Page 320 - Advanced Thermodynamics for Engineers, Second Edition

310 CHAPTER 14 CHEMICAL KINETICS

where
q ¼ 4
n ij ¼ stoichiometric coefficient of i in reaction j
0
00
A 1 ¼ CO 2 n ¼ 1 n ¼ 0
1 1
00
0
A 2 ¼ H 2 n ¼ 1 n ¼ 0
2
2
0
00
A 3 ¼ H 2 O n ¼ 0 n ¼ 1
3
3
00
0
A 4 ¼ CO n ¼ 0 n ¼ 1
4
4
The law of mass action, which is derived from the kinetic theory of gases, states that the rate of
formation, or depletion, of a species is proportional to the product of molar concentrations of the
reactants, each raised to the power of its stoichiometric coefficient. Hence the rate of formation of
species j, for an elementary reaction, is
n 1j n 2j n nj
R j f½A 1 Š ½A 2 Š ..::½A n Š
or
n (14.6)
Y
R j f ½A i Š n ij for ð j ¼ 1; ...sÞ:
i¼1
and s ¼ total number of simultaneous reactions.
Equation (14.6) may be written as
n
Y
n ij
R j ¼ k j ½A i Š for ð j ¼ 1; ...sÞ; (14.7)
i¼1
where k j is the rate constant for the reaction. In Eqns (14.1)–(14.5) the reaction was described as
having a forward and backward direction, with rates k f and k b . The reaction shown in Eqn (14.7) can be
described in this way as
n
n 0
Y
R fj ¼ k fj ½A i Š ij for ð j ¼ 1; ...sÞ; (14.8)
i¼1
and
n
n
Y 00
R bj ¼ k bj ½A i Š ij for ð j ¼ 1; ...sÞ: (14.9)
i¼1
The rate of change with time of species i is proportional to the change of the stoichiometric co-
efficients of A i in the reaction equation (the system is effectively a first-order one attempting to achieve
the equilibrium state). Thus, for the forward direction

n n
d½A i Š Y 0 Y 0
¼ n n ij k fj ½A i Š ¼ Dn ij k fj ½A i Š ij (14.10)
ij
j 0 00 n n
ij
dt
f i¼1 i¼1