Recap
Part 2 of this article was relatively short and explained two factors which have an effect on the rates of substitution reactions: the location of the carbon on the molecule, as well as its nucleophilicity. The location of a carbon is sometimes important, especially in the case of carbons in cyclic structures or bridgehead carbons, where in the latter case especially, it is not possible for SN2 reactions to occur due to steric hindrance. However, interesting, for cyclic structures, the more strained the molecule, the more energetically favorable the substitution reaction. This is because substitution reactions that occur on strained cyclic substrates typically have to undergo ring-opening reactions, of which the energetic barrier has to be overcome. The lowest energetic barrier is provided by the most highly strained molecule, and as such the ring-opening reactions of these molecules are more energetically favorable.
In the latter case, the nucleophilicity itself is of course highly important, in particular for SN2 reactions, because in such reactions the nucleophile is included. We mentioned this in the previous article; yet, we also want to make a slight correction. While it is usually true that the SN1 reaction follows a simple first-order rate law involving only the concentration of the substrate, it may be that in certain cases (where selectivity is greater), a different, more comprehensive rate law (Fig. 1) is followed. In this rate law, the solvolysis is taken to be a reversible reaction; as such, the removal of the product (the cation and anion) via reaction with the nucleophile would cause the forward reaction to increase in favorability. In such cases, the concentration of the nucleophile does indeed matter; but for many it is more convenient and generally easier to assume that the SN1 mechanism follows a simple first-order rate law.
Fig. 1: Comprehensive rate law for selective SN1 reactions.
Leaving Group
Obviously, the leaving group would influence the rate of the reaction, although typically it is not included in the rate law as it is formed as the product of substitution reactions. The key factor affecting the rate of reactions would be the ‘willingness’ of the leaving group to depart, and this applies to the case of both SN1 and SN2 reactions. There are generally two ways to alter this ‘willingness’. Firstly, the weaker the bond between the leaving group and the substrate backbone, the more favorable the rate-determining step of the substitution reaction. For SN1 reactions, the bond between the leaving group and the substrate must be broken to produce a cation and anion. For SN2 reactions, the leaving group-substrate bond must be broken as well for the transition state to transform into the product. Secondly, the more stable the leaving group as a free atom, the more energetically favorable the departure of the leaving group.
As such, if we want to speed up the rate of a substitution reaction, we can either tweak with the leaving group-substrate bond, or the stability of the free leaving group (though they are commonly interlinked). The stability of the free leaving group matters a lot, for one, meaning that the more basic the substituent, the poorer it is as a leaving group; this is seen, in particular, with the OH- substituent, which is a very poor leaving group. The reason for this is that the more basic the substituent, the more unstable it will be as a free atom, as it will seek protonation, forming a weaker conjugate acid that is more stable. This also happens to be the reason why these basic substituents become better leaving groups after protonation occurs. Where an SN1 or SN2 mechanism begins first with the protonation of the leaving group before the ‘conventional’ mechanism, it is known as an SN1cA or SN2cA mechanism (Fig. 2) respectively (cA for conjugate acid).
Fig. 2: Mechanism of SN1cA reaction.
The unusual, alternate case is where a proton is lost instead of gained, from a basic substituent. For a good majority of basic substituents, the formation of the conjugate acid (from protonation) occurs instead of this mechanism, which only usually happens to metal amine complexes. These metal amine complexes undergo a sort of ‘substitution’; it is known as a ligand exchange, since one of the substituents of the metal ion forming the complex (known as a ligand) is being substituted with another ligand. It is very interesting why the deprotonation of a base would make it a better leaving group; the answer lies in its higher reactivity as a substituent after deprotonation, and a different mechanism takes place which directly involves the substituent, allowing for the rate of the reaction to be higher. In the first step of this type of mechanism, the proton is first lost, resulting in an anion. The loss of the leaving group simultaneously occurs, preventing the formation of an overly-large energetic barrier. After the leaving group departs, more electron density is ‘forced’ upon it, forming a carbene. The carbene then undergoes typical carbene reactions, one of which happens to be substitution, and to an outside observer, it may seem that typical nucleophilic substitution has occurred. Such a mechanism is known as an SN1cB mechanism (Fig. 3).
We must, however, note the following: firstly, in Fig. 3, we note that the reaction is second-order with respect to OH- and the metal amine complex. While this is indeed the case, the OH- is not the nucleophile in the reaction; it is, in fact, a base, and it is used to deprotonate the amine. However, since it is a reactant in the rate-determining step of the SN1cB mechanism, it is considered part of the rate equation. This is misleading because the OH- can act simultaneously as a nucleophile and a base; in this case, it acts as a base, even though the end product results in the OH- anion being substituted onto the metal complex.
