Compuconc Inc. has developed a new bottle that it claims will store volatile materials for a long time without a cover (Figure P4.29). The key is that the cross sectional area of the device is designed to obey the function \(A=A_{o} e^{-\alpha z}\), where \(z\) is the distance from the bottom. To test the concept you must perform the experiment shown below. Assuming dilute solutions, constant total concentration, constant diffusivity, and steady-state operation,

a. Derive the differential equation for the mole fraction profile of \(a\).

b. What are the boundary conditions?

c. Solve the differential equation for the mole fraction profile and flux.

d. Can the mole fraction of \(a\) exceed \(y_{a o}\) at any point within the flask? What does this have to say about Compuconc's claims (what is the effect of the bizarre shape)?

Transcribed Image Text:

FIGURE P4.29 z=L Yace A(z) = a,e-x N(z+Az) Az N(2) z=0 Yao