交換表面、表面積與體積比及菲克定律：练习题

Using Fick’s law, calculate the relative rate of diffusion for a gas moving across a membrane with a surface area of \(0.5\text{ mm}^2\), a concentration difference of \(0.04\text{ mol dm}^{-3}\), and a membrane thickness of \(0.002\text{ mm}\).

\(\text{rate of diffusion} \propto \frac{\text{surface area} \times \text{concentration difference}}{\text{thickness of membrane}}\)

A scientist is studying the rate of diffusion across a synthetic membrane. The initial surface area is \( 2.0\text{ mm}^2 \) and the membrane thickness is \( 0.01\text{ mm} \). If the surface area is doubled and the thickness is halved, while the concentration gradient remains constant, what is the factor of increase in the rate of diffusion according to Fick's Law?

The diagram shows the human heart and its major blood vessels. Which vessel carries oxygenated blood from the lungs to the left atrium, and what is the relative thickness of the wall of the left ventricle compared to the right ventricle?

A research group is investigating Fick's Law of diffusion. They compare two different exchange surfaces, X and Y. Surface X has a surface area of \( 4.0\text{ mm}^2 \) and a membrane thickness of \( 0.02\text{ mm} \). Surface Y has a surface area of \( 12.0\text{ mm}^2 \) and a membrane thickness of \( 0.04\text{ mm} \). Assuming the concentration gradient is identical for both, calculate the ratio of the rate of diffusion for surface Y compared to surface X.

A person has a heart rate of \(80\) beats per minute and a stroke volume of \(65\text{ ml}\). Calculate the cardiac output using the following equation:
\(\text{cardiac output} = \text{stroke volume} \times \text{heart rate}\)

A spherical organism has a radius of \( 0.05\text{ mm} \). If it grows such that its radius doubles to \( 0.1\text{ mm} \), calculate the factor by which its surface area to volume ratio (SA:V) changes. Show your working using the formulas \( \text{Surface Area} = 4\pi r^2 \) and \( \text{Volume} = \frac{4}{3}\pi r^3 \).

A student investigated the effect of surface area on the rate of diffusion to model gas exchange in animals. They used two cubes of agar jelly containing phenolphthalein and sodium hydroxide.

Cube A has a side length of \(1\text{ cm}\).
Cube B has a side length of \(2\text{ cm}\).

a) Calculate the surface area to volume ratio (SA:V) for Cube B.
b) Both cubes were placed in a beaker of dilute hydrochloric acid. Predict which cube will have its center neutralized first and explain your answer with reference to its SA:V ratio.
c) Explain how the alveoli in the lungs are specifically adapted to overcome the limitations of a small SA:V ratio in large multicellular organisms.