Fick’s First Law of Diffusion and Lung Gas Exchange Vector

Fick’s First Law of Diffusion and Lung Gas Exchange (2024)

by | Updated: Feb 8, 2024

Fick’s First Law of Diffusion is a fundamental principle in the field of physics and physiology that describes the process of gas exchange in biological systems, particularly in the context of the human respiratory system.

This law, formulated by Adolf Fick in the 19th century, provides a mathematical framework to understand how gases move across membranes and tissues, ultimately enabling the exchange of oxygen and carbon dioxide in the lungs.

In this article, we will explore the principles of Fick’s First Law and its relevance to the crucial physiological process of gas exchange within the human respiratory system.

What is Fick’s First Law of Diffusion?

Fick’s First Law of Diffusion states that the rate of diffusion of a substance across a layer is proportional to the difference in concentration across that layer and inversely proportional to its thickness. This law is crucial in understanding gas exchange in the lungs.

Fick’s First Law of Diffusion Vector Illustration

In the lungs, oxygen and carbon dioxide diffuse across the alveolar membrane.

The high concentration of oxygen in the alveoli compared to the blood and the thinness of the alveolar membrane facilitate the rapid diffusion of oxygen into the blood.

Similarly, carbon dioxide diffuses from the blood (where its concentration is higher) into the alveoli, to be exhaled.


Mathematically, Fick’s First Law of Diffusion is represented as:

J = – D (dC/dx)


  • J is the flux or the amount of substance passing through a unit area per unit of time
  • D is the diffusion coefficient
  • dCdx is the concentration gradient along the direction x

Note: In the context of gas exchange in the lungs, Fick’s First Law can be employed to explain how oxygen (O2​) and carbon dioxide (CO2​) move between the alveolar air spaces in the lungs and the pulmonary capillaries.

What is Gas Exchange?

Gas exchange is a biological process through which different gases are transferred in opposite directions across a specialized exchange surface.

This primarily refers to the exchange of oxygen and carbon dioxide between the bloodstream and the external environment.

Oxygen from inhaled air diffuses into the blood, while carbon dioxide, a waste product of metabolism, diffuses from the blood to the air in the lungs to be exhaled.

This exchange is essential for respiration, allowing oxygen to be delivered to cells for metabolic processes and removing carbon dioxide, a byproduct of these processes.

Clinical Implications

Understanding Fick’s Law has significant clinical implications. Conditions that alter any component of the law can lead to impaired gas exchange.

For example, a decrease in alveolar surface area in emphysema, an increase in the thickness of the alveolar membrane in fibrosis, or changes in partial pressure gradients due to diseases like chronic obstructive pulmonary disease (COPD) or asthma, all affect lung efficiency.

What is Diffusion?

Diffusion is a fundamental process where particles move from an area of higher concentration to an area of lower concentration.

This movement is driven by the random motion of particles and continues until a uniform concentration is achieved throughout the medium.

Diffusion is a passive process, meaning it doesn’t require energy input.

It’s crucial in various biological and physical processes, such as the exchange of gases in the lungs of living organisms, the spread of substances in solutions, and the permeation of materials through membranes.

The rate of diffusion depends on factors like temperature, concentration gradient, and the size of the particles.

FAQs About Fick’s First Law and Gas Exchange

What Does Fick’s First Law Describe?

Fick’s First Law of Diffusion describes the rate of diffusion of a substance across a layer, such as a membrane.

It states that this rate is directly proportional to the concentration gradient (the difference in concentration across the layer) and the surface area of the membrane, and inversely proportional to the thickness of the layer.

Essentially, it quantifies how the diffusion rate of a substance increases with a steeper concentration gradient and a larger surface area, and decreases with a thicker membrane.

What is Fick’s Second Law?

Fick’s Second Law of Diffusion, extending from the first law, provides a more detailed description of diffusion. It explains how diffusion causes the concentration gradients to change over time.

This law is described by a differential equation that relates the rate of change in concentration of a substance with respect to time to its second spatial derivative.

This law is particularly useful in predicting how the concentration of a substance will change in a given medium over time.

What is the Difference Between Fick’s First and Second Law?

The primary difference between Fick’s First and Second Law lies in their focus and complexity.

Fick’s First Law deals with steady-state diffusion and is used to calculate the flux of particles across a membrane at a constant rate. It’s simpler and directly relates the diffusion rate to the concentration gradient.

On the other hand, Fick’s Second Law addresses non-steady-state, or dynamic, diffusion. It is more complex, involving calculus to describe how diffusion rates change over time and space.

This law is essential in scenarios where the concentration of a substance changes over time.

Why is Fick’s Law Important in the Field of Respiratory Care?

Fick’s Law is critically important in respiratory care because it explains the fundamental principles behind gas exchange in the lungs.

Understanding how gases like oxygen and carbon dioxide diffuse across the alveolar membrane is key to comprehending respiratory physiology.

Fick’s First Law helps explain the efficiency of gas exchange based on the concentration gradients of oxygen and carbon dioxide, and the thinness of the alveolar membrane.

In clinical settings, this understanding aids in managing conditions like chronic obstructive pulmonary disease (COPD) and pulmonary fibrosis, where gas exchange efficiency is compromised.

The laws of diffusion are also essential in designing effective respiratory therapies and understanding how various factors, such as altitude or disease, can affect gas exchange in the lungs.

Final Thoughts

Fick’s First Law of Diffusion is essential for comprehending the process of gas exchange in the lungs. 

Its simple yet powerful equation enables us to grasp the mechanisms that underlie the essential physiological processes of oxygen and carbon dioxide exchange.

By appreciating the significance of this law, we can better appreciate the marvel of the human respiratory system and its intricate mechanisms for maintaining the delicate balance of gases essential for survival.

Written by:

John Landry, BS, RRT

John Landry is a registered respiratory therapist from Memphis, TN, and has a bachelor's degree in kinesiology. He enjoys using evidence-based research to help others breathe easier and live a healthier life.


  • Egan’s Fundamentals of Respiratory Care. 12th ed., Mosby, 2020.
  • Fick’s laws of diffusion. (2023, November 22). In Wikipedia.
  • Butler JP, Tsuda A. Transport of gases between the environment and alveoli–theoretical foundations. Compr Physiol. 2011.

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