Research: Science and Education
Free Radical Halogenation, Selectivity, and Thermodynamics: The Polanyi Principle and Hammond’s Postulate Alfred A. Scala Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Worcester, MA 01609;
[email protected] www.JCE.DivCHED.org
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The central idea, which is beautifully expressed in Hammond’s postulate, is that the transition state will have a structure and therefore an energy that is characteristic of both the reactants and the products. The relative contributions of reactant and product properties to the properties of the transition state depend upon whether the transition state is of low energy and is achieved “early” or of high energy and achieved “late” along the reaction coordinate. This difference is usually a function of the reactivity of the system, which in turn is a function of the thermodynamics of the reactions. Very exothermic reactions are frequently very reactive, while endothermic reactions are quite unreactive. Here very reactive and unreactive refer to the magnitude of the rate constant and derive from the fact that exothermic reactions usually have low energies of activation. The more exothermic the reaction, the lower the energy of activation and earlier the transition state; endothermic reactions have energies of activation at least as large as the enthalpy of reaction and later transition states (5). It is essential to keep in mind that this discussion applies only to a comparison of similar reactions. This idea is graphically illustrated in Figure 1 using schematic reaction-coordinate diagrams. Methane Reaction It needs to be emphasized that the reactions being compared must be similar because, at least for the moment, we are neglecting the entropy. Figure 1 could be a comparison of any three similar reactions, but is in fact a comparison of methane halogenation with fluorine, chlorine, and bromine. The thermodynamics are different because the bond energies of the HX molecules are different: HF, HCl, and HBr bond dissociation energies are 568, 431, and 366 kJ兾mol, respectively (6). The products are methyl radical and HX. The early transition state is achieved for the most exothermic case of X = F and the late transition state is achieved for
Fluorination: early transition state
Chlorination: intermediate transition state
Bromination: late transition state
CH4 + F
CH3 + HBr CH4 + Cl CH + HCl 3
H°
The free radical halogenation of hydrocarbons, although often the first reaction covered in organic chemistry courses and texts, is usually not discussed in any depth because of the pressure to get into the more interesting and important reactions involving functional groups. Interestingly, this reaction is often only superficially examined precisely because it is described as being unselective.1 In the traditional, perhaps unrealistic, organic chemical definition of selectivity, that is, regioselectivity or “giving a single product”, the free radical halogenations are unselective. In fact when examined in depth, this reaction has the potential to be the most convenient and possibly the best vehicle for a realistic discussion of selectivity, as well as many other topics, that are important to organic chemistry, but also transcend organic chemistry because of their significance to all of chemistry. These topics include mechanisms, kinetics, reaction-coordinate diagrams, transition states, relative rates (selectivity), and the effect of thermodynamics on reaction rates and equilibria. A previous article, describing an undergraduate laboratory experiment, reported student results for the gas-phase chlorination and bromination of propane, butane, and isobutane (1). The results were close to the expected product ratios for the various isomeric products, if the reactivity ratios for 1⬚, 2⬚, and 3⬚ carbon–hydrogen bonds were 1:3.8:5 for chlorination, and 1:82:1600 for bromination. These are the usually quoted gas-phase reactivity ratios in the few organic text books that go into the topic in detail.1 The objective of this article is to present the topic of selectivity in a broader context and to suggest liquid-phase experiments that can serve as the basis for further in-depth analysis and discussion. Student results for the liquid-phase chlorination of isopentane are also presented. If selectivity is defined in terms of the relative rate constants for competing reactions, the basis for the observed selectivities is a difference in the free energies of activation of the competing reactions, which in turn results from the thermodynamics of the competing reactions, and is described by the Polanyi principle (PP), later reincarnated and qualitatively refined as Hammond’s postulate (HP) (2, 3). Linear free energy relationships (LFER) that deal with equilibria as well as reaction rates are similarly based, although they often rely on empirical measurements for an independent variable rather than the fundamental thermodynamics. This is largely a matter of convenience and utility that allows the wide application of the LFER to a broad range of reactions, even while ignoring some of the details, and does not change the ultimate thermodynamic origin of these effects, as their name implies (4). It is not the purpose here to discuss LFER but rather to discuss the underlying ideas of the PP and HP in relation to the simple free radical halogenation reactions and their selectivity. One might be tempted to imply that the approach presented by the Polanyi principle and Hammond’s postulate demonstrates the basis for all LFERs.
