Rates of Substitution Reactions (Part 1)

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Introduction

We will begin first by understanding the mechanism of substitution reactions, which should give us a better understanding of how the rates of such reactions will be affected between different types of molecules and under different reaction conditions. In this article, only aliphatic nucleophilic substitution reactions specifically are referred to; this is the most general field of substitution reactions. Other types of substitution reactions, especially electrophilic substitution reactions of benzene, also have interesting chemistry, but will not be discussed here. In the previous article it was mentioned that there are many types of mechanisms by which nucleophilic substitution can take place; here, we will focus solely on the two most common and important mechanisms, the SN1 (substitution nucleophilic unimolecular) and SN2 (substituion nucleophilic bimolecular) mechanisms; reactions that proceed via such mechanisms are in turn known as SN1 and SN2 reactions. Before we begin, it is worth noting the similarities of both of these reactions: both of them involve a nucleophile, a substrate and a leaving group, and both of them involve the substitution of the leaving group by the nucleophile, although each mechanism portrays this substitution in distinctly different ways, thus the rates of the reactions will be affected by different factors.

SN1 reactions follow the SN1 mechanism, which involves two steps. In the first step, the substrate (to which the leaving group is bonded to) solvolyses. The solvent in which this takes place can be of many types, including protic solvents such as water (hydrolysis) and acetic acid (acetolysis), which is generally where SN1 reactions take place. Regardless, the solvent always facilitates the ionization of the reactant molecule into the electrophile (cation) and the leaving group (anion). In the second step, the nucleophile then attacks the positively-charged electrophile using its pair of electrons, forming a bond with it. This ends the nucleophilic substitution reaction. As has been noted previously, the rate-determining step of an SN1 reaction is the first step, solvolysis, and thus the concentration of the nucleophile does not affect the rate of the SN1 reaction. Yet, the rate of the solvolysis appears to be deceivingly simple. Since the first step involves only one reactant, it may be logical to suggest that the reaction is first-order with respect to the concentration of the reactant. However, we realise that this first step is reversible, since the cation and anion can easily ‘recombine’ to reform the reactant. This complicates the calculation of the rate of the SN1 reaction. There are, in fact, three reactions taking place simultaneously that we need to consider: the forward reaction (solvolysis), the backward reaction (reforming the reactant), and the nucleophilic attack on the electrophilic substrate. To account for these factors, the rate law is greatly complicated, as shown in Fig. 1. Note, however, that some reactants are more selective than others, and while some reactants follow the rate law outlined in Fig. 1, others follow the simple first-order rate law.

Fig. 1: Rate law for selective SN1 reactions.

SN2 reactions, then, follow the SN2 mechanism. Unlike the SN1 mechanism, this mechanism involves only one step, also the rate-determining step. In this step, the nucleophile attacks the electrophilic carbon (bonded to the nucleophilic leaving group) on the substrate, and simultaneously the leaving group breaks its bond with the electrophilic carbon, and this in-between state is known as the ‘transition state’, which is pentavalent as the carbon possesses bonds both to the nucleophile and the leaving group. Fortunately for us and all undergraduates, the rate of the SN2 mechanism is much simpler, and is second-order with respect to the concentrations of the reactant (substrate + leaving group). While most SN2 mechanisms do not involve intermediates, some SN2 reactions, including what I believe is the Menshutkin reaction, have been observed to possess an intermediate (since intermediates are mostly stable, they have lower energies and this can be seen on an energy diagram).

