Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

Appendix C 269
— If 1 6= 2 we obtain
and thus
() = 1 [A] 0
2 − 1
( 2− 1 )
(C.25)
[B]
= () − 2
= 1 [A] 0
2 − 1
( 2− 1 ) − 2
= 1 [A] 0
2 − 1
− 1
(C.26)
(C.27)
(C.28)
— If 1 = 2 we obtain
()
= 1 [A] 0
( 2− 1 )
(C.29)
= 1 [A] 0
(C.30)
y
y
() = 1 [A] 0
(C.31)
[B]
= () − 2
= 1 [A] 0
− 2
(C.32)
(C.33)
• General solution:
y
Initial value condition at =0:
[B] = [B]
+[B]
(C.34)
⎧
⎪⎨ × − 2 + 1 [A] 0
− 1
if 1 6= 2
[B] =
2 − 1
(C.35)
⎪⎩
× − 2 + 1 [A] 0
− 2
if 1 = 2
[B ( =0)]=0 (C.36)
y
⎧
⎪⎨ − 1 [A] 0
if 1 6= 2
=
2 − 1
(C.37)
⎪⎩
0 if 1 = 2
Final solutions for [B ()]:
⎧
1 [A] ⎪⎨ 0
¡
− 1 − ¢ − 2
if 1 6= 2
[B ()] =
2 − 1
(C.38)
⎪⎩
1 [A] 0
− 2
if 1 = 2