The diffusion coefficient for calcium ions crossing a biological membrane 10nm thick is 300 micrometers squared/second and the concentration difference of calcium ions across the membrane is 400 mol/m^2 (Molar mass of calcium is 40 kg/mol)
Determine the number of moles of calcium ions that move through a 1 micrometer*1 micrometer cross sectional area of the membrane in 1 second
Diffusion rate (moles/area*sec) =
(Concentration gradient)*(Diff. coefficient)
Shouldn't the concentration difference have units of mole/m^3 ? Or are you providing the value of
(Diff. coefficient)/(thickness) ?
To determine the number of moles of calcium ions that move through a 1 micrometer * 1 micrometer cross-sectional area of the membrane in 1 second, you can use Fick's law of diffusion:
J = -D * dC/dx
Where:
J is the flux of ions (amount of ions crossing the membrane per unit time and area),
D is the diffusion coefficient,
dC/dx is the concentration gradient (change in concentration per unit distance).
In this case, we're given:
D = 300 micrometers^2/second
dC/dx = 400 mol/m^2
To apply Fick's law, we need to convert the units, so:
- Convert the diffusion coefficient from micrometers^2/second to meters^2/second:
1 micrometer = 10^-6 meters
(300 micrometers^2/second) * (1 * 10^-6 meters/micrometer)^2 = 3 * 10^-4 meters^2/second
- Convert the concentration gradient from mol/m^2 to mol/m^3:
1 m^2 = (1 meter * 1 meter) = 1 meter^2
1 mol/m^2 = 1 mol / (1 meter^2) = 1 mol/m^3
Now we have:
D = 3 * 10^-4 meters^2/second
dC/dx = 400 mol/m^3
Plug these values into Fick's law:
J = -(3 * 10^-4 meters^2/second) * (400 mol/m^3)
The result of this equation will give us the flux J, which represents the number of moles of calcium ions crossing the membrane per unit time and area.
So, in one second, the number of moles of calcium ions that move through a 1 micrometer * 1 micrometer cross-sectional area of the membrane can be calculated using the above equation.