1 Reaction Kinetics (2) Xuan Cheng Xiamen University Physical Chemistry.
18
1 Reaction Kinetics (2) Xuan Cheng Xiamen Universi ty Physical Chemistry
-
Upload
gunnar-sisley -
Category
Documents
-
view
218 -
download
2
Transcript of 1 Reaction Kinetics (2) Xuan Cheng Xiamen University Physical Chemistry.
1
Reaction Kinetics (2)
Xuan ChengXiamen University
Physical Chemistry
2
Order Reaction Rate Law t1/2
0 A P
1 A P
2 A P
n2 A P
okr
Akr
2Akr
nAkr
tko
AeAA
oA
o
Atk
AA
1
akkA
Ak
2ln
Ao kA][
1
Ano
n
kAn 1
1
)1(
12
A
o
k
A
2
tknAA
AA
no
n
o)1(1 1
1
tkAA Ao
Simple Order ReactionsPhysical
ChemistryReaction Kinetics
3
Typical Complex Reactions
Physical Chemistry
Reversible reaction
Consecutive reaction
Opposing reaction
Competing reaction
Parallel reaction
CA fk kb
CBA kk 21
CA k 1
DA k 2
(1)
(2)
(3)
Reaction Kinetics
4
Physical Chemistry Reversible First-Order
Reactions
Consider the reverse reaction (opposing reaction)
][Akr ff
CA fk kb
fFeEbBaA (17.1)
the first order in both forward and back directions
][Ckr bb
][][
Akrdt
Adff
f
][
][Ckr
dt
Adbb
b
Reaction Kinetics
5
Physical Chemistry
][][][][][
CkAkdt
Ad
dt
Ad
dt
Adbf
bf
(17.31)
][][ AC oo AACC ][][][][
][][][][ AACC oo
][][][][][
AACkAkdt
Adoobf
])[(][][][
AkkAkCkdt
Adbfobob (17.32)
Reversible First-Order Reactions
Reaction Kinetics
6
Physical Chemistry
0][
dt
AdAt equilibrium,
tkkAA
AAbf
eqo
eq)(
][][
][][ln
eqAA ][][
Reversible First-Order Reactions
])[(][][][
AkkAkCkdt
Adbfobob (17.32)
and
eqbfobob AkkAkCk ])[(][][ (17.33)
][][)(][
AAkkdt
Adeqbf
(17.34) jteqoeq eAAAA ][][][][ bf kkj
Reaction Kinetics
7
tko
AeAA (17.14)*
(17.34) jteqoeq eAAAA ][][][][ bf kkj
Physical Chemistry Reversible First-Order
Reactions
[A]/[A]o
[C]/[A]o
kf / kb=2
A C
jt
Fig. 17.2When [A]eq=0, kb=0
[A]/
[A] o
t
Fig. 17.1(a)
Reaction Kinetics
8
Physical ChemistryConsecutive First-Order
ReactionsConsider two consecutive irreversible first-order reactions
CBA kk 21 (17.35)
][11 Akr ][22 Bkr
][][
111
Akrdt
Bd
][][
222
Bkrdt
Bd
][][][][][
2121
BkAkdt
Bd
dt
Bd
dt
Bd
(17.36)][][
1 Akdt
Ad
][][][
21 BkAkdt
Bd
][][
2 Bkdt
Cd
Reaction Kinetics
9
Physical Chemistry
Let only A be present in the system at t = 0
0][ oA (17.37)
Consecutive First-Order Reactions
0][ oB 0][ oC
tko eAA 1 (17.38)
(17.36)][][
1 Akdt
Ad
][][][
21 BkAkdt
Bd
][][
2 Bkdt
Cd
AkdtAd A/ (17.11)
(17.39)][][][
211 BkeAk
dt
Bd tko
)(][
][ 21
12
1 tktko eekk
AkB
(17.40)Integration
Reaction Kinetics
?
10
Physical ChemistryConsecutive First-Order
ReactionsoACBA ][][][][ At all times (conservation of matter)
tko eAA 1 (17.38)
)(][
][ 21
12
1 tktko eekk
AkB
(17.40)
tktko e
kk
ke
kk
kAC 21
12
1
12
21][][ (17.41)
Reaction Kinetics
11
Physical ChemistryConsecutive First-Order
Reactions
oABy ]/[][oAAx ]/[][ oACz ]/[][
The intermediate’s concentration rises to a maximum, and then falls to zeroThe concentration of the product C rises from zero and reaches [A]o
(the position of maximum: k1/k2)
Reaction Kinetics
?
12
Physical ChemistryConsecutive First-Order
ReactionsSuppose that in an industrial batch process a substance A produces the desired product B which goes to decay to a worthless product C, each stage of the reaction being first-order. At what time will product B be present in greatest concentration?
)(][
][ 21
12
1 tktko eekk
AkB
(17.40)
The time dependence of [B]
A maximum should occur at 0][
dt
Bd
)(][
][ max2max1
12
1max
tktko eekk
AkB
0)(][][
2121
12
1
tktko ekek
kk
Ak
dt
Bd
CBA kk 21 21 kk
Reaction Kinetics
13
Physical ChemistryConsecutive First-Order
Reactions
Since [A]o 0, k1 0, so 02121 tktk ekek
12
12 lnlnkk
kktm
21
2
2
1max ][][
kk
k
o k
kAB
The maximum concentration of B
For a given value of k1 > k2, as k2 increases, both the time at which [B] is a maximum and the yield of B increase.
0)(][][
2121
12
1
tktko ekek
kk
Ak
dt
Bd
)(][
][ max2max1
12
1max
tktko eekk
AkB
Reaction Kinetics
?
14
Physical Chemistry Competing First-Order
ReactionsConsider two competing irreversible first-order reactions
CA k 1 DA k 2 (17.42)
AC
D
k1
k2Parallel reactions
])[(][][][
2121 AkkAkAkdt
Ad (17.43)
][11 Akr ][22 Akr
][][
111
Akrdt
Ad
][][
222
Akrdt
Ad
Reaction Kinetics
15
Physical Chemistry Competing First-Order
Reactions])[(][][
][2121 AkkAkAk
dt
Ad (17.43)
AkdtAd A/ (17.11)Compare with
tko
AeAA (17.14)*
tkko eAA )( 21
For C tkko eAkAk
dt
Cd )(11
21][][][
(17.44) tkko ekk
AkC )(
21
1 211][
][
0oA0t
Reaction Kinetics
?
16
Physical Chemistry Competing First-Order
Reactions
similarlytkk
o eAkAkdt
Dd )(22
21][][][
(17.45) tkko ekk
AkD )(
21
2 211][
][
0oA0t
Division of (17.44) and (17.45)
(17.44) tkko ekk
AkC )(
21
1 211][
][
tkko eAA )( 21
2
1
][
][
k
k
D
C (17.46)
At any time during the reaction
Reaction Kinetics
17
Physical Chemistry Competing First-Order
Reactions
Consider the reverse reactions
CA k 1 DA k 2 (17.42)
AC k 1 AD k 2 (17.47)
Moreover DC
At equilibrium][
][
]/[][
]/[][
2
1
D
C
AD
AC
K
K
Thermodynamic control
2
1
][
][
k
k
D
C (17.46)Kinetic control
When any reverse reactions or interconversion of C and D can be neglected
Reaction Kinetics
18
HomeworkPhysical
Chemistry
Page 591
Prob. 17.13
Supplemental Material
Page 145, Prob. 16
Page 149, Prob. 30
Page 158, Prob. 68
Reaction Kinetics
