Question

For a hydrogen–oxygen mixture undergoing homogeneous explosion in the second-limit regime, show that the maximum [H] production rate in terms of pressure variations is given by the relation 4k1 = 3k9[M].

Sketch/plot this relation as well as the second limit relation in the same graph. Discuss the results.

Combustion physics , Chung.K.Law

H+ O2 -> OH+O (H1)

O + H2 -> OH + H (H2)

H2 + OH -> H2O +H (H3)

H + O2 + M -> HO2 + M (H9)

d[H]/dt = (2k1 - k9[M])[H][O2]

Answer 1

Above is the plot of the given pressure variation relation 4 k₁ = 3 k₉ [M] as well as the explosion second limit relation.

Here since the reactant is taking part only in (H9), and H1, H2 and H3 reaction steps involve only H₂ and O.

Hence the dissociation of H₂ and dissociation of O₂ and the reaction between H₂ and O₂  shall take place first. With the production of H using either (H2) or (H3); futher chain reaction of M will be inititated. The reactions (H1) and (H2) are the reactions which involve the collision of two different radical species.

The second limit relation is calculated by competing among the growth of (H2) and (H3) and destruction of H atom in (H9).

Based on the given relation we determined the limit dependance and presented as p-T curve.

Here:  

Here the second limit will be given by the neutral conditions as : 4k₁ = 3k₉ [M].

and the pressure temperature relation of the second limit can be given as: