This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Chemical Engineering 140 September 26, 2005
Midterm #1 Solution (100) 1. V Conductivity
probe C(t) SCL Ň
Donor cell co A Given in problem statement: L Receptor cell A ≡ Area of membrane (SCL)
V ≡ Volume of receptor cell
L ≡ Thickness of membrane (SCL)
co ≡ Concentration of salt in donor cell,
CONSTANT
Both tanks are WELL MIXED
C(t = 0) = 0 (Upper chamber initially
contains no salt) ( ) i. Use transient species mass balance on salt in upper chamber
CV = Upper chamber volume = V
Mass balance for species i = salt. No reaction, no outlet streams
0
0
d (nM )
dmi
(m) nin M
mi ,in mi ,out Gi dt
dt
Constant species molecular weight M allows us to reduce mass balance to mole balance
d
d (CV ) C (r )dV dt nin (Well mixed tank C is indep. of position) (*)
dt V
But, rate of moles in varies with the concentration difference across the SCL:
PA
ˆ co C (t ) (Relationship for flux N is given in part (i).) (**)
nin NA L
Combining (*) and (**), we obtain
0
d (CV )
dV
dC PA co C (t ) (Expand by product rule; V constant)
C
V dt
dt
dt
L V dC PA co C (t ) dt
L Rearranging, we have a first order, linear ODE for C(t):
dC PA
PA C (t ) co
dt VL
VL
( ) (ii) Solve the ODE and use BC’s to get expression for concentration
Defining an integrating factor and writing the general solution to this linear first order ODE,
where is a constant of integration
PA exp[ dt ]
VL PAco
1 PA C (t ) dt , which simplifies to C (t ) c o exp t VL VL Applying the initial condition that C (t = 0) = 0 and simplifying gives PA C (t ) c o 1 exp t VL ( ) (iii) Express similar to Nicolas et al
1 C (t ) PA exp t co VL C (t ) PA
ln 1 t co VL Equation 1 given by Nicolas is correct. ( ) (iv) Examine procedure for determining P:
Plotting method by Nicolas et al is incorrect. Slope does not give P, as the slope has the
wrong dimensions. Permeability P should be given in length2/time.
Plotting ln(1C/co)(A/(LV)) versus t gives
length 2
1
1 3
length length
length 2
abscissa [=] time
ordinate [=] slope [=] 1
length 2 time V, L, and A are known for the system. C(t) is measured by the conductivity meter.
To obtain the proper value for P:
Plot VL C (t ) ln 1 versus t on rectangular coordinates; slope = P
A co Or C (t ) PA
Plot 1 versus t on semilog paper; slope =
co VL ( ) (v) Conclusion: Although the species mass balance on the salt was correct, any claimed
permeabilities P obtained for this product should be regarded as suspect, since P was found using
an improper plotting method. ...
View
Full
Document
This note was uploaded on 02/05/2010 for the course CHM ENG 140 taught by Professor Radke during the Fall '08 term at University of California, Berkeley.
 Fall '08
 RADKE

Click to edit the document details