How does increasing diffusion distance affect the rate of diffusion across a membrane (all else being equal)?

• A. The diffusion rate decreases because diffusion time increases with distance
• B. The diffusion rate decreases only if the diffusing molecule is charged; neutral molecules are unaffected by distance
• C. The diffusion rate increases because particles gain kinetic energy over longer distances
• D. The diffusion rate is unaffected by distance as long as the concentration gradient is constant

Answer: (A)

Verified step by step guidance

1. Recall Fick's First Law of Diffusion, which states that the rate of diffusion (J) is proportional to the concentration gradient and inversely proportional to the diffusion distance. The law can be expressed as: \[ J = -D \frac{\Delta C}{\Delta x} \] where \(J\) is the diffusion flux, \(D\) is the diffusion coefficient, \(\Delta C\) is the concentration difference, and \(\Delta x\) is the diffusion distance.
2. Understand that increasing the diffusion distance (\(\Delta x\)) means the molecules have to travel farther to cross the membrane, which affects the rate inversely because \(J\) is divided by \(\Delta x\).
3. Recognize that the diffusion time increases with the square of the distance, as described by the relation: \[ t \propto (\Delta x)^2 \] This means that even a small increase in distance significantly increases the time required for diffusion.
4. Consider that the diffusion rate decreases regardless of whether the molecule is charged or neutral, as diffusion depends on distance and concentration gradient, not on the charge of the molecule in this context.
5. Conclude that increasing diffusion distance decreases the diffusion rate because molecules take longer to traverse the membrane, reducing the overall flux, assuming all other factors like concentration gradient and diffusion coefficient remain constant.