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)
6
3
1 10
g g
ml m
!
“=
20
F
g
MW gmol
=
3 3
0.5 0.0005V dm m= =
9
1.2986 *10
!
“
=
( ) ( ) ( )
1.775
6
3
9 3
1.775
2 6
3
60
10
1.2986 *10 0.0005
20 0.2 2.3*10 100
g
gkgmol
mm
gg
m
gmol m
!
” #
” # $ %
$ % & ‘
$ %
=” #
$ % $ %
$ % & ‘
& ‘
0.775
3
7 1
3.224 *10 min
m
kgmol
! !
” #
=$ %
& ‘
Final concentration of HF
Initial concentration of HW = 0.2 (given) weight fraction = 20%
0.775
10.7
1.775
20 0
6
100
t
F
dw k dt
w MW
!
” #
$=% &
‘ (
) )
( )
0.775
10.7 6
7
0.775
20
1 1 10
6 3.224 *10
0.775 20 *100
t
w
!” #
“ # =$ %
$ %
& ‘ & ‘
4
0.775 0.775
1 1 1 2.389 *10
0.775 10.7 20
t
!
” #
!=
$ %
& ‘
331t=
min
P5-14 (a)
A + 3B C + 2D + E
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
343
0.05
0.10
0.008
0.004
363
0.20
0.01
0.02
0.01
Space time for differential reactor = 2 min
0P
P
P P
v C
F
V
r r
= =
! !
2 4
2
C H
P
P
C
C
r
!
= =
Rate law:
r
C=Ae “B/T
( )
CA
xCB
y
CC
2=Ae “B T
( )
CA
xCB
y
Where, A is Arrhenius constant
B = activation energy/R
x is the order of reaction wrt A
While using polymath for solving the rate law apart from guessing the initial values of n, m, and A , we
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
x 0.25 0.2508555 0.0032606
R^2 = 0.9323139
R^2adj = 0.8871898
5-20
Hence, by nonlinear regression using polymath
A = 3.649E+06(mole/dm3)-2. 6(1/s)
E = 6500R = 54.015 KJ/mol
P 5-14 (b) Individualized solution
P5-15 (a)
Model 1: Monod equation
ss
cs
g
c
CK
CC
r
dt
dC
+
== max
µ
See Polymath program P5-15-a.pol.
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
Ks 1 1.694347 2.2930643
P5-15 (b)
Model 2: Tessier Equation
rg=
µ
max 1“exp “Cs
k
#
$
% &
‘
(
)
*
+
,
–
.
CC
See Polymath program P5-15-b.pol.
POLYMATH Results
Nonlinear regression (L-M)
Variable Ini guess Value 95% confidence
umax 0.5 0.3258202 0.0034969
k 100 20.407487 5.7120407
R^2 = 0.9999454
R^2adj = 0.9999345
5-21
rg=0.33 1“exp “CS
20.4
#
$
% &
‘
(
)
*
+
,
–
.
CC
g/dm3.h
P5-15 (c)
Model 3: Moser Equation
max
1
C
gy
S
C
rkC
µ
!
=+
See Polymath program P5-15-c.pol.
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
k 1.6 162.599 34.273983
R^2 = 0.9999447
R^2adj = 0.999917
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
3
2.4 x 10-3
0.05
800
5
1.18 x 10-1
0.1
900
Rate law:
( )
/E RT n
A A
r Ae C
!
!=
Where, A is Arrhenius constant
E is the activation energy
5-22
POLYMATH Results
Nonlinear regression (L-M)
Model: rA = A*exp(-E/(8.314*T))*(CA)^n
Variable Ini guess Value 95% confidence
A 100 1.01E+04 327.35758
E 1000 5.805E+04 237.32096
Precision
R^2 = 0.6690419
R^2adj = 0.4484032
Rmsd = 0.0097848
Hence, by nonlinear regression using polymath
A = 10100 (mole/dm3)-2. 6(1/s)
CDP5-A
5-23
5-24
From the plot, it is evedent that linear relationship exists between (1/A∞ – A) and time;
Therefore the reaction is second order.
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
PA = CART = CA0RT(1– X) = PA0(1– X)
PB = CBRT = CA0RT(
“
B– X) = PA0 (
“
B– X)
5-25
X=ypFT0
2FA0
=yp
2yA0
=yp(1+
“
B)
2
“r‘A=“r‘B=FA0X
W=
Fp
2W=
ypFA0
2W
“r‘A=kP
A
#
P
B
$
ln(“r‘A)=ln k+
#
ln PA+
$
ln P
B
y=A0+A1X1+A2X2
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
0.6
0.5
0.5
0.16
0.16
1
0.42
0.42
1.2
0.75
0.6
0.6
0.1
0.1
1
0.54
0.54
0.9375
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
beta 1 –1.9669749 0.1668241
hence, the rate law is:
‘
2
0.5 / .
A
A
P
r gmol kg hr
P
!=
5-26
CDP5-D
CDP5-E
5-27
5-28
5-29
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:
2
a b
A P O
r kP P=
5.0=!W
g
Using Polymath non linear regression, the following results were obtained:
Nonlinear regression (L-M)
Model: ra = k*Pp^a*Po2^b
Variable Ini guess Value 95% confidence
k 5 0.006609 2.685E-05
a 1 0.9948724 0.0046367
CDP5-H
1)
So,
5-33
CDP5-I
CDP5-I (c) No solution
CDP5-J No solution will be given.
5-34
CDP5-K No solution will be given.