How do you list all possible reactions and intermediates of a reaction?

Question

Ins this video https://youtu.be/txk-VO1hzBY?t=2391 the speaker claims that $$\ce{H2 + O2 -> H2O}$$ involves 23 reactions and 11 species. How do you list all of that ?

Answer 1

You've discovered a secret. In undergraduate chemistry classes, the field of chemical kinetics is treated with a level of detail very far from reality. The truth is that virtually any reaction you can devise is vastly more complicated than we would like to think. This is especially true for gas phase reactions like the one you write down because it is possible for very unstable intermediates to exist for long enough to collide with lots of different species or undergo an internal conversion (when the molecule is large enough to do so) which introduces minute components that could nonetheless make a big difference in the kinetics.

Some people actually attempt to study these reactions without just ignoring the small sideways paths that lead to weird intermediates or weird products. Generally they do this by using what is called a Master Equation. I would encourage anyone to read about these and a very nice overview can be found here: Miller, J. A., & Klippenstein, S. J. (2006). Master equation methods in gas phase chemical kinetics. The Journal of Physical Chemistry A, 110(36), 10528-10544.

What you'll find when reading this is that they care a lot about what the potential energy surface looks like everywhere. This is because one formulation of the Master Equation is as follows:$$\frac{dn_i}{dt}=\sum_j(p_{ij}\cdot n_j(t)-p_{ji}\cdot n_i(t))$$This basically says that we are looking at the change in probability of finding the system in a state $n_i$ as a function of time and we are doing this by describing the probability per unit time $p_{ij}$ of moving from state $j$ to state $i$ as well as the process which goes the other way. Note that $n_i$ is essentially the same as a number density for a large number of molecules, but strictly this is a probability.

You can imagine then that in order to use this equation (which isn't very usable in its current form), one would need a detailed picture of what possible intermediates can form immediately from the state the system is in right now.

Thus, the answer to how you write all these down is that you look very carefully at the state of any system and ask yourself, what intermediates could I possibly imagine forming? Many of these intermediates are very unstable at low temperatures, but these kinds of models are frequently used when studying combustion chemistry or flames, so the number of intermediates can becomes very large and the number of reactions those intermediates can undergo (the number of states $j$ you can jump to from state $i$) is even larger. To operationalize this, you would basically write out all known intermediates, from experiment or theory, and imagine what reasonable combinations you could make of those that eventually lead to your product.

In the video you link, some unusual intermediates are listed, such as $\ce{HO2}$, and it is said that this is a simplified model. Basically what that means is that they had even more possible combinations of intermediates, but for computational simplicity or good experimental reasons, decided that many combinations of those intermediates contributed negligibly to the reaction of interest.

One final note is that it's not really as simple as combining everything you can imagine because you have to consider where a given intermediate came from. For instance if a single molecule is formed by means of a bimolecular reaction, the angular momentum must be conserved. This can lead to situation where certain states you could imagine hopping to are not actually possible because it would violate conservation of angular momentum. Indeed, one could imagine this leading to some reaction mechanisms which are very different from what intuition would dictate. The paper I linked above notes that when angular momentum becomes an important factor, the intermediate usually undergoes an internal conversion to basically store that angular momentum before reacting with other things... So, when you're writing out all of these intermediates don't forget that $\ce{HO2}$ might very well exist as $\ce{HOO}$ or $\ce{OHO}$ (though that seems unlikely I only meant it as an illustration).

I hope this addressed the spirit of what you were really asking.

Answer 2

You generally only list the intermediates of a net chemical reaction if they are relevant in some context of your study, experiment, discussion, etc. For example, if you have developed a model for the reaction of $\ce{H2}$ and $\ce{O2}$ that invokes 23 intermediate reactions, then you would want to explicitly show each of those reactions.

If you are only interested in the net reaction, the stoichiometry, etc. of a reaction that has many intermediates (and all but the simplest reactions will have many intermediates), then you simply give the net reaction. In your example, the balanced reaction would usually just be given as

$$\ce{2H2 + O2 -> 2H2O}$$

and it is understood that this is the net reaction that may have a very complex mechanism with multiple intermediates species and reactions, but there is generally no need to list them all.