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78 3 Basics of Gas Combustion

Then the mole fraction of each species is determined as follows:

y CO ¼ 0:17; y NO ¼ 0:03; y CO2 ¼ 0:29; y O2 ¼ 0:30; y N2 ¼ 0:21:

3.3.4 The Pseudo-Steady-State Approximation

Many combustion reactions involve free radicals, which are very reactive inter-
mediate species. They are consumed rapidly and present at very low concentration,
but are critical to the combustion reactions. It is important to understand how they
affect the chemical equilibrium and overall rate of constant.
Consider an overall reaction A ! B þ C, which proceeds through the free
radical of A*. Molecules of A first collide with other molecule (M) that does not
change, to produce free radicals A*, followed by decomposition of A to B þ C.

These two step reactions can be described as follows:
k f 1

A þ M $ A þ M ð1Þ
k b1

k 2

A ! B þ C ð2Þ
Note that the first reaction is reversible and the second is one way. The rate of

reaction before reaching equilibrium in terms of A for the first reversible reaction is

½
d A½Š d A Š

¼ ¼ k f 1 A½Š M½Š þ k b1 ½A Š½MŠ ð3:39Þ
dt dt

And for the second step, A is consumed only and the corresponding rate is

d½A Š

¼ k 2 ½A Š ð3:40Þ
dt

The overall consumption rate of [A ] considering both reactions is

d A Š
½

¼ k f 1 A½Š M½Š þ k b1 ½A Š½MŠ k 2 ½A Š ð3:41Þ
dt
Since A* is so reactive that it is consumed almost immediately after its forma-
tion; this is referred to as the pseudo-steady-state approximation [7]. Thereby,
mathematically, the left hand side of the above equation is zero, and it becomes
k f 1 A½Š M½Š k b1 ½A Š½MŠþ k 2 ½A Š¼ 0 ð3:42Þ