Photoinduced and Microbial Degradation of Dissolved Organic Matter in Natural Waters - Photobiogeochemistry of Organic Matter - page 295

where 3 is the amount of primary C-H bonds, A prim denotes the Arrhenius fre-
quency factor for the reaction of HO• with CH 3 R 1 , R is the universal gas constant,
and T denotes absolute temperature. However, for (Eqs. 2.6 - 2.8 ), the functional
group contribution is ignored for cases where the neighboring functional groups
have no effect on the H-atom abstraction (i.e., E - a , abs is zero, where a valence bond
of the H-atom is expressed as a line before H).
In (Eqs. 2.6 - 2.8 ), the group rate constants, which represent H-atom abstraction
from the primary, secondary and tertiary C-H bond are defined as k 0 prim , k 0 sec , and
k 0 tert , respectively. They are expressed in (Eqs. 2.9 - 2.11 ).

k prim = A prim e − E a ,prim

RT

(2.9)

k sec = A sec e − E a ,sec RT

(2.10)

k tert = A tert e − E a ,tert

RT

(2.11)

•

interaction with
the functional group R 4 (e.g. -OH and -COOH). The group contribution factor,
X R i , that represents the influence of functional group Ri i can be denoted as (Eq.
2.12 )

In addition, the group rate constant k R4 is defined for the HO

X R i = e − E Ri

RT

(2.12)

a , abs

The rate constant for H-atom abstraction, k abs , can be written as the sum of the
partial rate constants in (Eq. 2.13 ) because each reaction is independent from one
another

I J k

k prim X R 1 + 2 k sec X R 1 X R 2 + k tert X R 1 X R 2 X R 3 + k R 4

k abs = 3

(2.13)

0 0 0

where, I , J , and K denote the number of the fragments CH 3 R 1 , CH 2 R 2 , and
CHR 1 R 2 R 3 , respectively.
As a typical example the rate constant calculation for 1,2-dichloro-3-bromopro-
pane (CH 2 Cl-CHCl-CH 2 Br) can be written as below (Eq. 2.14 )

k overall = 2 k sec X − Cl X − CHCl + k tert X − Cl X − CH 2 Cl X − CH 2 Br + 2 k sec X − Br X − CHCl −

(2.14)

It is shown that group rate constants of k º prim , k º sec , and k º tert are 1.18 × 10 8 ,
5.11 × 10 8 , and 1.99 × 10 9 M − 1 s − 1 , respectively and follow the order
k º tert > k º sec > k º prim that is consistent with the radical stability of primary, second-
ary, and tertiary carbon-centered radicals due to the hyperconjugation. The term
k R4 is accounted for by the group rate constants k − OH and k − COOH , respectively
(Eq. 2.13 ). The k -OH is 1.00 × 10 8 M − 1 s − 1 , representing 33, 8.5, and <5 % of the