HW04, ChE 120C 2012
Due May 30th
1. Cussler 8.2: Water flows through a thin tube, the walls of which are benzoic acid. So the water
is saturated with benzoic acid at the pipe’s wall. The water flows slowly, at room temperature
and 0.1cm/s. The pipe is 1cm in diameter. Under these conditions, the mass transfer coefficient
k varies along the pipe as
1/3
 vd 2 
kd
 1.62 

D
 DL 
where d and L are the diameter and length of the pipe and v is the average velocity in the pipe.
What is the average concentration of benzoic acid in the water after 2 m of pipe?
2. Cussler 8.12: The largest liquid liquid extraction process is probably the dewaxing of lubricants.
After they are separated by distillation, crude lubricant stocks still contain significant quantities of
wax. In the past these waxes were precipitated by cooling and separated by filtration. Now they
are extracted with mixed organic solvents. For example, one such process uses a mixture of
propane and cresylic acid. You are evaluating a new mixed solvent for dewaxing that has
physical properties like those of catechol. You are using a model lubricant with properties of
hydrocarbons. Waxes are 26.3 times more soluble in the extracting solvent than they are in the
lubricant. You know from pilot plant studies that the mass transfer coefficient based on a
lubricant side driving force is
K L a  16200 lb / ft 3 / hr
where a is a process specific interfacial area per volume in the extractor. What will be the value
of KSa, the overall mass transfer coefficient for a driving force based on the solvent side.
3. Cussler 8.13: Estimate an overall mass transfer coefficient for solute adsorption from an aqueous
solution of density 1.3g/cm3 into hydrogel beads 0.03cm in diameter. The coefficient sought, Ky,
is defined by NA = Ky(y-y*) where NA has units g/cm2/sec, and the y’s are solute mass fractions in
the water phase. On the solution film side the mass transfer coefficient is kS = 10-3cm/sec. The
mass transfer coefficient within the hydrogel beads is given by kB = 6D/d where d is the bead
diameter and D = 3 x 10-6cm2/s. Note that the partition coefficient is one because the beads are
hydrogels. Estimate Ky in the units given.
4. At steady state in a gas filled tube of radius R and length L, dilute component A is diffusing with
diffusivity D. Let z be distance along the tube axis. The tube walls catalytically decompose A so
that the heterogeneous rate of decomposition on the wall (in mol A/m2/s) is kcA where k is a first
order rate constant and cA is the concentration of species A. On the midterm, you assumed that
radial concentration gradients are negligible. You derived a differential equation for steady-state
diffusion and reaction. Identify a single dimensionless parameter (a Damkohler number)
involving R, D, L, and k. Solve the resulting ODE with boundary conditions cA|z=L = cA,L and
dcA/dz|L = 0.
5. Dilute reactant A diffuses from an inert gas into a thin liquid film, e.g. the surface of a bubble. In
the liquid film, a rapid and reversible reaction A ↔ B occurs with first order rate constants k1 for
A→B and k2 for B→A. At steady state the species balance equations are
d 2C A
 k1C A  k2CB  0
dz 2
d 2CB
DB
 k2CB  k1C A  0
dz 2
DA
The equilibrium constant for the reaction A ↔ B is K = k1/k2 = CB/CA. A partition coefficient H
relates the surface concentrations inside and outside the liquid film: HCA(liq) = CA(gas). Let the film
be of thickness 2l and let the concentrations be as defined in figure 1. The boundary condition at
z=l is that nA = kc(CA∞-HCAs). Note that the reaction only occurs within the liquid film, and
therefore the reactants and products are at equilibrium with each other only within the liquid film.
Solve for CA(z) when the flux of A to the film is related to the surface concentration of A in the
film.
to the fluxto the surface concentration CA(0) = CA(l) = CAs, where the film is of thickness l.
Hint: first show that (DACA + DBCB) is a linear function of z. Then it will become clear from
symmetry that the concentration wit
Let the film have thickness l, and let the concentration at the boundary