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

2.6 Kinetics of simple composite reactions 31
I
Figure 2.13: Kinetics of consecutive first-order reactions (case II).
I Caveat: As seen, the general solution for [B] is the difference of two exponentials,
[B] = 1 [A] 0
2 − 1
¡
− 1 − − 2 ¢ , (2.116)
One exponential describes the rise, the other the fall of [B]. It is sometimes implicitly,
but wrongly assumed that the rise time corresponds to 1 and the decay time to 2 .
The truth is that we cannot tell just from the shape of the concentration-time profile
whether 1 or 2 correspond to the rise or to the fall of [B].
I Quasi steady-state approximation: Under the condition that
2 À 1 (2.117)
we can find a simple solution for the DE’s. Under this condition, after a short initial
induction time (see Fig. 2.13), the change of [B] is very small compared to that of
[A]. Therefore,wehaveapproximately
[B]
≈ 0 (2.118)
This important approximation is known as the (quasi)steady-state approximation. 19
19 Deutsch: Quasistationaritätsannahme.