Equation of State and Gas Model
To understand gas exchange, the gaseous environment is modeled as a mixture of ideal gases. Under physiological conditions, physiologically relevant gases fully obey the ideal gas law.
The equation is expressed as: PV = MRT
Where each variable has a specific physical meaning:
- P — pressure of the gas;
- V — volume occupied;
- M — amount of gas in moles;
- R — universal gas constant;
- T — absolute temperature (measured in Kelvin).
Partial Pressure and Dalton's Law
Air is a multicomponent mixture. To understand how each individual gas participates in respiration, the concept of partial pressure is used — representing the pressure exerted by a specific component within the total mixture.
According to Dalton's law, the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas comprising the mixture.
Dalton's law formula: P = P₁ + P₂ + P₃ + … + Pₙ
Notably, the partial pressure of any gas in a mixture is directly proportional to its percentage concentration.
Gas Environments and Their Composition
During respiration, air passes through several stages, altering its composition. Traditionally, three main gas environments are distinguished:
- Atmospheric (inspired) air.
- Alveolar air (located directly within the alveoli).
- Expired air.
Percentage compositions of key gases vary significantly across these environments:
- Oxygen (O₂): inspired air contains 20.94%, alveolar air drops to 14.5%, and expired air is 16.3%.
- Carbon dioxide (CO₂): atmospheric concentration is negligible (0.03%), alveolar concentration reaches 5.5%, and expired concentration drops to 4.0%.
- Nitrogen (N₂): remains relatively stable (79.03% inspired, 80% alveolar, and 79.7% expired).
Consider this paradox: alveolar air contains less oxygen and more carbon dioxide than expired air. This occurs because expired gas is formed by mixing alveolar air with air from the anatomical "dead space." Dead space air does not participate in gas exchange and maintains a composition close to atmospheric air.
Pressure Calculations and Gradients
For gases to move between the lungs and blood, a pressure gradient is required. Gases always move from an area of high partial pressure to an area of low partial pressure.
When calculating pressures for alveolar air, an important factor must be considered: air in the respiratory tract is heavily humidified. Therefore, water vapor pressure (47 mmHg) must be subtracted from standard atmospheric pressure (760 mmHg). Thus, the baseline calculation for the alveoli equals 713 mmHg.
The partial pressure (or tension) cascade for gases is as follows:
- Atmospheric air (at 760 mmHg): pO₂ is 159 mmHg, and pCO₂ is 0 (only trace amounts present).
- Alveolar air (at 713 mmHg): pO₂ drops to 100 mmHg, while pCO₂ rises to 40 mmHg.
- Body tissues: pO₂ drops to 40 mmHg, while pCO₂ peaks at 46 mmHg.
This pressure difference (e.g., for oxygen: 159 → 100 → 40) generates the driving force ensuring a continuous oxygen flow into tissues and the removal of carbon dioxide.