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My project is going to concern the chemistry of the gas phase 2H₂ + O₂
à 2H₂O reaction.

This reaction is usually thought of as being solely explosive (it’s used in rocket fuel, for example), but this isn’t necessarily always the case. The reaction itself has many individual ‘sub-reactions’, is very complex and as a result it’s quite hard to get any accurate data for any specific part of the reaction mechanism, aside from the general view of what actually happens to the system overall.

Also there are really two main definitions of a gas phase explosion either or both of which must be true for an explosion to occur:

1. Thermal Explosion:

The distribution of heat in a reacting mixture is stable when the heat produced by a reaction in a volume element is equal to the heat lost by the same volume element. When the heat loss can’t compensate for the heat being produced by the reaction, the internal heat of the reaction increases exponentially, thus driving the rate of reaction faster and faster until a point of explosion is reached.

1. Branched Chain (Radical) Explosion:

For a reaction mixture of fixed composition and fixed initial temperature we can see that there will be a corresponding critical pressure, above which an explosion will occur. Below this the steady state approximation applies (see later).

The main reactions involved within the overall reaction are as follows:

(NB: A ·
implies species is a radical)

Initiation:    H2 à H· + H· (1) Branch 1:    H· + O2 à ·OH + O· (2) Branch 2:    O· + H2 à ·OH + H· (3)

Propagation:    ·OH + H2 à H2O + H· (4)         H· + O2 à HO2· (5)         HO2· + H2 à H2O + ·OH (6)

Termination: Combination of radicals: E.g. H· + H· à H2 (7) Reaction with walls of vessel: E.g. Absorbance of HO2· on wall (8)

As the external conditions, temperature (T) and pressure (P), are changed, the importance of various individual ‘sub-reactions’ rises and falls dramatically. This in part exemplified by reactions (2) and (3).

Reactions (2) and (3) are the ‘key-stones’ in terms of whether the gaseous mixture will explode or not, as all you need for an explosion to happen is a way of generating many radicals in a very short space of time. Which is exactly what equations (2) and (3) do under the right conditions.

Many chemical reactions involve the formation of (very reactive) radicals as intermediary species, and usually this is fine as they tend to be used up as soon as they are produced (i.e. they are straight chain reactions). However, in some reactions under the correct conditions, these intermediate reactions involving the radicals are able to branch out along other reaction pathways, which in some cases form more and more radicals which go on branching out through the whole reaction mixture until the concentration of radicals is so great that explosive effects occur.

The effect of branching means that in the overall scheme of things these intermediary products can no longer be ignored (as their concentrations are so high), and therefore the steady state (SS) approximation (i.e. the approximation that the overall concentration of intermediary species is zero) breaks down quite readily.

To initiate the reaction the H—H bond has to be broken in some way, either by raising the temperature of the reaction to such an extent that it occurs ‘naturally’ or by forcing it at lower (room) temperature via a (high energy) electrical spark for example.

This is a typical example of a thermodynamically driven reaction with a kinetic barrier (the barrier being the splitting of the H—H bond, whilst not forgetting the loss in entropy of the system, which is a lesser problem). I.e. If there is no activation via sparking, or other such high energy phenomena, at room temperature, then a mixture of H₂ and O₂ is quite safe, but as soon as the first few H—H bonds are broken the reaction will be over in a fraction of a second.

At low T i.e. approx T < 730 K the reaction is heterogeneous (doesn’t occur solely in the gas phase), and the gases react via the walls of the reaction vessel. This in turn means that at room temperature reactions (2) and (3) are really very slow and the gas mixture is quite safe. Also any radicals that may be produced in the bulk of the gas itself are able to diffuse through to the walls of the vessel (as the environment of the gas at RTP [Room temperature and Pressure] isn’t particularly harsh), where they are ‘destroyed’ by adsorption.
If however, whilst within this temperature range, we set up a situation where P is the only variable, then only below the critical pressure (the point where the pressure is so great explosion will occur) will H· diffuse through the gas to the walls. So, overall, below 730 K and the critical pressure a steady state will occur, but the reaction is so slow in this region that it’s hard to measure the rate of any reactions happening at all.

The point at which the conditions are right for an explosion to occur is called an explosion limit. The limit depends on both temperature and pressure as the diagram on the right for the H₂/O₂ reaction illustrates:

In the range 730 K < T < 890 K, the situation is quite complex, as there are regions where then change in pressure has a quite marked effect on the likelihood of explosion.

And for the range T > 890 K the reaction is almost always explosive. This is because the formation of radicals becomes more frequent than their removal; the overall concentration of radicals increases exponentially and leads to a branched-chain explosion. The explosion again occurs at a critical pressure, which is usually very low.

From this diagram we can also see that as P is increased above the 1^st explosion limit, the reaction remains explosive until a second critical pressure is reached, above which a second steady state is observed until we reach the third (and final) explosion limit.

A graph, which corresponds to this diagram, is the plot of rate vs. log P as in the following:

From this graph it’s easy to see how the rate depends upon the pressure. As the pressure approaches the 1^st explosion limit the reaction rate rises slowly and steadily to begin with, and then exponentially as it approaches the limit. Then, as the pressure increases further the rate remains very fast, until the effect of reaction (5) comes into play and the rate decreases exponentially, but this time the rate of the steady state reaction is faster overall than the rate at the start. Lastly the rate rises slowly and steadily as before until we approach the 3^rd explosion limit where the rate increases exponentially again but this time it stays there!

There are three main factors that can influence the formation of radicals in the H₂/O₂ reaction (and for that matter most other explosions) and therefore the likelihood of the onset of explosive conditions, these are:

1. The rate of initiation of the reaction – How many individual reactions are able to start within a

   certain initial time period.

