Page 319 - Advanced Thermodynamics for Engineers, Second Edition

14.2 REACTION RATES 309

(a) FIGURE 14.2
Diagrammatic representation of molar con-
centration. Molar concentration in (a) is
(b) approximately half that in (b).

Reactions occur when two, or more, reactants are capable of reacting. Many simple chemical
reactions are second order, e.g.

k f
A þ B 5 C þ D
k b
(14.1)
k f
CO 2 þ H 2 5 H 2 O þ CO
k b
where the first reaction is a general one and the second is an example based on the water gas reaction
(chosen because the same number of reactants and products exist on both sides).
These reactions can be written as
k f
00
0
00
n A 1 þ n A 2 þ ..:: 5 n A 1 þ n A 2 þ ..: (14.2)
0
2
1
1
2
k b
where A 1 , A 2 , .etc. are the elements or compounds involved in the reaction, and n 1 , n 2 , .etc. are the
respective stoichiometric coefficients. Equation (14.2) can be further generalised to
q q
X k f X
0
n A i 5 n A i : (14.3)
00
i
i
k b
i¼1 i¼1
0
where q ¼ total number of species being considered, n represents the stoichiometric coefficients of the
00
reactants, and n that of the products.
In this case q has been taken as the same on both sides of the equation because it is assumed that the
same species can exist on both sides. If a species does not exist on one of the sides it is represented by a
stoichiometric coefficient of zero (n ¼ 0). e.g.
CO 2 þ H 2 5H 2 O þ CO (14.4)
can be represented by
4 4
X k f X
n A i 5 n A i : (14.5)
0
00
ij ij
i¼1 k b i¼1