In regards to Fick’s first law, what would happen to the diffusion of a drug if you increase the surface area by 4-fold but increase the membrane thickness by 2-fold? Please show y... In regards to Fick’s first law, what would happen to the diffusion of a drug if you increase the surface area by 4-fold but increase the membrane thickness by 2-fold? Please show your math to support your answer choice.
Understand the Problem
The question is asking how changes in surface area and membrane thickness affect the diffusion of a drug, according to Fick’s first law of diffusion. It requires us to analyze the relationship and provide mathematical support for the conclusion.
Answer
The diffusion rate ($J$) is given by $J = -D \frac{A \Delta C}{d}$; increased surface area increases $J$, while increased thickness decreases $J$.
Answer for screen readers
The rate of diffusion ($J$) is directly proportional to surface area ($A$) and inversely proportional to membrane thickness ($d$), represented by the equation:
$$ J = -D \frac{A \Delta C}{d} $$
An increase in surface area increases diffusion, while an increase in membrane thickness decreases it.
Steps to Solve
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Fick's First Law of Diffusion
To understand how surface area and membrane thickness affect diffusion, we start with Fick's first law, which states that the rate of diffusion (J) of a substance across a surface is directly proportional to the surface area (A) and the concentration gradient (ΔC) and inversely proportional to the thickness of the membrane (d). This can be expressed mathematically as: $$ J = -D \frac{A \Delta C}{d} $$ where $D$ is the diffusion coefficient. -
Surface Area Increase
Increasing the surface area ($A$) will increase the rate of diffusion ($J$). This relationship can be seen by considering the equation; if $A$ increases, $J$ must also increase as long as the concentration gradient and thickness remain constant. -
Membrane Thickness Increase
Increasing the thickness of the membrane ($d$) will decrease the rate of diffusion ($J$). Again, referencing the equation, if $d$ increases, the fraction $\frac{A \Delta C}{d}$ will decrease, which means $J$ will decrease, assuming surface area and concentration gradient remain constant. -
Combining the Effects
By analyzing both changes—an increase in surface area and an increase in membrane thickness—we can conclude that maximizing surface area while minimizing thickness will optimize the rate of diffusion.
The rate of diffusion ($J$) is directly proportional to surface area ($A$) and inversely proportional to membrane thickness ($d$), represented by the equation:
$$ J = -D \frac{A \Delta C}{d} $$
An increase in surface area increases diffusion, while an increase in membrane thickness decreases it.
More Information
Fick's first law of diffusion is fundamental in understanding how substances move across membranes. It highlights the importance of both surface area and membrane characteristics in processes such as drug delivery.
Tips
- Misunderstanding that increasing surface area always increases diffusion without recognizing the impact of membrane thickness.
- Incorrectly assuming that the concentration gradient always stays constant, which may not be the case in real-life scenarios.
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