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

11.2 Diffusion-controlled reactions 231
I
Figure 11.3: Radial distribution of reactants in a diffusion-controlled reaction.
(1) We start by considering the boundary conditions for the concentration [] (cf.
Fig. 11.3):
• At a distance →∞, the concentration of is identical to the mean
concentration in the solution, i.e.,
→∞y []
=[] =∞
=[] (11.12)
• At the distance = for a diffusion controlled reaction, the concentration
of vanishes because of its fast reaction with , i.e.,
→ 0 y [] =0
=0 (11.13)
(2) The result is a concentration gradient []
around , which gives rise to a net
flux ←− by diffusion as described by Fick’s first law:
= × × []
(11.14)
We define this flux, measured in units of molecules/s, in the direction from = ∞
(high concentration) to = (low concentration); thus there is no − sign in
the usually written form of Fick’s law.
is the mean diffusion coefficient, measured in m 2 s,
= + (11.15)