A permeation tube is a device for preparing gas standards having a known concent

Question

A permeation tube is a device for preparing gas standards having a known concentration of some trace constituent of interest. For example, one could be made for carbon tetrachloride, CCI_4, by sealing some liquid in a plastic tube of small but finite permeability for the chemical. When the tube is placed into the gas stream. What rate of CCI_4 release do you expect to occur if the tube has a wall area of 8 cm^2 and a thickness of 1 mm? Assume the concentration of CCI_4 in the plastic tube wall,in equilibrium with liquid CCI_4, is 1 mg/cm^3. Use a diffusion coefficient of 10^-10 cm^2/sec. For this to be a useful standard, the permeability of the tube must be well known. What conditions must be met to ensure that the concentration of CCI_4 created in the gas stream is constant? (There are at least three additional conditions required if accurate results are desired.)

Explanation / Answer

a. Using Fick's first law of diffusion

J = - D dc/dt

J = NUMBER OF PARTICE / ( AREA x THICKNESS x Time )

  = 1 / ( 8 x 1 x 10^-3 x 100 x 1 )

= 1.25 m-2 s-1

D = 10^-10 cm^2/sec = 10^-10 / 10^4 m^2/sec = 1 x 10^-14 m^2/sec

- J / D = dc/dt

dc/dt   = - J / D = 1.25 m-2 s-1 /  1 x 10^-14 m^2/sec = - 1.25 x 10^14 m^-4

b. The first law can only be applied to systems in which some conditions remain the same

1. If the flux coming into the system equals the flux going out.

2. Fick’s second law is more applicable to physical science and other systems that are changing. This second law is applied to systems in which the condition are not steady, or the solution in not equal throughout.

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