Module 3: Properties of Air, the Gas Laws, and Functional Lung Volumes

Overview

This module explores the physical properties of air, the fundamental gas laws relevant to respiratory physiology, and the measurement and significance of lung volumes. Understanding these concepts is essential for comprehending how gases are exchanged and transported in the human body.

Properties of Gases and the Atmosphere

Pressure and Atmospheric Composition

• Pressure is defined as the force exerted per unit area. The equation for pressure is:

$P = \frac{F}{A}$

• Atmospheric pressure is the pressure exerted by the weight of air in the atmosphere. At sea level, it is approximately 760 mm Hg (millimeters of mercury).

• Atmospheric pressure is measured using a barometer, as first demonstrated by Evangelista Torricelli.

• The composition of dry atmospheric air is approximately:

  • Nitrogen (N2): 78%

  • Oxygen (O2): 21%

  • Carbon dioxide (CO2): 0.03%

  • Other gases (including argon, neon, etc.): trace amounts

The Gas Laws

Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a mixture of gases is the sum of the partial pressures of each individual gas.

• The partial pressure of a gas is the pressure it would exert if it alone occupied the entire volume.

$P_{total} = P_{N_2} + P_{O_2} + P_{CO_2} + P_{H_2O}$

• This law is fundamental for understanding gas exchange in the lungs, where oxygen and carbon dioxide diffuse according to their partial pressures.

Partial Pressures of Gases in Air as a Function of Temperature

The partial pressure of each gas in air depends on its percentage and the total atmospheric pressure. Water vapor pressure increases with temperature and humidity, reducing the partial pressures of other gases.

Additional info: The sum of all partial pressures equals the total atmospheric pressure (760 mm Hg at sea level).

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas:

$PV = nRT$

• P: Pressure (in atmospheres or mm Hg)

• V: Volume (in liters)

• n: Number of moles of gas

• R: Universal gas constant

• T: Temperature (in Kelvin)

When the amount of gas and temperature are constant ($nRT$ constant):

$P \propto \frac{1}{V}$

This relationship leads to Boyle's Law.

Boyle's Law

Boyle's Law describes the inverse relationship between the pressure and volume of a gas at constant temperature:

$P_1V_1 = P_2V_2$

• As volume increases, pressure decreases, and vice versa.

• This principle is fundamental to pulmonary ventilation:

  • Changes in lung volume create changes in pressure.

  • Gases flow from areas of higher pressure to areas of lower pressure.

Example: During inspiration, the diaphragm contracts, increasing thoracic volume and decreasing intrapulmonary pressure, causing air to flow into the lungs.

Henry's Law

Henry's Law states that the amount of gas dissolved in a liquid is proportional to its partial pressure in the gas phase and its solubility constant:

$C = H_e \times P_{gas}$

• C: Concentration of dissolved gas

• He: Henry's solubility constant (varies for each gas)

• Pgas: Partial pressure of the gas

• CO2 is about 20 times more soluble in plasma than O2.

Application: This law explains why oxygen and carbon dioxide diffuse at different rates across the alveolar-capillary membrane.

Ventilation: Airway Resistance and Gas Flow

Airway Resistance

• The flow of air through the airways is directly proportional to the pressure difference and inversely proportional to airway resistance:

$\text{Flow} = \frac{P_{alveoli} - P_{atm}}{\text{Resistance}}$

• Airway resistance depends on:

  • Airway diameter (smaller diameter increases resistance)

  • Length of the airway

  • Viscosity of the air

• Branching of airways increases total cross-sectional area and decreases air flow velocity.

• Diseases such as asthma or chronic bronchitis increase airway resistance.

Example: In Coal Worker's Pneumoconiosis (Black Lung Disease), airway resistance increases due to inflammation and fibrosis.

Lung Volumes and Capacities

Measurement of Lung Volumes

• Lung volumes and capacities are measured using a spirometer during pulmonary function tests.

• Key lung volumes include:

  • Tidal Volume (TV): Volume of air inhaled or exhaled in a normal breath (~500 mL).

  • Inspiratory Reserve Volume (IRV): Additional air that can be inhaled after a normal inspiration.

  • Expiratory Reserve Volume (ERV): Additional air that can be exhaled after a normal expiration.

  • Residual Volume (RV): Air remaining in the lungs after maximal exhalation (cannot be measured by simple spirometry).

• Lung capacities are combinations of two or more volumes:

  • Functional Residual Capacity (FRC): Volume of air remaining in the lungs at the end of a normal expiration (FRC = ERV + RV).

  • Total Lung Capacity (TLC): Maximum volume of air the lungs can hold (TLC = TV + IRV + ERV + RV).

Measurement of Functional Residual Capacity (FRC)

• FRC is measured using the Helium Dilution Technique:

  1. A known quantity of helium is added to a known volume of gas (initial concentration C1).

  2. After equilibration with the lungs, the concentration drops to C2 as helium mixes with the FRC.

  3. Since helium is not absorbed, the change in concentration allows calculation of FRC.

$V_2 = V_A \left( \frac{C_1}{C_2} - 1 \right)$

• FRC is a useful index of lung function, reflecting the balance between lung recoil and chest wall expansion.

• RV cannot be measured by spirometry alone; it is determined indirectly.

Summary Table: Key Lung Volumes and Capacities

Key Points to Consider

• Understand the origin and measurement of atmospheric pressure.

• Know the determinants of bulk air flow: pressure differences and airway resistance.

• Be able to apply the Ideal Gas Law and its variables.

• Describe Boyle's Law and its relevance to lung ventilation.

• Distinguish between positive and negative pressure ventilation.

• Recall the basic composition of air and the effect of humidity on partial pressures.

• Explain Dalton's and Henry's Laws and their physiological significance.

• Identify the determinants of airway resistance and their clinical implications.

• Describe the use of spirometry and the measurement of lung volumes and capacities, especially FRC.