Using the Einstein-Stokes equation, calculate the time for urea to diffuse across a cuboidal kidney cell with sides of 100micrometers. Assume the diffusion coefficient (D) of urea in solution is 2 x 10^-8 m2 sec -1
To calculate the time for urea to diffuse across a cuboidal kidney cell, we will use the Einstein-Stokes equation for diffusion:
D = (k * T) / (6 * pi * r)
Where:
D = Diffusion coefficient
k = Boltzmann constant (1.38 × 10^-23 J/K)
T = Temperature in Kelvin
r = Radius of the kidney cell
First, we need to convert the radius of the cell from micrometers to meters:
Radius = 100 micrometers = 100 × 10^-6 meters = 0.0001 meters
Next, we need to convert the diffusion coefficient (D) from m^2/sec to m^2/s:
Diffusion coefficient (D) = 2 × 10^-8 m^2 sec^-1
Since the Boltzmann constant (k) is in SI units, we can use it directly. Assuming room temperature (T ≈ 298 K), we can now substitute the values into the equation:
2 × 10^-8 m^2 sec^-1 = (1.38 × 10^-23 J/K) * (298 K) / (6 * pi * (0.0001 meters))
To calculate the time (t), we isolate it in the equation:
t = (6 * pi * (0.0001 meters) * D) / (k * T)
Substituting the values, we have:
t = (6 * pi * (0.0001 m) * (2 × 10^-8 m^2 sec^-1)) / ((1.38 × 10^-23 J/K) * (298 K))
By performing the calculation, you will obtain the time it takes for urea to diffuse across the cuboidal kidney cell.