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

2.2 Kinetics of irreversible first-order reactions 16
2.2 Kinetics of irreversible first-order reactions
A → B (2.27)
I Solution of the rate equations for A and B:
− [A]
=+ [B]
= [A] (2.28)
Mass balance:
[A]
+ [B]
=0 (2.29)
Integration of the rate equation (Eq. 2.28):
Z
− [A] = (2.30)
[A]
Z
Z
ln [A] = −= − (2.31)
y
ln [A] = −+ (2.32)
Initial value condition at =0:
[A ( =0)]=[A] 0
(2.33)
y
Solution for [A ()]:
y
Solution for [B ()]:
y
=ln[A] 0
(2.34)
ln [A] = −+ln[A] 0
(2.35)
[A ()] = [A] 0
− (2.36)
[B ()] = [A] 0
− [A ()] (2.37)
¡
[B ()] = [A] ¢ 0 1 −
−
(2.38)