# Does the first step in electrophilic aromatic substitution follow equilibrium? If so, can equilibrium constant be calculated?

Using chlorine (a Lewis base) and ferric chloride (a Lewis base) as an example, the first step I saw in the textbook looks like this:

The picture above depicts the Step 1 in the EAS mechanism using chlorine as an example.

I noticed that this step has two reversible arrows. I think it means chlorine, ferric chloride, the molecular complex and the ion pair will all be present in a system and their concentration values follow chemical equilibrium.

From high school knowledge (I am a freshman), we can calculate equilibrium constant using concentration. Can we still do it in this case? If so, how?

• The intermediate molecular complex would only exist for a very brief period of time. It would be important in the kinetics of the overall reaction. However the equilibrium would probably be best expressed as an overall equilibrium.
– MaxW
May 27 '20 at 15:05
• If there’s an equilibrium, a constant can be calculated. Often, however, the results aren’t very meaningful especially in a case like this where the intermediate complex does not have a long lifetime.
– Jan
Jun 3 '20 at 2:34

Let me put it this way: Every compound exist in a 3N dimensional configuration space (may be simple XYZ coordinates of the system, may be internal coordinates, based on your choice), and based on the configuration, its potential energy is defined. The potential energy surface (PES) can be calculated quantum mechanically or using some force field classically. The probability of the system to be found in the given set of coordinates is given by the distribution function defined according to statistical mechanics. For a canonical ensemble, the formula is given as (Z is the partition function):

$$P(\vec{r}_{3N})= \frac{1}{Z}e^{-E(\vec{r}_{3N})/k_BT}$$

Now imagine this, a reaction between compounds containing M and N atoms is actually an exploration of the potential energy surface in 3(M+N) dimensions. Reactants, product and intermediates are given by local minima in the PES while transition state is given by maxima along one dimension and minima along all other dimensions. In other words, for a stable state (reactant, product, intermediate, etc.) all the frequencies (square root of the second derivate of the PES) is real, while for transition state one of the frequencies is imaginary.

Now coming to your question: You will require to calculate the energetics of each of the step of reaction considering the presence of solvent (this is probably happening in presence of solvent), plug in your values to the appropriate statistical ensemble (if it is inside solvent without release of gaseous products, canonical ensemble should be good enough) probability function and you will get an idea about the percentage of intermediates you get.

In most high school textbooks, the reaction marked with double arrows simple means the reactant, product (and in your case the intermediate) is not too much different in terms of potential energy. For a single headed arrow, it means that the difference between potential energies of the minimas (reactant and product) is significant and most of the compounds (in an ensemble) will be trapped in the lower minima.

In case you want to read more about it, I suggest the following books:

• Statistical Mechanics by McQuarrie
• Physical Chemistry by Atkins
• Physical Chemistry by Levine

For more details about reaction dynamics, you may refer to:

• Molecular Reaction Dynamics by R. D. Levine