2. The rate of chain branching      – The rate at which the reaction is able to branch throughout

                 the reaction mixture.

1. The rate of radical termination    – How quickly the radicals are used up or ‘removed’ from the

                 reacting mixture.

These factors can be related and modelled by the following differential equation:

        [r] = Concentration of radicals        R_i = rate of initiation

             e = rate of branching            k = rate of termination

Which has the solution:

[r](t) =         f = e – k

This plot shows the two possible regimes:

(a): f is negative:

Termination is the dominant factor, the rate is slow and the reaction comes to a steady state.

(b): f is positive:

Branching occurs much faster than termination, the concentration of radicals increases exponentially and the mixture explodes.

Which is what should be expected for a reaction of this type.

Figure Adapted From Atkins, Physical Chemistry 6^th Edition

When the H₂/O₂ reaction is studied it is usually examined in a spherical Pyrex ‘bulb’ whose surface is coated with KCl. The KCl acts as a good adsorber for the radicals that make it to the walls and thus ‘removes’ them from the reaction mixture, which helps to control the explosion. An important radical to be controlled is HO₂· as this is mainly responsible for the position of the second explosion limit.

Reaction (5) producing the HO₂· radical can be considered as a ‘chain braking’ reaction as this radical can diffuse quite easily to the wall and it basically serves to ‘mop up’ H·
in this respect. In this regime as pressure increases (5) becomes more frequent, the rate of removal of radicals is higher than the rate

of formation, and as a result it takes an even higher T to cause he explosion to occur. This is exemplified in the diagrams above in the region between the 2^nd and 3^rd explosion limits, where a steady state is attained for the second time.

Under the ‘wrong’ conditions though, the HO₂·
can be regarded as a propagator as in the reaction:

HO₂· + H₂
à H₂O₂ + H·                    (9)

This is the reaction of HO₂· in the gas phase, and it counteracts the chain braking effect in (5), to such an extent that it has to be included when forming a rate equation for the H₂/O₂ reaction.

This reaction is favoured rather than (5) as a true picture of what is going on, as large amounts of H₂O₂ are found to exist in the reaction mixture, between the 2^nd and 3^rd limits. But also the traces of H₂O₂ disappear quite fast under these harsh conditions via the reaction:

HO₂· + H₂O₂
à H₂O + O₂ + HO·                (10)

Absorption spectroscopy has to be used to give any good indication of the quantities present, and in fact that this is really happening at all.

Note that the reactions that produce H₂O₂ with or via the walls are also possible, but are so slow that they can be neglected. A piece of evidence to support this is that the high reflectance walls (Pyrex, etc.) actually cause the reaction rate for reaction (10) to increase a lot. Therefore the reaction must be occurring mostly in the gas phase, as there are few reactions happening at the walls, but the rate of production of H₂O₂ still increases.

If the vessel is coated with something other than KCl the ‘reflectance’ of the HO₂· at the walls can be affected greatly. For just clean silica or Pyrex (which cause more radicals to be reflected back into the gas mixture, and therefore a vast reduction in the chain breaking processes) the 2^nd explosion limit is much higher and the tip of the explosion peninsula (the region between the 1^st and 2^nd explosion limits) moves to such a low temperature and pressure that it is hard to observe the 1^st explosion limit at all. I.e. The explosion region becomes greater at lower temperatures, if the walls are coated with a chemical that isn’t a very good adsorber of radicals.

Lastly, if we raise P until a third limit is reached we find that above this limit the conditions are so harsh that the reaction is always explosive. This 3^rd limit is probably a combination of both thermal and branched chain limits. In other words, as at high P the effect of T is more important than the effect of chemical termination i.e. reaction (8) is reduced as this depends upon HO₂· being long lived, then under these conditions HO₂· reacts as in reaction (6) and the gas phase reaction chain begins again, thus causing the 3^rd explosion limit.

Conclusion:

Studying the H₂/O₂ reaction is very useful when it comes to trying to learn about the way gas phase explosions occur and what reactions may be happening with the bulk of the reacting gas.

It’s good because it contains the elements of both thermal and radical explosions and the reaction overall can be quite carefully controlled, using different coatings on the reaction vessel wall for example.

Also the products are just radicals and water – no corrosive acids or poisonous gasses that may cause harm or injury to the experimenter, or in the case of corrosive acids as in the H₂/Cl₂ reaction react with the reaction vessel itself or the coatings on it, causing all kinds of problems.

It’s also good as it allows us to predict the properties and the ways of dealing with explosive or potentially explosive reactions. A good example of this may be in predicting the properties of the reactions where hydrocarbons are burned in a combustion engine. The explosions in this case have to be controlled very specifically and this is can be achieved by controlling the number of radicals produced. In the H₂/O₂ reaction we use the coated walls of the vessel to terminate the reaction, but as

this is fairly impractical in the case of a car engine for example, and additive is put into the petrol mixture to help regulate the explosions c.f. leaded petrol.

Lastly the outcome of this reaction could be used to predict the results, or the characteristics (explosion limits, etc.) for any high pressure/temperature reaction, which is potentially very useful c.f. the production of ammonia.

References:

The Foundations Of Chemical Kinetics, Benson, 1982

Physical Chemistry, Atkins, 6^th Edition

Combustion, Flames And Explosions Of Gasses, Lewis & von Elbe, 2^nd Edition

Elementary Reaction Kinetics, Latham & Burgess, 3^rd Edition

Reaction Kinetics Volume One, Laidler, 1970

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