II The small capillaries in the lungs are in close contact...

II The small capillaries in the lungs are in close contact with the alveoli. A red blood cell takes up oxygen during the $0.5 \mathrm{s}$ that it squeezes through a capillary at the surface of an alveolus. What is the diffusion time for oxygen across the $1-\mu \mathrm{m}$ -thick membrane separating air from blood? Assume that the diffusion coefficient for oxygen in tissue is $2 \times 10^{-11} \mathrm{m}^{2} / \mathrm{s}$. Give your answer to 1 significant figure.

II The small capillaries in the lungs are in close contact with the alveoli. A red blood cell takes up oxygen during the $0.5 \mathrm{s}$ that it squeezes through a capillary at the surface of an alveolus. What
is the diffusion time for oxygen across the $1-\mu \mathrm{m}$ -thick membrane separating air from blood? Assume that the diffusion coefficient for oxygen in tissue is $2 \times 10^{-11} \mathrm{m}^{2} / \mathrm{s}$. Give your answer to 1 significant figure.

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Key Concepts

Fick’s Laws of Diffusion

Fick’s Laws provide the mathematical framework for understanding diffusion. The first law relates the diffusive flux to the concentration gradient, while the second law predicts how diffusion causes the concentration to change with time. Estimation of diffusion time over a specific distance typically uses the relation that the time is proportional to the square of the distance divided by the diffusion coefficient.

Diffusion Coefficient

The diffusion coefficient is a parameter that quantifies how quickly a substance diffuses through a medium. It is influenced by factors such as temperature, the medium’s viscosity, and the size of the diffusing particles. In problems like this, its value is used in diffusion equations to estimate the time needed for molecules to travel a certain distance.

Diffusion Process

This concept refers to the movement of molecules from regions of higher concentration to regions of lower concentration. In the context of gases like oxygen diffusing through a thin membrane, the process is random and is characterized by a time scale that increases with the square of the distance that the molecule needs to travel.

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