Carbocations thermodynamic equilibria

Positional Isomerization. A different type of isomerization, substituent migration, takes place when di- and polyalkylbenzenes (naphthalenes, etc.) are treated with acidic catalysts. Similar to the isomerization of alkanes, thermodynamic equilibria of neutral arylalkanes and the corresponding carbocations are different. This difference permits the synthesis of isomers in amounts exceeding thermodynamic equilibrium when appropriate reaction conditions (excess acid, fast hydride transfer) are applied. Most of these studies were carried out in connection with the alkylation of aromatic hydrocarbons, and further details are found in Section 5.1.4. 

It is important to point out that thermodynamic equilibria of hydrocarbons and those of derived carbocations are substantially different. Under appropriate conditions (traditional acid catalysts, longer contact time), the thermodynamic equilibrium mixture of hydrocarbons can be reached. In contrast, when a reaction mixture in contact with excess of strong (super) acid is quenched, a product distribution approaching the thermodynamic equilibrium of the corresponding carbocations may be obtained. The two equilibria can be very different. Since a large energy difference in the stability of primary < secondary < tertiary carbocations exists, in excess of superacid solution, generally the most stable tertiary cations predominate. This allows, for example, isomerization of n-butane to isobutane to proceed past the equilibrium concentrations of the neutral hydrocarbons, as the er -butyl cation is by far the most stable butyl cation. 

As thermodynamic stability indexes for the hydrocarbon ions, pA R+ and pA a values [(4) and (5)] have been widely applied for the carbocation and carbanion, respectively, in solution. Here K + stands for the equilibrium constant for the reaction (6) of a carbocation and a water molecule stands for the equilibrium constant for the reaction (7) of a hydrocarbon with a water molecule to give the conjugate carbanion. The equilibrium constants are given by (8) and (9) for dilute aqueous solutions. Obviously, the reference system for the pKn+ scale is the corresponding alcohol, and... 

We consider the relatively high pKA values of 6-8 to be typical value for a cation-quinone methide equilibrium. The formation of a resonance-stabilized aromatic carbocation is one reason for these high pKA values. Another reason is the high energy of the quinone methide. The thermodynamic cycle shown in... 

As a measure of their thermodynamic stability, the pAfR+ values for the carbocation salts were determined spectrophotometrically in a buffer solution prepared in aqueous solution of acetonitrile. The KR+ scale is defined by the equilibrium constant for the reaction of a carbocation with water molecule (/CR+ = [R0H][H30+]/[R+]). Therefore, the larger p/CR+ index indicates higher stability for the carbocation. However, the neutralization of these cations was not completely reversible. This is attributable to instability of the neutralized products. The instability of the neutralized products should arise from production of unstable polyolefinic substructure by attack of the base at the aromatic core. 

Perhaps less obviously, the hydrocarbon also provides a reference for the carbocation. It is worthwhile examining the implications of such a reference, by considering briefly thermodynamic measurements of carbocation stabilities in terms of heats (enthalpies) or free energies of formation. Mayr and Ofial contrast our ability to measure the relative energies of tertiary and secondary butyl cations with the significant differences in relative stabilities of secondary butyl and isopropyl cations derived from different equilibrium measurements, namely, hydride, chloride, or hydroxide ion affinities. It is convenient to focus on this example and to assess the effectiveness of hydride affinities for comparing the stabilities of these three ions. 

For such unstable carbocations, an alternative approach to pAR can be developed, by recognizing the relationship that exists between pATR and pAa implied in Equation (15) (p. 30). For carbocations with [3-hydrogen atoms, loss of a proton normally yields an alkene. Then, as discussed by Richard, pATR and pAa form two arms of a thermodynamic cycle, of which the third is the equilibrium constant for hydration of the alkene, pAH2o, as already indicated in Scheme 1. The relationship between these equilibrium constants is shown for the t-butyl cation in Scheme 4. In the scheme the equilibria are... 

There have been more equilibrium measurements for reactions of carbocations with azide than halide ions. Regrettably, there is little thermodynamic data on which to base estimates of relative values of pARz and pAR using counterparts of Equations (17) and (18) with N3 replacing Cl. Nevertheless, a number of comparisons in water or TFE-H20 mixtures have been made87,106,226,230 and Ritchie and Virtanen have reported measurements in methanol.195 The measurements recorded below are for TFE-H20 and show that whereas pA" 1 is typically 4 log units more positive than pA R. pA Rz is eight units more negative. The difference should be less in water, perhaps by 2 log units, but it is clear that azide ion has about a 1010-fold greater equilibrium affinity for carbocations than does chloride (or bromide) ion. 

It seems clear that for reactions of carbocations with nucleophiles or bases in which the structure of the carbocation is varied, we can expect compensating changes in intrinsic barrier and thermodynamic driving force to lead to relationships between rate and equilibrium constants which have the form of extended linear plots of log k against log K. However, this will be strictly true only for structurally homogeneous groups of cations. There is ample evidence that for wider structural variations, for example, between benzyl, benzhydryl, and trityl cations, there are variations in intrinsic barrier particularly reflecting steric effects which lead to dispersion between families of cations. 