CH4 + Br
CH3 + HF
Reaction Coordinate
Reaction Coordinate
Reaction Coordinate
Figure 1. Methane halogenation, thermodynamics, and schematic reaction coordinate.
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the most endothermic case of X = Br. The case for chlorine is intermediate. The enthalpies of these reactions, 1a, along with the subsequent propagation step, 1b, are presented in Table 1.
CH4 + X CH3 + X2
CH3X + HX net reaction CH3 + HX CH3X + X
mechanism
(1) (1a)
The later the transition state, the more the formation of the H⫺X bond and the cleavage of the C⫺H bond contribute to its energy. The weakest bond, H⫺Br must be formed to a greater extent and the C⫺H bond must be broken to a greater extent in order to achieve the transition state for bromination, compared to the H⫺F bond, which is so strong it only barely forms, and the C⫺H bond is barely stretched when the transition state for fluorination is achieved. Unrestricted Hartree–Fock SCF calculations using Gaussian-98 and the 3-21G basis set indicate that the C⫺H bond distances in the transition states for fluorination, chlorination, and bromination of methane are 1.31, 1.50, and ≈1.66, respectively (7). The length of the H⫺X bonds that are forming also show that the H⫺Br bond is almost totally formed, only 6% extension, in the transition state. The extension in the H⫺Cl and H⫺F bonds are 12 and 32% respectively.2,3 In reaction 1a, because bromination has a late transition state, the energy of the transition state has a significant contribution from the energy of the products, that is, methyl radical and HBr. The opposite is true for the fluorination reaction, which has an early transition state whose energy is characteristic of the reactants, methane and fluorine atom. Chlorine is an intermediate case. The stability of the carbon radical, or alternatively the strength of the C⫺H bond that is broken, is therefore most important in the bromination reaction and least important in the fluorination. Since the mechanism of fluorination is complicated and hydrogen abstraction by fluorine atom is so indiscriminate and difficult to control without special precautions such as dilution, it will not be considered further. The remainder of the discussion will contrast chlorination with bromination of hydrocarbons that have more than a single site for reaction. Propane Reaction When the hydrocarbon is methane there is no selectivity to speak of; the product is the methyl radical. If on the other hand one considers another hydrocarbon, for example, propane, then the question of selectivity becomes significant.4 If the halogenation of propane with either chlorine or bromine is considered, then it is possible for either of two different hydrogen atoms to be abstracted from propane. The C3H7• radical may have the radical center on either the primary or the secondary carbon. It is the relative rates of these reactions that determine the relative yields of 1-Xpropane and 2-Xpropane and consequently the selectivity of the reaction: C3 H8 + X
CH3CH2CH2 + HX (primary) (2)
(secondary) (3)
CH3CHCH3 + HX 1662
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X
∆H° of Eq 1a/ (kJ/mol)
∆H° of Eq1b/ (kJ/mol)
F
᎑140
᎑303
Cl
᎑4.2
Br
+62.7
I
᎑100 ᎑89.9 ᎑79.4
+134
(1b) Chlorination: early transition state (small β)
Bromination: late transition state (large β)
‡ ∆∆G = β∆∆H°
[C--H-----Cl]‡
H°
CH4 + X2
Table 1. Thermodynamics of Methane Halogenation
[C-----H--Br]‡ 1°-C3H7 + HBr ∆∆H° 2°-C3H7 + HBr
C3H8 + Cl
∆∆H°
1°-C3H7 + HCl 2°-C3H7 + HCl
C3H8 + Br
Figure 2. The schematic reaction-coordinate diagrams for H-atom abstraction from propane by chlorine and bromine.
