Key Gas Laws and Concepts for Respiratory Therapists

Understanding gas laws is essential for respiratory therapists, as these principles directly impact patient care. Respiratory therapists constantly work with gases whether to deliver medications, drive respiratory equipment, or titrate gases to meet the physiological needs of the patient. Below is an overview of relevant gas laws, equations, and other key terms to support your practice.

Gas Laws and Equations

Boyle’s Law

Boyle’s law states at constant temperature and mass, the volume of a gas varies inversely with pressure.  In a given system, as the pressure goes up, the volume will go down. This is a concept that has application in the measurement of lung capacities and volumes in a body plethysmography box in a pulmonary function laboratory. (See Figure 1^[1])

Therefore, if we have a container at a known pressure and volume, then the pressure changes.  Utilizing basic algebra you can solve for the unknown volume. The algebra formula is as follows:

[latex]V2 = \frac {P1V1}{P2}[/latex]

Charles’ Law

Charles’ law states, at constant pressure and mass, the volume of a gas varies directly with temperature.  You should remember that Kelvin is the only linear temperature scale, and all temperatures must be converted to Kelvin.

[latex]V1T1 = V2T2[/latex]

Utilizing basic algebra you can solve for the second volume.  The algebra formula is as follows:

[latex]V2 = \frac {V1T1}{T2}[/latex]

Gay-Lussac’s Law

Gay-Lussac’s law states at constant volume and mass, the pressure of a gas varies directly with temperature.

[latex]P1T1 = P2T2[/latex]

Utilizing basic algebra you can solve for the second pressure (P2).  The algebra formula is as follows:

[latex]P2 = \frac {P1T1}{T2}[/latex]

Dalton’s Law of Partial Pressures

The total pressure of a gas mixture is the sum of the partial pressures of each constituent gas. This gas law is important in several contexts in the clinical experience of the respiratory therapist. A patient who is placed in a hyperbaric chamber is breathing supra-atmospheric (in other words giving higher than atmospheric pressure) pressurized O2 to enhance wound healing. In determining the oxygen content inside the lung structure of the alveolus, the different primary gas pressures are accounted for so when the math is complete, the respiratory therapist can accurately determine the PAO2 in the alveolar tissue of the lung.

• The partial pressure of each gas is what it would exert if alone.
• Each partial pressure is proportional to the percentage of the gas in the mixture.

Partial Pressure of a Gas

The partial pressure of a gas can be calculated using Dalton’s Law, which states the gas pressure in a system is the sum of the independent gasses (P_N = P_H2o + P_AO2 + P_N2). In other words, the total is the sum of the parts.

Key Terms for Respiratory Therapy to use with gas laws

• BTPS: Body Temperature and Pressure, Saturated (conditions within the lungs).
• ATPS: Ambient Temperature and Pressure, Saturated.
• STPD: Standard Temperature (0°C) and Pressure (760 mm Hg), Dry.

Composition of Atmospheric Gases

It is important for respiratory therapists to know the primary gasses in Earth’s atmosphere.  These gasses include the following:

• Nitrogen (N₂): 78.08%
• Oxygen (O₂): 20.95%
• Argon (Ar): 0.93%
• Carbon Dioxide (CO₂): 0.03%
• Trace Elements: 0.01%

Diffusion and Solubility Laws

Diffusion is the intermolecular mingling of gas molecules, resulting in a homogenous mixture due to random molecular motion. Diffusion is always a passive action of a gas movement from a higher to a lower pressure gradient.

Graham’s Law

Graham’s Law states that the rate of diffusion of a gas into a liquid is inversely proportional to the square root of its density; denser gases diffuse more slowly.

Henry’s Law

Henry’s Law states that the amount of gas dissolving in a liquid at a given temperature is proportional to the partial pressure of that gas.

• Gases with higher partial pressures dissolve more readily in liquids.
• Although oxygen is less dense, carbon dioxide has a much higher solubility coefficient, resulting in CO₂ diffusing 19 times faster than O₂.
• Graham and Henry’s law combine to demonstrate that there is 20 times more solubility of CO2 compared to O2 in the blood.

Fick’s Law

In its simplest form, Fick’s Law identifies the diffusion across a permeable membrane. The thicker the membrane, the less diffusion occurs. Graham and Henry’s law together form the basis for the coefficient for diffusion for the Fick equation.

Flow and Related Principles

Flow is the movement of a gas volume from one place to another over time and typically measured in liters per minute (L/min).

Flow can be increased by the following:

• Increasing the pressure gradient.
• Increasing the size of the opening or reducing resistance or opposition to flow.

Bernoulli Principle

The Bernoulli Principle states that as the forward velocity of a gas increases, its lateral pressure decreases, with a corresponding increase in forward pressure.

Venturi Principle

The Venturi Principle suggests that by adding a gradually widening tube (funnel) after a jet orifice and keeping the angulation below 15°, lateral pressure can be restored to pre-jet levels. (See Figure 2^[5])

Effects of Resistance to Flow (i.e., “back pressure”) and Obstruction

An obstruction downstream of an air entrainment device creates back pressure, reducing entrainment, total flow, and increasing oxygen concentration.

Jet Entrainment System

The amount of entrainment (air intake) is influenced by the following:

• Jet Orifice Size: Smaller orifices increase entrainment, total flow, and reduce oxygen concentration.
• Entrainment Port Size: Larger ports increase entrainment, total flow, and reduce oxygen concentration.

Poiseuille’s Law

Poiseuille’s Law is critically important as it reflects the change in resistance in the lung in opposition to gas flow.  This is true of the gas flow in the small airways of the lung, where the flow in the larger airways is a mixture of a linear flow and a turbulent flow, which is advantageous for the body to mobilize secretions.

The pressure needed to drive a gas (overcome airway resistance) increases if the following occurs:

• The length of the tube increases.
• The viscosity of the gas increases.
• The flow rate of the gas increases.
• The radius of the tube decreases.

Reynold’s Equation and Turbulent Flow

Gas flow is more likely to become turbulent when the following occur:

• Gas density is high.
• Flow rate is high.
• Tube diameter is large.
• Gas viscosity is low.

Turbulent flow typically begins when the Reynold’s number exceeds 2,000.