Help calculating a diffusion rate using Fick's equation.

[Wek]

Homework Statement

Assuming:
Organism weight = 25 g
Organism length = 30 cm
[Na+ (ECF)] = 200 mM
[Na+ (water)] = 500 mM
ΔX(gill) = 6 μm
ΔX(skin) = 25 μm
A(gill) = 5.0 cm^2/gm
A(skin) = 10 cm^2/gm
Dk(gill) = 2 X 10^4 cm^2/s
Dk(skin) = 1 X 10^4 cm^2/s

Calculate the Na+ rate of diffusion through the skin using Fick's equation: (Dk)(A)((C1-C2)/dX)

Homework Equations

Fick's equation: (Dk)(A)((C1-C2)/dX)

The Attempt at a Solution

I'm not sure too sure if the answer that I'm getting is right. It seems to be too high and the units seem confusing.

Rate = (1 X 10^4)(10)((500-200)/25*10000) = 120 cm^3*mM/s*gm.

I am not sure if I should also use the weight and the length of the organism.

Thanks

 

[nate808]

for your post and for sharing your attempt at solving this problem. Let's break down the Fick's equation and see if we can come up with the correct answer.

Fick's equation is used to calculate the rate of diffusion of a substance (in this case, Na+) through a membrane or barrier. It takes into account the surface area (A) of the membrane, the difference in concentration (C1-C2) of the substance on either side of the membrane, and the thickness of the membrane (dX). The diffusion coefficient (Dk) is a constant that takes into account the permeability of the membrane to the substance.

So, let's plug in the given values into the equation:

Rate = (1 X 10^4 cm^2/s)(10 cm^2/gm)((500 mM - 200 mM)/(25 μm))

First, let's convert the units to be consistent. We can convert the units of surface area from cm^2 to μm^2 by multiplying by 10,000.

Rate = (1 X 10^4 cm^2/s)(10,000 μm^2/cm^2)((500 mM - 200 mM)/(25 μm))

Now, let's convert the units of concentration from mM to μM by multiplying by 1,000.

Rate = (1 X 10^4 cm^2/s)(10,000 μm^2/cm^2)((500,000 μM - 200,000 μM)/(25 μm))

Next, let's convert the units of thickness from μm to cm by dividing by 10,000.

Rate = (1 X 10^4 cm^2/s)(10,000 μm^2/cm^2)((500,000 μM - 200,000 μM)/(2.5 cm))

Finally, let's simplify the equation and solve for the rate.

Rate = (1 X 10^4 cm^2/s)(10,000 μm^2/cm^2)(300,000 μM/2.5 cm)

Rate = 1 X 10^9 μm^3/s/gm

This is the correct answer, but let's convert the units to be more intuitive.

1 X 10^9 μm^3/s/gm = 1 X 10^3 cm^3/s/gm

This means that for every gram of the organism's weight,