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The alveolar gas equation estimates alveolar oxygen partial pressure from inspired oxygen fraction, ambient pressure, carbon dioxide and respiratory quotient.
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Formula
Partial pressures in mmHg or kPa, consistently · FiO2 and RQ dimensionless
| Symbol | Meaning | Unit |
|---|---|---|
| Estimated alveolar oxygen partial pressure | mmHg or kPa | |
| Inspired oxygen fraction | dimensionless | |
| Barometric ambient pressure | mmHg or kPa | |
| Water-vapor pressure in humidified inspired air | mmHg or kPa | |
| Arterial CO2 partial pressure used to approximate alveolar CO2 | mmHg or kPa | |
| Respiratory quotient VCO2/VO2 | dimensionless |
P_{AO_2}=F_{IO_2}(P_B-P_{H_2O})-\frac{P_{aCO_2}}{R_Q}The simplified equation uses a steady alveolar gas balance and substitutes PaCO2 as an approximation for alveolar CO2. RQ depends on substrate metabolism; 0.8 is a common resting value, not universal. The equation estimates PAO2 and is not a measurement or clinical assessment. Altitude, FiO2, non-steady breathing and major ventilation-perfusion inequality affect interpretation.
A steady alveolar gas balance and an appropriate respiratory quotient approximately apply.
Inspired oxygen and alveolar CO2 removal determine estimated PAO2.
CO2 partial pressure from PAO2
Only within the same simplified gas balance.
Given FiO2=0.21, PB=760, PH2O=47, PaCO2=40 mmHg and RQ=0.8, calculate PAO2.
0.21·713−50=99.7 mmHg.
Entering partial pressures in mixed units.
Convert to one pressure unit and enter FiO2 as a fraction.
Formula cluster
more inspired oxygen raises, and higher CO2 lowers, estimated PAO2.
On room air, FiO2=0.21, PB=760 mmHg, PH2O=47 mmHg, PaCO2=40 mmHg and RQ=0.80 give PAO2=0.21·(760−47)−40/0.80=99.7 mmHg. Check: both terms are in mmHg; increasing PaCO2 lowers estimated PAO2.
Estimate alveolar oxygen partial pressure as a model quantity in respiratory physiology
Here is how to work through a typical Alveolar Gas Equation (PAO₂ = FiO₂(PB−PH₂O) − PaCO₂/RQ) task step by step:
Task
Given FiO2=0.21, PB=760, PH2O=47, PaCO2=40 mmHg and RQ=0.8, calculate PAO2.
Solution path
0.21·713−50=99.7 mmHg.
the alveolar oxygen partial pressure estimated from inspired gas and CO2 balance. Its output is PAO2, not arterial oxygen content in blood.. more inspired oxygen raises, and higher CO2 lowers, estimated PAO2. The quantity answers a specific biological or statistical question, not automatically the full cause of an observed pattern. Tie it to the population, sample or model level from which inputs came. A number without that reference can be misleading across studies. Keep description separate from explanation: the metric summarizes data but does not by itself establish the underlying mechanism.
Use FiO2 is a fraction; PB, PH2O and PaCO2 are partial pressures, and RQ is a ratio. The units are All pressure values must use mmHg or all use kPa.. Check that numerator and denominator refer to the same time interval, target population and scale. Proportions entered as percentages usually need conversion to values between zero and one. Write units and definitions beside the observations. This helps catch swapped groups, mismatched age intervals or a wrong denominator before they distort the result. Also document measurement definitions and preprocessing, because studies can operationalize the same symbols differently.
The central assumption is: PaCO2 approximates alveolar CO2 and breathing is sufficiently steady. RQ=0.8 is a common reference, not a fixed universal value. If altitude, supplemental oxygen or major V/Q disturbance affect interpretation., interpretation changes or the formula no longer fits. State sampling, measurement method and biological scale. A model is useful because it simplifies a question, but its limits belong in the report. Do not automatically transfer parameters to different species, populations, laboratories or sampling conditions. Report these assumptions with the result so readers can judge which populations and conditions the conclusion can cover.
In the example, the room-air values give PAO2≈99.7 mmHg. The check is: each term has pressure units; the CO2 term is divided by RQ. Substitute calculated values back into the original relation and check whether ranges and units are biologically plausible. Rounded data can create a small discrepancy, but should not change direction or order of magnitude. Also test a simple limiting case, such as zero, complete detection or equal groups. This separates arithmetic errors from model limitations. Round intermediate values only at the end, and check the order of magnitude against the biological question.
A nearby quantity is alveolar ventilation. The substantive distinction is that ventilation is a volume flow per time; the gas equation estimates an alveolar partial pressure. Both can appear in the same biological analysis, but they use different inputs and answer different questions. Choose by the requested output and verify the data definition before comparing values. A related name does not imply identical units or interchangeable interpretation. This matters when a descriptive statistic is reported alongside a model parameter. Before comparing values, align definitions, populations, observation periods and analysis rules; otherwise the difference may be methodological.
Quanta exam set
Curated exam set for "Alveolar Gas Equation":
Question (front)
Which formula describes Alveolar Gas Equation?
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Question (front)
How do you rearrange Alveolar Gas Equation for CO2 partial pressure from PAO2?
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Question (front)
Which common mistake happens with Alveolar Gas Equation?
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Create a curated FSRS exam set for PAO₂ = FiO₂(PB−PH₂O) − PaCO₂/RQ: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
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