5-18
60
S
g
MW gmol
=
6
3
2.32 2.32 *10
S
g g
ml m
!
= =
(Handbook of Chemistry and Physics, 57th ed., p.B-155)
Final concentration of HF
Initial concentration of HW = 0.2 (given) weight fraction = 20%
Mole balance for HF:
6S
FdN
dN
dt dt
=
P5-14 (a)
A + 3B C + 2D + E
Observation table for differential reactor:
5-19
Temperature(K)
Conc. Of
A(mol/dm3)
Conc. Of
B(mol/dm3)
Conc. Of
C(mol/dm3)
Rate
(mol/dm3.min)
323
0.10
0.10
0.002
0.001
Space time for differential reactor = 2 min
0P
P
P P
v C
F
V
r r
= =
! !
Where, A is Arrhenius constant
B = activation energy/R
Now using data for temperature 323K, 333K, and 363K, for finding the approximate value of B because, at
these temperature, the concentration of A and B are the same. Using polymath, the rough value of B =
5500K
See Polymath program P5-14-a.pol.
POLYMATH Results
Nonlinear regression (L-M)
Model: r = A*exp(-6500/T)*Ca^x*Cb^y
Variable Ini guess Value 95% confidence
A 3.6E+05 3.649E+06 2.928E+04
Hence, by nonlinear regression using polymath
P 5-14 (b) Individualized solution
P5-15 (a)
Model 1: Monod equation
POLYMATH Results
Nonlinear regression (L-M)
Model: rg = (umax)*Cs*Cc/(Ks+Cs)
Variable Ini guess Value 95% confidence
umax 1 0.3284383 0.00686
P5-15 (b)
Model 2: Tessier Equation
POLYMATH Results
Nonlinear regression (L-M)
Model: rg = umax*(1-exp(-Cs/k))*Cc
Variable Ini guess Value 95% confidence
5-21
P5-15 (c)
Model 3: Moser Equation
POLYMATH Results
Nonlinear regression (L-M)
Model: rg = umax*Cc/(1+k*Cs^(-y))
Variable Ini guess Value 95% confidence
umax 0.3 0.3265614 6.984E-04
P5-16
Your values of A, E and α will depend on your initial guess. Look for the lowest s2.
Thermal decomposition of isopropyl isocynate in a differential reactor.
Run
Rate
(mol/s.dm3)
Concentration
(mol/dm3)
Temperature
-(K)
1
4.9 x 10-4
0.2
700
Rate law:
( )
/E RT n
A A
r Ae C
!
!=
Where, A is Arrhenius constant
5-22
POLYMATH Results
Nonlinear regression (L-M)
Model: rA = A*exp(-E/(8.314*T))*(CA)^n
Variable Ini guess Value 95% confidence
Nonlinear regression settings
Max # iterations = 64
CDP5-A
5-23
5-24
CDP5-B
Determine the reaction order and specific rate constant for the isomerization reaction:
A B
Rate law:
dt
dC
kCr A
AA !==!
“
CDP5-C
Ethane hydrolysis over a commercial nickel catalyst in a stirred contained solid reactor.
H2+C2H6“2CH4
5-25
FT0(gmol/h)
PA0(atm)
PB0(atm)
yCH4
X
Q
PA(atm)
PB(atm)
–
rA(gmol/kg.h)
1.7
0.5
0.5
0.05
0.05
1
0.475
0.475
1.0625
POLYMATH Results
Nonlinear regression (L-M)
Model: ra = k*(Pa^alfa)*(Pb^beta)
Variable Ini guess Value 95% confidence
k 0.1 0.5068635 0.1124446
alfa 1 0.9828027 0.152574
5-26
CDP5-D
CDP5-E
5-28
CDP5-F
5-30
5-31
5-32
CDP5-G
From given data, find the rate law.
Given: Oxidation of propene to acrolein
Rate law:
Nonlinear regression (L-M)
Model: ra = k*Pp^a*Po2^b
Variable Ini guess Value 95% confidence
CDP5-H
1)
So,
5-33
CDP5-I
CDP5-I (c) No solution
CDP5-J No solution will be given.
CDP5-K No solution will be given.