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

3.1 Determination of the order of a reaction 42
I Half lifetime method (for n 6= 1): 22
y
Z
− [A] = [A] (3.3)
Z
[A] − [A] = − (3.4)
y
−
1
( − 1) [A]−(−1) = −+ (3.5)
Initial value condition at =0:
[A ( =0)]=[A] 0
(3.6)
y
y
Half lifetime:
y
y
y
= − 1
( − 1) [A]−(−1) 0
(3.7)
1
[A] −1 − 1
[A] −1
0
2 −1
[A] −1
0
=( − 1) (3.8)
£
A
¡
12
¢¤
=
1
2 [A] 0
(3.9)
− 1
[A] −1
0
12 = 2−1 − 1
( − 1)
=( − 1) 12 (3.10)
1
[A] −1
0
(3.11)
lg 12 ∝−( − 1) lg [A] 0
(3.12)
y A log-log plot of 12 vs. [A] 0
gives a straight line with slope −( − 1).
22 We leave aside a usually occuring stoichiometric factor ν here, since we can always define νk = k 0
as rate constant k 0 .