table 7a,7b kft 131
TRANSCRIPT
32
TABLE 7a: For reaction aA→ Products
Order n = 0 n =1 n =2 n any integer, ≠1
Rate Law =−
dt
Ad ][ak [A]
0= kA =−
dt
Ad ][ak[A]=kA[A] =−
dt
Ad ][ak[A]
2=kA[A]
2 =−
dt
Ad ][ ak[A]n=kA[A]
n
Derivation
of the
integrated
rate law tkAA
tkAA
dtkAd
Ato
Aot
A
A
t
A
t
o
=−
−=−−−
=− ∫ ∫
][][
0)][(][
][
][
][ 0
tknAA
tknAA
tkn
A
n
A
tkAdA
dtkA
Ad
Ann
t
A
n
o
n
t
A
n
o
n
t
A
A
A
n
A
A
t
An
t
o
t
o
)1(][
1
][
1
)1(][][
1
][
1
][
][][
][
][
1
0
1
11
11
][
][
][
][ 0
−=−
+−=+−
=
+−
−−
+−
−
=−
=−
−−
+−+−
+−+−
−
∫
∫ ∫
Unit of k
Mol L-1
s-1
s-1
Graph
[A]t vs. t with m = -kA
ln[A]t vs. t with m = -kA
1/[A]t vs. t with m = kA
log t1/2 vs. [A]0 with m= -(1-n)
Derivation
of the half-
life
A
o
A
o
Ao
Aoo
A
A
t
A
k
At
k
At
tkA
tkAA
dtkAd
o
o
2
][
][5.0
][5.0
][][5.0
][
2/1
2/1
2/1
2/1
][5.0
][ 0
2/1
=
=
=
=+−
=− ∫ ∫
Ak
t2ln
2/1 =
oAAk
t][
12/1 =
1
0
1
2/1][)1(
12−
−
−
−=
n
A
n
Aknt
33
TABLE 7b: For reaction aA+ bB→ Products with rate law, rate = k[A]x[B]
y
Condition
Rate Law
Integrated rate law
a = b =1, x = 0, y = 0 =−
dt
Ad ][ak [A]
0 = kA
ktAAto
=− ][][
a = b =1, x =1, y = 0 =−
dt
Ad ][k[A]
ktAAto
=− ]ln[]ln[
a = b =1,x = 0, y = 1 =−
dt
Bd ][k[B]
ktBBto
=− ]ln[]ln[
a = b =1, x =2, y = 0 =−
dt
Ad ][k[A]
2 tkAA
t
=−
0][
1
][
1
a = b =1,x =0, y = 2 =−
dt
Bd ][k[B]
2 tkBB
t
=−
0][
1
][
1
a = b =1,x =1, y = 1
[A]o=B]o =−
dt
Ad ][k[A][B]= k([A]o-x)([B]o-x)
= k([A]o-x)2 = k[A]
2
tkAA
t
=−
0][
1
][
1
a = b=1 or ≠1,x =1, y = 1
[A]o≠B]o
=−
dt
Ad ][k[A][B]
==
−
−
dt
dx
adt
axAdo 1)]([
k([A]o-ax)([B]o-bx)
==
−
−
dt
dx
bdt
bxBdo 1)]([
k([A]o-ax)([B]o-bx)
o
o
oo
o
o
B
AktBaAb
bxB
axA
][
][ln)][][(
)]([
)]([ln +−=
−
−
a = b ≠1,
x =1or 2, y = 1or 2
[A]o≥B]o
[A]o≤ B]o
=
dt
dxk[A]o ([B]o-bx) =k‘[B]
y
=
dt
dxk([A]o-ax)[B]o =k‘[A]
x
34