The molecular diffusivity of potassium ferricyanide in a solution was determined by filling a capillary with the
solution and immersing it in a bath (at 25 ) of the solution from which the
ferricyanide was omitted. The solution compositions were:
The capillary tube is 1.0 mm in diameter and 2.1 cm long. After 15 hours the capillary was removed from the bath and its contained fluid titrated for ferricyanide. It was found to contain 2.308 micro-moles of potassium ferricyanide.
(Derive the differential equation and boundary conditions for this process and put the problem in dimensionless form. The error function solution may then be written down, if known.)
Let: A = potassium ferricyanide
B = all other components
Initial condition
t = 0, CA = 0, Z 0
Boundary Conditions
A mass balance on component "A" in the capillary element SZ gives:
Dividing by SZ and taking the limit
Fick's first law for dilute solutions is
from which
Thus we arrive at Fick's second law in the form
Utilizing:
The following solution results
differentiating for (dCA/dZ) and substituting
evaluating @ Z = 0
for the period of the experiment, the weight loss (M)
Rearranging and evaluating
To evaluate the error introduced by assuming Z utilize
0.9999 |
2.0 |
2.17 |
0.99 |
1.81 |
1.97 |
Thus (0.99 < < 0.9999) @ t = 15 hr.,
the assumption (Z , = 1.0) was pretty good.
For liquid diffusivity
Assuming for this dilute solution