The previous discussion of methane halogenation should and does lead to the conclusion that propane bromination, the reaction whose transition state should be late and involve more of the radical structure that is equivalent to more of the C⫺H bond cleavage, should be more selective than the chlorination, which is characterized by an earlier transition state with less C⫺H bond cleavage. The origin of the difference in the two competing reactions lies in the fact that it is more difficult to break the primary C⫺H bond (410 kJ兾mol) than it is to break the secondary C⫺H bond (395 kJ兾mol) (6). The chlorination should be less selective because there is less of the C⫺H bond broken in the transition state for chlorination. The schematic reaction-coordinate diagrams for these competing reactions for both chlorination and bromination are shown in Figure 2. Thermodynamic and Kinetic Considerations The thermodynamic, ∆H ⬚, and kinetic, Ea, data for these reactions are presented in Table 2. The origin of the PP兾HP formulation of this idea is expressed in the Eyring equation: kB T −∆G ‡ exp h RT
(4)
∆G = ∆H − T ∆S
(5)
k =
These equations, while expressing the idea well, are obviously not meant for the calculation of absolute rate constants. However the application of these equations to two competing reactions is ideally suited to the measurement and prediction
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Research: Science and Education Table 2. Thermodynamics of H-Atom Abstraction from Propane By Chlorine and Bromine (6, 8) Primary H/ (kJ/mol) Compound
Ea
∆H°
Cl2 Br2
Secondary H/ (kJ/mol) ∆H°
Ea
᎑20.9
4.1
᎑35.5
02.8
+43.9
a
+29.3
42.4
53.
a
The Ea for the reaction of bromine with the primary hydrogen of propane has been estimated from the measured Ea for the secondary reaction 42.4 kJ/mol and the selectivity ratio of 82:1. The selectivity ratio is assumed to be entirely due to the difference in the energies of activation, that is ∆Ea.
of relative rates of similar reactions. The ratio of two such equations, which represents a competition, then becomes (9), k1 k2
= exp
∆∆S ‡ −∆∆H ‡ exp R RT
(6)
( )
(7)
∆G ‡ = f ∆G °
where the free energy of activation in the Eyring equation is a function of ∆G⬚, the free energy of reaction:
(
)
(
)
(
)
∆∆G ‡ = β ∆∆G ° = β ∆∆H ° − β T ∆∆S ° (8) The function that relates the free energies of activation to the enthalpies and entropies of reaction, given in eq 8, is a constant, β, multiplied by the difference in the enthalpies and entropies of reaction for the two competing reactions. β has values between 0 and 1. As the reactions 1 and 2 have rate constants k1 and k2, the terms ∆∆H ⬚ and ∆∆S ⬚ refer to the difference in the enthalpies and entropies of reactions 1 and 2, that is, (∆H ⬚1 − ∆H ⬚2) and (∆S ⬚1 − ∆S ⬚2). In the PP兾HP formalism small β applies to an “early”, reactant-like, transition state and large β indicates a “late”, product-like, transition state. The equation may be further simplified by normalization to a per-reactive-site basis by including the number of sites available for each reaction. k1 k2
N1 = e xp N2
(
β ∆∆S ° R
)
exp
(
)
−β ∆∆H ° RT
(9)
For similar, almost identical, reactions it is not unreasonable to assume that the entropy of reaction would be the same and the exponential term exp[β(∆∆S ⬚)兾R] reduces to 1, resulting in eq 10: k1 k2
=
(
)
−β ∆∆H ° N1 exp N2 RT
(10)
Equation 10 enables the plot of enthalpy in Figure 2. The normalization allows the simple prediction of product yields for any hydrocarbon from its structure and the measured rewww.JCE.DivCHED.org
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activity ratios, that is, k1兾k2 from a standard compound such as isopentane, which contains primary, secondary, and tertiary C⫺H bonds. A closer look at the data presented in Table 2 provides further insight to the principles being elucidated here. First of all, since the ∆∆H ⬚ is the same, 14.6 kJ兾mol, for both chlorination and bromination (because it originates in the C⫺H bond strengths) an examination of the energies of activation, which are much smaller for the chlorinations, immediately suggests that β is smaller for the chlorination. This is equivalent to saying that the chlorination reactions have earlier transition states. If the difference in the reactivity, per site available, is attributed entirely to a difference in the energies of activation, then