Equation of state and gas model
To understand gas exchange processes, the gaseous environment is modeled as a mixture of ideal gases. Under physiological conditions, the gases relevant to respiration fully obey the ideal gas law equation of state.
This equation is expressed as follows: PV = MRT
Where each variable has its specific physical meaning:
- P — gas pressure;
- 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 multi-component mixture. To understand how each individual gas participates in respiration, the concept of partial pressure is used — that is, the pressure exerted by a specific component within the total mixture.
According to Dalton's law, the total pressure of a gas mixture is determined by the simple mathematical sum of the partial pressures of each gas making up that mixture.
The formula for Dalton's law: P = P₁ + P₂ + P₃ + … + Pₙ
It is important to note that the partial pressure of any gas in a mixture is strictly proportional to its percentage composition.
Gaseous environments and their composition
During respiration, air passes through several stages, changing its composition. Traditionally, three main gaseous environments are distinguished:
- Atmospheric (inspired) air.
- Alveolar air (located directly within the alveoli).
- Expired air.
The percentage of key gases varies significantly depending on the environment:
- Oxygen (O₂): its proportion is 20.94% in inspired air, drops to 14.5% in alveolar air, and equals 16.3% in expired air.
- Carbon dioxide (CO₂): it is practically absent in the atmosphere (0.03%), reaches a concentration of 5.5% in the alveoli, and decreases to 4.0% upon expiration.
- Nitrogen (N₂): remains relatively stable (79.03% in inspired air, 80% in alveolar air, and 79.7% in expired air).
Note the paradox: alveolar air contains less oxygen and more carbon dioxide than expired air. This is because expired gas is formed by mixing alveolar air with the air from the anatomical "dead space". Air in the dead space does not participate in gas exchange, and its composition is close to that of atmospheric air.
Pressure calculation and gradients
For gases to move between the lungs and the 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 the pressure for alveolar air, an important factor must be considered: the air in the respiratory tract is heavily humidified. Therefore, the water vapor pressure of 47 mmHg must be subtracted from the standard atmospheric pressure (760 mmHg). Thus, the baseline calculation for the alveoli is 713 mmHg.
The partial pressure (or tension) cascade of gases is as follows:
- Atmospheric air (at 760 mmHg): pO₂ is 159 mmHg, and pCO₂ is 0 (only trace amounts are present).
- Alveolar air (at 713 mmHg): pO₂ decreases to 100 mmHg, and pCO₂ increases to 40 mmHg.
- Body tissues: pO₂ drops to 40 mmHg, and pCO₂ reaches a maximum of 46 mmHg.
It is this pressure difference (for example, for oxygen: 159 → 100 → 40) that creates a powerful driving force ensuring a continuous flow of oxygen into tissues and the removal of carbon dioxide.
Briefly: answers to topical questions
What are the values of oxygen and carbon dioxide tension in arterial and venous blood?
The values of oxygen and carbon dioxide tension depend on the type of blood and determine the partial pressure gradient for respiration. The driving force of gas exchange represents the difference between the partial pressures of these gases in the alveolar mixture and their tension in the blood.
| Blood type | O₂ (mmHg) | CO₂ (mmHg) |
|---|---|---|
| Arterial | 100–120 | 40 |
| Venous | 40 | 48 |
By what formula is the partial pressure of a specific gas in moist alveolar air calculated?
The partial pressure of a specific gas in moist alveolar air is calculated as the fraction of that gas from the calculated baseline after subtracting the water vapor pressure:
p gas = (760 − 47) × (% gas / 100) = 713 × (% gas / 100) mmHg.
The water vapor pressure is 47 mmHg; therefore, at an atmospheric pressure of 760 mmHg, the baseline for alveolar air is 713 mmHg.
To memorize the oxygen gradient, use the number sequence "159 — 100 — 40" (Street — Lungs — Tissues). Oxygen "rolls down the hill" from high pressure to low pressure.
Class and exam questions
Why is there more oxygen in expired air than in alveolar air?
Upon expiration, alveolar air mixes with a portion of air from the "dead space". The composition of the dead space air is close to atmospheric, so it increases the total proportion of oxygen in the expired mixture.
Why is 47 mmHg subtracted when calculating alveolar pressure?
This figure reflects the water vapor pressure. In the respiratory tract, atmospheric air is warmed and intensively humidified, so part of the total pressure in the lungs is accounted for by vapor.
What drives oxygen to diffuse into tissues?
Partial pressure gradient. In the alveoli, the oxygen pressure is 100 mmHg, and in the tissues, it is 40 mmHg. The gas passively diffuses toward the lower pressure.
What else to study on this topic
- Mathematical application of the ideal gas law in physiology
- Impact of anatomical dead space on pulmonary ventilation
- Mechanisms of inspired air saturation with water vapor
- Dynamics of carbon dioxide partial pressure from tissues to the atmosphere
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