In addition to the linear free energy studies discussed, there have been many attempts to estimate the thermodynamic stabilities of electrophilic species, such as carbocations.7 The pKr+ values for carbocations reveal trends in relative stability and is defined as, according to the equilibrium established between the carbinol... 

Table 3 compares the thermodynamic driving force AG°, calculated from the equilibrium constant Aadd (Scheme 50), and the derived Marcus intrinsic reaction barriers for reversible addition of nucleophiles Y to 48 and the tri-phenylmethyl carbocation (Ph3C+).4 There are nearly constant differences between the values for the thermodynamic driving force for addition of nucleophiles to 48 and Ph3C+ ((A(j°(48) AG0(PhC+) = 8.4 kcal/mol) and those for... 

At the higher temperature, the reaction becomes reversible and is under thermodynamic control. This means there is enough energy available for either product to reform the allylic carbocation by an SN1 type ionization and then form the other product. As a result the products are in equilibrium. At equilibrium, the relative amount of the products is controlled only by the difference in energy between them (AG). In this case, the 1,4-addition product (called the thermodynamic product) is more stable than the 1,2-addition product, so more of it is present in the equilibrium mixture. This same equilibrium mixture of products (15% of the 1,2-addition product and 85% of the 1,4-addition product) is produced when the low-temperature reaction product mixture (80% of the 1,2-addition product and 20% of the 1,4-addition product) is heated to 45°C. 

Reaction-energy diagram for the second step of the addition of HBr to buta-1,3-diene. The allylic carbocation (center) can react at either of its electrophilic carbon atoms. The transition state ( ) leading to 1,2-addition has a lower energy than that leading to the 1,4-product, so the 1,2-product is formed faster (kinetic product). The 1,2-product is not as stable as the 1,4-product, however. If equilibrium is reached, the 1,4-product predominates (thermodynamic product). 

Allylic halides can undergo slow dissociation to form stabilized carbocations (SnI reaction). Both 3-bromo-l-butene and l-bromo-2-butene form the same allylic carbocation, pictured above, on dissociation. Addition of bromide ion to the allylic carbocation then occurs to form a mixture of bromobutenes. Since the reaction is run under equilibrium conditions, the thermodynamically more stable l-bromo-2-butene predominates. 

In the same way as changes in reactivity reflect the nature of the transition state, a change in equilibrium constant corresponds to a change in the thermodynamic stability of the carbocation intermediate. For example, substituent effects on the basicities of arylcarbonyl derivatives ArCOR provide a reference for the formation of a-hydroxycarbocations (17). 

Additions [reactions (b) and (d)] are normally favored by thermodynamics (Section 12-1). For elimination to occur, conditions have to be established to drive the equilibria the opposite way. In (a) the water lost in the reversible El process is protonated by the concentrated H2SO4, removing it from the equilibrium. No good nucleophiles are present therefore, the carbocation undergoes loss of a proton to form the alkene. In (c) the strongly basic ethoxide ion induces bimolecular elimination and... 

The more favored product is dictated by the stability of the alkene being formed. The conditions for the reaction (heat and acid) allow equilihrium to he achieved between the two forms of the alkene, and the more stable alkene is the major product because it has lower potential energy. Such a reaction is said to be under equilibrium or thermodynamic control. Path (b) leads to the highly stable tetrasubstituted alkene and this is the path followed by most of the carbocations. Path (a), on the other hand, leads to a less stable, disubstituted alkene, and because its potential energy is higher, it is the minor product of the reaction. 

Protolytic ionization of methylcyclopentane gives an equilibrium mixture of the tertiary 1-methyl-1-cyclopentyl cation (29) (more stable by about 40 kJ/mol) and the secondary cyclohe l cation (32) (Scheme 5). At low temperature, irreversible reaction of 29 with CO leads to ion 30, which, after reaction writh ethanol, gives the 31 ester. Product composition, in this case, reflects the difference in stability of the intermediate carbocations. Since the carbonylation step is reversible at higher temperature, and carbocation 32 has a much higher affinity for CO, the concentration of 33 in solution continuously increases to yield, after quenching with ethanol, the 34 ester. This is an example of a kinetically controlled product formation through a thermodynamically unfavorable intermediate. 

How does this information lead to an understanding of the reaction of the alkene and HBr Remember that an acid-base reaction is an equilibrium, and an equilibrium tends to favor the more stable product (see Chapter 2, Section 2.2, and Chapter 7, Section 7.10). Because the reaction of 2-methyl-2--butene with HBr is categorized as an acid-base reaction, the first reaction that forms the carbocation will be reversible. If this reaction is reversible, it is an equilibrium reaction, and the more stable carbocation 7 will be favored over the less stable carbocation 6 based on formation of the thermodynamically more stable product. In other words, the reaction is under thermodynamic control and it generates the thermodynamically more stable product. Formation of the more stable tertiary carbocation can also be rationalized using the Hammond postulate, which states that a reaction under thermodynamic control will have a late transition state and that the energy of the transition state will be influenced by the structure and nature of the product. In this case, the product is the carbocation, so the Hammond postulate suggests that relative stability of each carbocation product should play a major role is determining which carbocation is formed preferentially. 

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