L3 The Gas Laws

The Gas Laws

Importance of equations in understanding gas laws.

Overview

Key concepts to study:

  • Pressure

  • Properties of gases

  • Composition of the atmosphere

  • Dalton's Law

  • Ideal Gas Law

  • Boyle's Law and its relation to ventilation

  • Lung volumes

  • Henry's Law

Pressure and the Atmosphere

Pressure (P):Defined as Force (F) divided by Area (A).Atmospheric pressure (P_atm) measured with a Torricellian barometer.Mercury rises in an inverted tube indicating atmospheric pressure.

Units of Pressure

Common units include:

  • mmHg

  • cmH2O

  • inchesH2O

  • Pascals (Pa)

760 mmHg equals 1 atmosphere.Example of atmospheric pressure recorded at sea level is 760 mmHg.

Impact of Altitude on Gases

Atmospheric oxygen levels decrease with altitude:At 8,000m: Oxygen pressure drops to 160 mmHg. Composition of inspired air: ~21% O₂. Changes in gas composition observed with altitude:

  • Nitrogen: thinner at higher altitudes.

Dalton’s Law

Formula: P_total = P_gas1 + P_gas2 + ... + P_gasNThe total pressure of a gas mixture equals the sum of the partial pressures of each gas.Important for understanding respiration and gas exchange.

Partial Pressures in Air

Example calculation of oxygen partial pressure:(760 mmHg - 47 mmHg) x 0.21 = 150 mmHg O₂.

Ideal Gas Law

Equation: PV = nRT

  • P: Pressure

  • V: Volume

  • n: Number of molecules

  • R: Gas constant

  • T: TemperatureSpecial case: when nRT remains constant, it leads to Boyle’s Law relationship.

Boyle’s Law

Describes relationship between volume and pressure:Changes in volume generate changes in pressure (inverse relationship).Pressure differences cause gas to flow towards lower pressure areas.Mathematically expressed as P1V1 = P2V2.

Ventilation Mechanics

Ventilation linked to pressure differences and resistance to flow.Flow of air through airways is described by:

  • Flow = (P_atm - P_alveoli)

Airway resistance described by Poiseuille’s Law:

  • R = (η * L)/(r^4)

    • η = viscosity, L = length, r = radius.

Factors Affecting Airway Resistance

Includes:

  • Length of the airways

  • Viscosity of air

  • Diameter of airways

  • Airflow Velocity

Velocity decreases with increased branching of airways.Example: reducing radius of airway significantly reduces airflow velocity.

Henry’s Law

Relation of gas concentration: C = Hcp * P (partial pressure)Henry’s solubility constant: for CO₂ is higher than for O₂, meaning CO₂ is more soluble in liquids (20x greater).Important for understanding gas exchange between lungs and blood, particularly for CO₂ and O₂.

Lung Volumes and Spirometry

Spirometry measures lung capacity and function:

  • Invented by John Hutchinson in 1846.

  • Measures volumes such as Tidal Volume (TV), Expiratory Reserve Volume (ERV), Inspiratory Reserve Volume (IRV), and more.

Important Lung Capacities:

  • Total Lung Capacity (TLC)

  • Vital Capacity (VC)

  • Functional Residual Capacity (FRC)

Measurement Techniques for FRC

Helium dilution technique to calculate FRC: Measures changes in concentration as helium is diluted in a known volume of gas.Key concept: Residual volume (RV) is not exhaled and cannot be measured with simplicity.

FRC Summary

FRC is the total air in lungs at the end of normal expiration (approx. 2.5 L).Represents balance between lung recoil and chest wall expansion.Measured using helium dilution technique, reflecting lung function.

Summary of Concepts

Key objectives related to gas laws:

  • Understanding pressure, Dalton's Law, Ideal Gas Law, and the impact of altitude.

  • Knowledge of lung volumes, spirometry, and factors affecting respiratory physiology.

Questions to Consider

  • Define pressure and its origin.

  • What determines bulk flow of air?

  • Understand Ideal Gas Law determinants and relations.

  • Differences between positive and negative pressure ventilation.

  • Composition of air and Dalton's Law significance.

  • Importance of Henry’s Law in respiratory understanding.

  • Measure and understand FRC in lung function.