10-41
P10-18 (c)
10-42
10-43
P10-18 (d)
10-44
P10-18 (e)
10-45
P10-19(a)
D
da k
dt =!
S
W U t=
S
dW U dt=
D
S
k
dt da
dW dt U
!
=
If
0 1 D
S
k W
U
=!
then
.5 2.5
.2
S
D
U
W kg
k
= = =
( )
( ) ( )2
2
0
0 0 0
1
0A
A
A
A A A
akC X
r
dX a r
dW F F F
!
!
= = !=
( )2
0
1
1A
D
kC X
k W
dX
dW U v
!
” #
=!
$ %
10-47
1.5
S
kg
Us
=
P10-19(e)
0 1 D
S
k W
U
=!
0.2 * 5 1
S D
kg
U k W s
= = =
P10-19(f)
a = 0 means there is no reaction is taking place. Activity can never be less than 0.
P10-19(g)
S
U U=!
D
S
k
da
dW U
=
when
t
W W=
,
1a=
D
S
k W
a C
U
= +
1D t
S
k W C
U
= +
1
D e D t
S S
k W k W
a
U U
= + !
Now find We.
0 1
D e D t
S S
k W k W
U U
= + !
.5 .2 * 5
1 1
.2 .5
S D t
e
D S
U k W
W
k U
! ” ! “
=#=#
$ % $ %
& ‘
& ‘
2.5
e
W=
( )2
0
0
1
1A
D t
S
kC X
k W
dX W
dW U v
!
” #
=!+
$ %
& ‘
0
0
1
1
A D t
S
kC k W
XW dW
X v U
! “
=#+
$ %
#& ‘
(
10-48
( ) 0.2 * 5 25 6.25
0.2 5 2.5 1
1 0.5 2
X
X
! “
#
$ %
=# # +
& ‘
( )
#* +
, –
1.875
1
X
X=
!
0.65X=
P10-19(h)
0
$ 160 10
A S
F X U=!
1D
S
k W
dX ka k
dW U
! “
= = #
$ %
& ‘
2
2
D
S
kk W
X kW
U
=!
To maximize profit, a maximum in profit is reached and so we set the differential of
profit equal to 0.
0
$0 160 10
A
S S
d dX
F
dU dU
= = !
2
2
2
D
S S
kk W
dX
dU U
=
2
02
160 10
2
D
A
S
kk W
F
U=
2 2
0
8A D S
F kk W U=
( )( )( )( )
2
0
8 8 2 .2 .2 25
S A D
U F kk W= =
4
min
S
kg
U=
P10-19(i) No solution will be given
10-49
P10-20 (a)
P10-20 (b)
10-50
P10-20 (c)
P10-20 (d)
10-51
P10-20 (e)
10-52
P10-21 (a)
A B Elementary reaction with 1st order decay.
D
da k a
dt =!
( )
exp D
a k t=!
P10-21 (b)
The activity is never zero for first order decay. When
( )
exp D
a k t=!
there is no t such
P10-21 (c)
Mole balance:
0 0 0 0 0
‘ ‘ ‘
AAA
A A A
r W r W r
dX W
dt N C v C v
! ! !
= = =
Decay:
( )
exp D
a k t=!
10-53
Stoichiometry:
( )
01
A A
C C X=!
Combine:
( ) ( )
1
0
exp 1
D
dX W
k t k X
dt v
=! !
( )
1
0
1
ln 1 exp
1D
D
k W k t
X k v
! “ # $
=% %
& ‘ ( )
%
* +
( )
1
0
1 exp 1 exp D
D
k W
X k t
k v
! “
# $
=% % % %
& ‘
( )
* +
P10-21 (d)
( )( )
( )( )
1
0
0.2 1
2
0.1 1
D
k W
k v = =
( )
( )
1 exp 2 1 exp 1 0.97X! “
=# # # # =
$ %
P10-21 (e)
Decay rate increases more rapidly with temperature than does the specific reaction rate.
P10-21 (f)
( )
1
0
1 1
2exp 1500 0.57
310 400
D
k W T
k v
! “
# $
=% % =
& ‘
( )
* +
, –
1 1
0.1exp 2000 0.53
300 400
D
k! “
# $
=%=
& ‘
( )
* +
, –
( )
( )
1 exp 0.57 1 exp 5.3 0.43X! “
=# # # # =
$ %
P10-22 (a)
P10-22 (b)
10-54
P10-22 (c)
10-55
P10-22 (d)
10-56
P10-22 (e)
10-57
P10-23 (a)
P10-23 (b)
10-58
P10-24 (a)
10-59
10-60
P10-24 (b)