K
Na
OS= A e−VkT4
3000
π^3
()/ (1.24)where a is the distance of closest approach of the oppositely charged ions
(∼ 5 Å ), NA is Avogadro ’ s number, and V is the electrostatic potential at that
distance (equation 1.25 ).
V
Ze
Ra=^12
2(^40)
Z
πε ε(1.25)
where
a = distance of closest approach of oppositely charged ions ( ∼ 5 Å )
NA = Avogadro ’ s number, 6.022 × 10^23 mol − 1
V = electrostatic potential (dependent on distance between oppo-
sitely charged ions)
k = rate constant for a reaction
K = equilibrium constant for a reaction
Z 1 Z 2 = absolute value of the charge on an ion
e = charge on the electron, 4.8030 × 10 − 10 esu or 1.6022 × 10 − 19
Coulombs (C)
ε 0 εR : ε 0 = permittivity in a vacuum 8.854 × 10 − 12 (C^2 /Jm), εR or εr = dielectric
constant = relative permittivity = 1 (for vacuum by defi nition, 80.4
for H 2 O at 20 ° C), ε 0 εR = actual permittivityAs the above discussion indicates, assigning mechanisms to simple anation
reactions of transition metal complexes is not simple. The situation becomes
even more diffi cult for a complex enzyme system containing a metal cofactor
at an active site. Methods developed to study the kinetics of enzymatic reac-
tions according to the Michaelis – Menten model will be discussed in Section
2.2.4. Since enzyme - catalyzed reactions are usually very fast, experimentalists
have developed rapid kinetic techniques to study them. Techniques used by
bioinorganic chemists to study reaction rates will be further detailed in Section
3.7.2.1 and 3.7.2.2.
1.6 ELECTRONIC AND GEOMETRIC STRUCTURES OF METALS
IN BIOLOGICAL SYSTEMS
Tables 1.2 – 1.6 list some of the important geometries assumed by metal ions
in biological systems. Common geometries adopted by transition metal ions
that will be of most concern to readers of this text are illustrated in Figure 1.3.
It is important to remember that in biological systems these geometries are
usually distorted in both bond length and bond angle.
ELECTRONIC AND GEOMETRIC STRUCTURES 13