Fig. 3: Mechanism of SN1cB reaction.
We will also discuss ‘naturally’ excellent leaving groups, which usually amounts to leaving groups that are exceedingly stable as free atoms. Such leaving groups will also naturally have a weak bond with its substrate, because the energy of the substrate-leaving group molecule would then be higher than the energy of the substrate and the leaving group (separated). Thus making the bond dissociation more energetically favorable. The case of exceedingly stable leaving groups as free atoms comes most prominently from diazonium ions (the diatomic N2 cation) as a leaving group (Fig. 4). Even simple analysis of the structure can reveal how stable N2 is; it involves a triple bond formed between two nitrogen atoms, which of course is very strong. The small size of each of the nitrogen atoms forces the two atoms closer to each other, which is already highly stabilizing in general.
Fig. 4: Structure of the aromatic diazonium ion.
The problematic issue, in fact, is not with the stability of the leaving group as a free atom; it is with how to ‘force’ the N2 molecule onto the carbon backbone of the substrate. Due to the instability of the substrate-diazonium ion molecule, it can exist only for a very short time as an intermediate. This means it has to be generated in-situ and cannot be stored (although some aromatic diazonium ions are relatively stable). The diazotization of the substrate is done by conversion of an amine, and the reaction involves a primary amine, R-NH2, which reacts with nitrous acid (HONO), also usually generated in-situ. As for the mechanisms of diazotization, they are still under debate because the intermediates disappear too fast to be isolatable or for spectra analysis. Sadly it is usually not convenient to utilize diazonium ions as leaving groups, because they are so reactive that a mixture of products, difficult to separate, are formed.
Solvent
As the solvent aids in solvolysis for the first step of the SN1 mechanism (which is the rate-determining step), it is reasonable to assume that the rate of the SN1 reaction is affected by the solvent. In addition to this, we note that even the rates of SN2 reactions are affected by solvent, because the ionic transition state can easily be affected by the solvent, especially polar solvents. In the case of these polar solvents, the charges of the reactants have to be considered; SN1 reactions can involve either a neutral or negatively-charged substrate, but never a positively-charged substrate, because the departure of the leaving group would be destabilizing, taking away even more electrons. For SN1 reactions, we could consider the transition states as ionic molecules, because an ‘ion pair’ (not an intimate ion pair) involves oppositely-charged ions. Neutral substrates would dissociate into a partially positively-charged alkyl as well as a partially negatively-charged leaving group. This dissociation is favored in polar solvents because the resulting ions can solvate well. As such, the more polar the solvent, the faster the reaction.
As for SN1 reactions with a negatively-charged substrate, the transition state would involve both the leaving group and the alkyl possessing a partial negative charge. This is problematic because no ion pair is formed, and the ions cannot solvate well in the polar solvent, since there is a lack of a ‘counter-ion’. This means that the increase in polarity of a solvent would result in a small decrease in the rate of the reaction. The SN1 reactions are also aided by protic solvents, since they are able to hydrogen bond to the substrate and facilitate the departure of the leaving group, which would increase the rate of the reaction. We will name some common protic and aprotic solvents: protic solvents include water (‘the universal solvent’), alcohols and carboxylic acids), while aprotic solvents include DMF (dimethyl formamide) as well as DMSO (dimethyl sulfoxide), which is shown in Fig. 5.
Fig. 5: Structure of dimethyl sulfoxide (DMSO).
As for SN2 reactions, they are more problematic, mostly because there are four different types of SN2 reactions. Since the substrate (electrophile) can be neutral or positively-charged, and the nucleophile can be neutral or negatively-charged, four possible reactions can result. To consider whether the SN2 reaction will be faster in a polar solvent, we must see whether there is a net ‘reduction’ or ‘gain’ in charge. In the case of transition states which have a higher charge than the starting substrate (this is compared in terms of partially charged transition states and ‘fully’ charged substrates, an increase in polarity would result in an increase in the rate. Where the transition state has instead a lower charge, the increase in polarity would cause a decrease in the rate instead.
At last, all of the factors affecting SN1 and SN2 reactions have been discussed! In the next article (which would be quite a while!), hopefully some discussion of the rates of electrophilic substitutions can occur as well.
Part 2 of this article is here.