Exam 6:
Name:
CHE 3121-Spring 2023
Section:
Problem 1 (13 points): Consider a spherical organism of radius R within which
respiration occurs at a uniform volumetric rate of rA = − k1CA. That is, oxygen
(species A) consumption is governed by a first-order, homogeneous chemical
reaction. A molar concentration of CA(R) = CA,0 is maintained at the surface of the
organism, and an expression for the radial distribution of oxygen, CA(r), within the
organism is given by
CA(r) = CA,0
R sinh(αr )
r sinh(αR)
Data: R = 0.15 mm, diffusion coefficient for oxygen transfer DAB = 10-8 m2/s, CA,0 =
6×10-5 kmol/m3.
a) If α = 4×104 m-1, the concentration of oxygen at the center of the organism is
_________Unit kmol/m3
b) If α = 4.0×104 m-1, the consumption of A within the particle is
____________Unit kmol/s
c) If the reaction is zero order with rate constant = 0.15 kmol/s⋅m3,
consumption of A within the particle is
the
__________Unit kmol/s
Problem 2 (12 points): Species A diffuses into a cylindrical pore where it reacts at
the cylindrical surface to produce B (A ! B) according to a zero order reaction
r”A(mol/cm2⋅s) = − k1 where k1 = 1.5×10-6 mol/cm2⋅s. There is no reaction at the end
of the pore and the end is impermeable to A. The inside diameter D of the pore is 0.1
cm and its length L = 2.0 cm. You can assume CA(z) is a function of z where z is the
distance along the pore with z = 0 at the entrance to the pore. The concentration of A
at the end of the pore is not zero and CA(z = 0) = CA0 = 5×10-3 mol/cm3. Diffusivity of
A in B is DAB = 0.12 cm2/s.
d 2C A
4k1
The differential equation that can be solved CA(z) is
−
=0
2
DDAB
dz
a) Determine the molar flux of A at z = 0 ___________ Unit mol/cm2⋅s
From the problem statement, the concentration CA(z) can be obtained as
CA(z) = Cz2 + C1z + C2 where z is in cm
b) C (numerical value with units) = _________
c) C1(numerical value with units) =________
d) C2 (numerical value with units) =_________
Problem 3 (15 points): A distillation column receives a feed that is 40 mole % ibutane and 60 mole % i-pentane. Feed is saturated liquid at 1,000 lbmol/hr. The
column is at 14.7 psia. A distillate that is 95 mole % i-butane is desired. A total
condenser is used. Reflux is a saturated liquid. The external reflux ratio is L0/D = 2.3
Bottoms from the partial reboiler is 9 mole % i-butane. Determine the number of
equilibrium trays in the stripping section and the vapor composition leaving the
reboiler and the last two trays.
Equilibrium K values for light hydrocarbon systems
=============================================================
ln K = −A/T2 + B − C ln(P) , where P is in psia, T is in oR
Compound
A
B
C
=============================================================
i-Butane
1166846
7.72668
.92213
i-Pentane
1481583
7.58071
.93159
=============================================================
Problem 4 (10 points): A distillation column receives a feed that is 42 mole % Benzene
and 58 mole % Toluene. The feed is 25% saturated liquid. The column is at 1 atm. A
distillate that is 70 mole Benzene is desired. A total condenser is used. Reflux is a saturated
liquid. The external reflux ratio is L0/D = 1.5. Bottoms from the partial reboiler is 90 mole %
Toluene.
a) draw q-line
b) draw the operation line for the rectifying and stripping section
c) Find the number of equilibrium stages and feed location if the overall tray efficiency is 1.