanding why alveolar oxygen changes across room air, supplemental oxygen, and high-altitude conditions.
The key idea is that oxygen entering the alveoli is first limited by the available dry gas pressure, and then alveolar oxygen is reduced further by the carbon dioxide term. In other words, alveolar oxygen depends both on what is being inspired and on how much carbon dioxide must be accounted for in the alveolar gas mixture.
Main equation
The standard teaching form is:
\[
\begin{aligned}
P_{AO_2} = F_{IO_2}(P_{atm} - P_{H_2O}) - \frac{P_{aCO_2}}{RQ}
\end{aligned}
\]
Here:
- \(P_{AO_2}\) is alveolar oxygen partial pressure
- \(F_{IO_2}\) is inspired oxygen fraction
- \(P_{atm}\) is atmospheric pressure
- \(P_{H_2O}\) is water vapor pressure
- \(P_{aCO_2}\) is arterial or alveolar carbon dioxide partial pressure used in the correction term
- \(RQ\) is the respiratory quotient
Stepwise interpretation
The equation is often easiest to understand in two parts. First, calculate the effective inspired oxygen pressure:
\[
\begin{aligned}
P_{IO_2} = F_{IO_2}(P_{atm} - P_{H_2O})
\end{aligned}
\]
This shows that inspired oxygen is based on the dry gas pressure, not the full atmospheric pressure, because water vapor occupies part of the total pressure once gas becomes humidified in the airways.
Then calculate the carbon dioxide correction term:
\[
\begin{aligned}
\frac{P_{aCO_2}}{RQ}
\end{aligned}
\]
Finally subtract that term from inspired oxygen pressure:
\[
\begin{aligned}
P_{AO_2} = P_{IO_2} - \frac{P_{aCO_2}}{RQ}
\end{aligned}
\]
What raises or lowers alveolar oxygen
Alveolar oxygen rises when inspired oxygen fraction increases or when atmospheric pressure is higher. Alveolar oxygen falls when atmospheric pressure decreases, when water vapor pressure takes up part of total pressure, when carbon dioxide rises, or when the respiratory quotient makes the correction term larger.
- Higher \(F_{IO_2}\) raises \(P_{IO_2}\) and usually raises \(P_{AO_2}\).
- Lower \(P_{atm}\), such as at altitude, lowers the dry gas pressure term and reduces alveolar oxygen.
- Higher \(P_{aCO_2}\) increases the subtraction term and lowers alveolar oxygen.
- Water vapor pressure must be subtracted before applying inspired oxygen fraction.
Common teaching values
At sea level, room air is commonly represented with \(F_{IO_2} \approx 0.2093\), \(P_{atm} = 760\ \text{mmHg}\), \(P_{H_2O} = 47\ \text{mmHg}\), \(P_{aCO_2} = 40\ \text{mmHg}\), and \(RQ = 0.8\). These values give a typical alveolar oxygen estimate near 100 mmHg.
Micro example
Using a room-air teaching example:
\[
\begin{aligned}
P_{IO_2} &= 0.2093(760 - 47) \\
&= 0.2093(713) \\
&\approx 149.2\ \text{mmHg}
\end{aligned}
\]
\[
\begin{aligned}
\frac{P_{aCO_2}}{RQ} &= \frac{40}{0.8} = 50\ \text{mmHg}
\end{aligned}
\]
\[
\begin{aligned}
P_{AO_2} &= 149.2 - 50 \\
&\approx 99.2\ \text{mmHg}
\end{aligned}
\]
This example shows that alveolar oxygen is not equal to inspired oxygen pressure. The carbon dioxide correction meaningfully lowers the final oxygen pressure inside the alveoli.
Common mistakes
- Using atmospheric pressure directly without subtracting water vapor pressure first.
- Entering inspired oxygen fraction as a percent when the formula expects a decimal.
- Forgetting to divide carbon dioxide by the respiratory quotient.
- Mixing pressure units without converting them consistently.
This calculator is best used to compare normal room air, supplemental oxygen, and altitude-style examples. It is a teaching and estimation tool, not a full clinical acid-base or gas-exchange analyzer.