the value of β may be calculated both from the experimental Ea data and also from the selectivity ratio. For propane chlorination, the difference in the measured Ea’s, 1.3 kJ兾mol, and that calculated from the reactivity ratios, 3.3 kJ兾mol, are not very different and indicate values for β of 0.09 and 0.23, respectively. Realizing the errors inherent in the absolute measurement of energies of activation, it would seem that for the present purpose the value of β derived from the reactivity ratio would be more reliable. In any case a β of about 0.2 would be indicative of early transition states for the more exothermic reactions, chlorination. Bromination is a slower, more endothermic reaction, which would be expected to have a later transition state and be more selective. The only data available here are the relative reactivity data, which indicates that a secondary C⫺H bond is 82 times more reactive than a primary C⫺H bond. The experimental measurement of the Ea for the secondary reaction, 42.4 kJ兾mol, is a preliminary indication of a large β, but does not permit a calculation because the Ea for the reaction at the primary site has not been measured. If the reactivity ratio is used to calculate the ∆Ea, then the resulting value of 11.0 kJ兾mol indicates a value of β = 0.75, definitely a late transition state (10). These ideas are fraught with problems if one attempts to apply them to even slightly dissimilar reactions, for example, comparing the rate of an SN2 reaction with the corresponding E2 reaction for the same reactants; however, applied to similar reactions, they constitute the essence of our understanding of selectivity in reactions. In fact the inverse relationship between selectivity and reactivity may have universal applicability not only in chemistry, but also in areas of human activity beyond physical science. These ideas present the opportunity to stress the importance of thermodynamics to all students, but especially those who view themselves as organic or biochemists, that is, those with more qualitative inclinations. Isopentane Reaction Over the course of three terms, students in the organic laboratory course at WPI have been measuring the selectivity of the liquid-phase chlorination and bromination of isopentane5 (11). Because bromine is so selective, essentially one product is formed from the abstraction of the tertiary hydrogen of isopentane. Since the chlorination reaction is less selective as discussed above, it is possible to determine reactivity ratios for the chlorination of isopentane in the liquid phase. The reactivity ratios determined by three different
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Research: Science and Education Table 3. Results for the Selectivity of the Liquid Phase Chlorination of Isopentane with Chlorine Relative Reactivity per H-Atom (Standard Deviation)
Number of Exp
1°Aa
1°Ba
2°
3°
21
1.00
1.08(0.083)
3.06(0.116)
3.86(0.307)
14
1.00
1.04(0.081)
2.97(0.117)
3.73(0.307)
28
1.00
1.03(0.053)
2.91(0.171)
3.50(0.076)
a
The primary hydrogen atoms labeled A are the six hydrogens on the iso-methyl groups and the primary hydrogen atoms labeled B are the three hydrogens on the methyl group next to the secondary carbon.
classes during three different terms, involving 63 individual experiments and analyses, are presented in Table 3. The results indicate that chlorine atom is slightly less selective in the liquid phase, compared to the gas phase. The 1⬚B primary hydrogens appear to be slightly more reactive than the 1⬚A primary hydrogens. Although the difference is quite small, and may not be statistically significant, it might suggest a minor steric interaction in the transition state. The measured average reactivity of the secondary and tertiary hydrogens are 2.97 and 3.67, respectively, compared to the gasphase values of 3.8 and 5.0 (1). The liquid phase6 apparently reduces the selectivity of the chlorine atom by slowing the reaction at the secondary and tertiary sites compared to the primary site. This is consistent with a steric–solvent effect on the already structurally more crowded transition states for the reactions at the secondary and tertiary sites. Extensive speculation on this point is not justified by the data. Russell and coworkers, as well as others, have studied solvent effects in the selectivity of free radical reactions extensively (12, 13). Summary The