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

2.4 Kinetics of second-order reactions 26
I
Solution of the rate equation:
− [A]
= − [B]
= [A] [B] (2.91)
(1) Substitution:
=([A] 0
− [A]
)=([B] 0
− [B]
) (2.92)
[A] = [A] 0
− (2.93)
y
= ([A] 0 − )([B] 0
− ) (2.94)
(2) Integration using partial fractions (skipped here):
(3) General solution:
[B] 0
[A]
[A] 0
[B]
=exp([A] 0
− [B] 0
) (2.95)
2.4.3 Pseudo first-order reactions
In experimental studies of second-order reactions of the type A+B→ C, onelikesto
use a high excess of one of the reactions partners (e.g., [B] À [A]) sothat[B] ≈ const
Under this condition, the reaction is said to be pseudo first-order, because
[B] = 0 (2.96)
y Solution of [A ()]:
[A] = [A] 0
−0 =[A] 0
−[B] (2.97)
I
Experimental investigation of pseudo first-order reactions:
(1) Measurements of the pseudo first-order decay of [A] vs. at different concentrations
of [B]: Plotofln [A] vs. give pseudo first-order rate constant 0 = [B]
for each value of [B].
(2) Plot of 0 = [B] vs. [B] gives straight line with slope .
⇒ We do not need the absolute concentration of [A], only the concentration of [B] is
needed.