Effects of Structure

Effects of the structure of molecules on their reactivity in nucleophilic substitution reactions is by far one of the most important factors to consider. The absence and presence of some substituents can make entire reactions viable or impossible. We will start by considering something ‘on the fringe’, which is the neighboring group mechanism. The neighboring group mechanism involves the presence of neighboring groups, and follows a first-order rate law. When a neighboring group is present on the substrate, it attacks the electrophilic carbon (such a reaction does not require collision making it significantly faster), resulting in a three-membered intermediate with the neighboring group positively-charged. This is followed by nucleophilic attack by the actual nucleophile on the same carbon, breaking its bond with the neighboring group and ending the reaction. The reason why such a reaction is faster than normal SN1 and SN2 reactions is clearcut. In both the SN1 and neighboring-group mechanisms, the second step is the same, and does not determine the rate. Logically speaking, the SN1 mechanism’s first step would be slower than that of the neighboring-group mechanism, because the neighboring-group mechanism does not require a collision and can take place almost instantaneously; furthermore, it only results in a small decrease in entropy, making it have a high rate, more than that of both SN1 and SN2 mechanisms. Besides, the fact that we can even detect the neighboring-group mechanism gives evidence that it takes precedence over both SN1 and SN2 mechanisms at times, suggesting it is faster than them! The main problem with the neighboring-group mechanism is just that - it is a mechanism, and it is factually inaccurate to say that the presence of a neighboring group speeds up the reaction, because it does not, and only provides an alternate path of reaction for the reactants. However, we realise that catalysts perform the exact same function, but yet they are considered to speed up the reaction. So though there are some differences between catalysts and neighboring groups, we will still include them here as they represent ‘changes in structure’, and do in fact have an effect on the rate. But take note that the reaction operates by a different mechanism when they are present. Neighboring groups include carboxylate, OR, OH, and many other moieties.

Other than the neighboring-group mechanism, there are also many other factors to consider in structure, mostly relating to the presence of certain substituents or groups on the alpha and beta carbons. We begin with the alpha carbons first; these refer to the carbons to which nucleophilic attack is directly occurring. As we have touched on briefly on the previous article, the substitution of the electrophilic carbon can affect its reactivity. The more substituted the electrophilic carbon, the easier it is for the cation formed after solvolysis to be stabilized, which makes the SN1 reaction energetically favorable. As such, the more substituted the alpha carbon, the faster the rate of the SN1 reaction. For the SN2 reaction, this is directly opposite; while some would expect that the more substituted the carbon, the more susceptible the carbon to nucleophilic attack, this is not true because the steric effect of the substituents takes precedence, preventing the SN2 reaction from taking place as the nucleophile is unable to reach the electrophile to attack it. In such cases, the SN1 reaction is preferred; in cases where the electrophilic carbon is minimally substituted, such as in CH3Cl, the SN2 reaction is highly favored. This effect for the alpha carbon is also followed by the beta carbon.

Lastly, we will also discuss unsaturation at the alpha and beta carbons. The unsaturation is provided by the alpha carbon being a part of an aryl or vinyl. This typically greatly slows the rate of both SN1 and SN2 mechanisms, although alternative mechanisms are still possible for such unsaturated substrates. For aryls, although nucleophilic substitution can still occur, it occurs to the ring as a whole and not just to one specific carbon; additionally, it is beyond the scope of this article to discuss such reactions. Vinyls, in contrast, are much more interesting; the alpha carbon will become sp2 hybridized, which is relatively more electronegative than sp3 hybridized carbons (as can be seen by the acidity of alkanes, alkenes, and alkynes). This diminishes its electronegativity, making it less susceptible to nucleophilic attack, slowing the SN2 reaction; furthermore, solvolysis is also slower since the cation will be more unstable, slowing the SN1 reaction as well. We note one special case of RCOX (acyl halides), where the electronegative oxygen, although not the leaving group, makes the carbon even more electronegative and speeds up the nucleophilic substitution reaction. In contrast to unsaturation at the alpha carbon, unsaturation at the beta carbon is much more useful, and no matter vinyl or aryl, increases the rate of an SN1 reaction, since resonance can occur to delocalize the positive charge formed after solvolysis, making it more stable. Particularly stable is triphenylmethyl chloride (Fig. 2), where the presence of three benzenes greatly delocalizes the positive charge. Surprisingly, it also increases the rate of SN2 reactions, again attributed to resonance in the transition state. 

Fig. 2: Structure of triphenylmethyl chloride.

There are many more factors that have an effect on the rate of SN1 and SN2 reactions, and they usually concern the location of the electrophilic carbon, such as on bridgeheads (where a backside attack is not possible due to steric hindrance). However, a good number of factors have been covered in this article that greatly influence the rate of nucleophilic substitution reactions.

By the way, Part 2 of this article is here.

Tags: All Posts Substitution Reactions

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