reactions presented here are amenable to the collection of more (student) data, for chlorination and bromination reactions, which may elucidate other influences on selectivity (14). These experiments may utilize both intramolecular and intermolecular competitions. Discussions similar to those above serve as a vehicle for introducing students to some of the ways in which professional chemists think about chemistry and some of the subtleties of what makes chemical reactions behave as they do. Invariably students come away from these discussions with a finer appreciation of reaction dynamics and many contributions for other selectivity experiments, which they cannot wait to investigate. Acknowledgments I thank WPI for support of this work and Ladislav H. Berka for his meticulous review of this manuscript. Notes 1. Most current texts do not treat this topic in the depth presented here. The one exception to this statement is the comprehensive treatment of this subject in all of the editions of Morrison, R. T.; Boyd, R. N. Organic Chemistry; Allyn and Bacon Inc.: Boston. 2. The bond extension is defined here as the bond length in the transition state, minus the equilibrium bond length, all divided by the equilibrium bond length. 3. A reviewer has suggested that using a less expensive calcu1664
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lation method such as AM1 might make an interesting project for students in a computational chemistry course. 4. In functional group organic chemistry propylene may be converted to either 2-bromopropane or 1-bromopropane by choosing conditions referred to as Markovnikov or anti-Markovnikov, respectively. The anti-Markovnikov reaction occurs by a free radical chain mechanism that operates because the thermodynamics of both propagation steps are exothermic. This is not true for HCl, which does not give the anti-Markovnikov reaction. 5. Chlorinations generate chlorine by treating aqueous sodium hypochlorite with aqueous HCl and extracting the chlorine into the hydrocarbon with everything in the same centrifuge tube. Brominations use either neat bromine or an aqueous solution (~3%) of bromine. 6. The solvent is assumed to be isopentane because the reaction clearly occurs in the isopentane. Although not studied, the effect of the presence of the aqueous phase it is thought to be insignificant.
Literature Cited 1. Scala, A. A. J. Chem. Educ. 1972, 49, 573. 2. Horiuti, J.; Polanyi, M. Acta Physicochim. 1935, 2, 505. Ogg, R. A.; Polanyi, M. Trans. Faraday Soc. 1935, 31, 604. Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1938, 34, 91. 3. Hammond, G. S. J. Amer. Chem. Soc. 1955, 77, 334. 4. Leffler, J. E.; Grunwald, E. Rates and Equilibria of Organic Reactions; Wiley: New York, 1963. 5. Melander, L. The Transition State; Chemical Society Special Pub.: Washington, DC, 1962; No. 16, p 119. 6. Benson, S. W. Thermochemical Kinetics; Wiley: New York, 1968. Benson, S. W. Chem. Rev. 1969, 69, 279. Benson, S. W. J. Chem. Educ. 1965, 42, 502. 7. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen,W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998. 8. Trotman-Dickenson, A. F.; Milne, G. S. Tables of Bimolecular Gas Reactions NSRDS-NBS 9; National Bureau of Standards: Washington, DC, 1967. 9. Johnston, H. S.; Parr, C. J. Amer. Chem. Soc. 1963, 85, 2544. Previtali, C. M.; Scaiano, J. C. J. Chem. Soc., Perkin Trans. 1972, 1667, 1672. Scala, A. A.; Colangelo, J. P.; Hussey, G. E.; Stolle, W. T. J. Amer. Chem. Soc. 1974, 96, 4069. 10. For a strictly algebraic approach to these ideas see le Noble, W. J.; Miller, A. R.; Hamann, S. D. J. Org. Chem. 1977, 42, 338. 11. Mohrig, J. R.; Hammond, C. N.; Morrill, T. C.; Neckers, D. C. Experimental Organic Chemistry; W. H. Freeman and Co.: New York, 1998; pp 49–54. 12. Russell, G. A. J. Amer. Chem. Soc. 1958, 80, 4987, 4997, 5002. Russell, G. A.; Haffley, P. G. J. Org. Chem. 1966, 31, 1869. 13. Shaw, H.; Perimutter, H. D.; Gu, C.; Arco, S. D.; Quibuyen, T. O. J. Org. Chem. 1997, 62, 236. Sadeghipour, M.; Brewer, K.; Tanko, J. M. J. Org. Chem. 1997, 62, 4185. Dneprovskii, A. S.; Kuznetsov, D. V.; Eliseenkov, E. V.; Fletcher, B.; Tanko, J. M. J. Org. Chem. 1998, 63, 8860. Fletcher, B.; Suleman, N. K.; Tanko, J. M. J. Amer. Chem. Soc. 1998, 120, 11839. 14. Weiss, H. M.; Ganz, L. J. Chem. Educ. 1999, 76, 534.
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