Il gruppo di reazioni di cicloaddizione [4 + 2] conosciuto con il nome di reazione di Diels-Alder costituiscono il metodo di sintesi più versatile e largamente utilizzato. Ridotta ai suoi componenti di base, questa reazione è rappresentata dall'addizione dell'1,3-butadiene all'etene, come illustrato sotto. Le funzioni termodinamiche allo stato standard per questa reazione, può essere calcolato a partire dai calori di formazione e dalle entropie dei componenti.
La natura esotermica di questa reazione è il risultato della conversione di due deboli legami π in due legami σ più forti. L'entropia fortemente negativa rispecchia la formazione di una molecola di prodotto da due molecole reagenti indipendenti, e la necessità di disporre una conformazione del diene di tipo cis. Entrambe le cose, impongono un aumento dell'ordine nel sistema. Poiché il fattore entropia si oppone alla variazione di entalpia, il valore calcolato di ΔGº è più piccolo di ΔHº di una quantità pari a 298 ´ ΔSº/1000, ma rappresenta ancora una reazione fortemente esoergonica. Nonostante che la variazione complessiva di energia sia favorevole, questa reazione possiede un notevole valore dell'energia libera di attivazione, e richiede calore per avviarsi. A 200 ºC il TΔSº cresce a 20,6 kcal/mole, ma il ΔGº resta al valore fortemente esoergonico di -19,4 kcal/mole. La costante di equilibrio calcolata che favorisce la formazione del cicloesene è quindi maggiore di 1012. I sostituenti funzionali presenti sul dienofilo o sui reagenti dienici spesso abbassano la barriera di attivazione, ed in alcuni casi avvengono reazioni di addizione [4 + 2] spontanee. Esempi di questo genere includono: 1,3-butadiene + anidride maleica, 1,3-ciclopentadiene + propenale e 1,3-cicloesadiene + dimetil acetilendicarbossilato.
E' interessante notare che un processo di preparazione industriale dell'1,3-butadiene consiste nel far passare cicloesene gassoso su di una spirale metallica riscaldata al calor rosso (ca. 900 ºC), come mostrato nell'equazione seguente.
Questa reazione è l'inversa della cicloaddizione di Diels-Alder, dove le funzioni termodinamiche hanno segno opposto a quelle definite prima. Il successo di questo procedimento può essere spiegato in termini di funzioni di stato standard. A 900 ºC (1173 ºK), l'entropia è più elevata dell'entalpia, per cui il ΔG della decomposizione ha un valore esoergonico di -11.1 kcal/mole. Questo valore equivale ad una costante di equilibrio di 108 che favorisce il desiderato butadiene, facilmente separabile dall'etene grazie al suo più elevato punto di ebollizione (- 4,5 ºC ). Si dovrebbe notare che ΔH e ΔS non sono costanti a tutte le temperature, benché non subiscano grandi variazioni.
Un sistema di Diels-Alder che si studia più facilmente è la dimerizzazione dell'1,3-ciclopentadiene mostrato sotto. Il ΔHº di questa reazione è quasi 10 kcal/mole più basso di quello dell'addizione del butadiene + etene, riflettendo la tensione presente nel prodotto triciclico. Il ΔSº, d'altra parte, è di circa 10 eu più negativo come risultato dell'orientazione di tipo cis imposta al diene.
ΔHº = -18.4 kcal/mole ΔSº = -34 cal/ ºK mole ΔGº = -8.3 kcal/mole
ΔH‡ = +15 kcal/mole ΔS‡ = -32 cal/ ºK mole ΔG‡ = +24.5 kcal/mole
A temperatura ambiente, il ciclopentadiene dimerizza lentamente, con un valore esoergonico di ΔGº corrispondente ad una costante di equilibrio di 106, che favorisce la formazione del dimero. Il valore di ΔG‡ proibisce una reazione immediata, ma, tuttavia, un campione di ciclopentadiene puro dimerizza lentamente impiegando più di una settimana o due a temperatura ambiente. Di conseguenza, la breve durata del monomero, importante per le sintesi, richiede che esso sia preparato di fresco appena prima che venga utilizzato in una reazione. Si può facilmente isolare il monomero riscaldando la miscela appena al di sotto del punto di ebollizione del dimero (170 ºC) e raccogliendo il monomero stesso che presenta un punto di ebollizione più basso (42 ºC). Sebbene il ΔG della dimerizzazione resti a 170 ºC ancora negativo (-3.3 kcal/mole), esso è stato abbassato in modo sostanziale dal fattore TΔSº, permettendo al monomero di avere una concentrazione significativa all'equilibrio.
La disponibilità dei parametri relativi all'attivazione riguardanti questa reazione rende possibile l'esplorazione di altri dettagli circa il percorso di reazione. La stereospecificità della reazione di Diels-Alder sottintende una trasformazione in un singolo stadio, ed il carattere esotermico della reazione prevede un profilo del grafico dell'entalpia simile a quello mostrati sulle destra. Il postulato di Hammond, che utilizza ΔHº quale indicatore, suggerisce che lo stato di transizione rassomiglierebbe più ai reagenti che ai prodotti. Tuttavia, la grandezza paragonabile di ΔSº e ΔS‡ ed il loro segno, richiede che lo stato di transizione abbia una struttura molto simile al dimero prodotto. Questa incongruenza rappresenta un avvertimento riguardante il postulato di Hammond che fu inteso per essere utilizzato per profili di reazioni implicanti intermedi ad alta energia, ed è probabilmente inappropriato il tenerne conto per reazioni di sostituzione SN2 a stadio singolo e per le addizioni di Diels-Alder.
Una reazione cheletropica è definita come un processo in cui due legami sigma, diretti ad un singolo atomo di un anello, si formano o si rompono di concerto. Il numero di legami π aumenta o diminuisce di 1 unità, a seconda del verso della reazione (formazione dell'anello o apertura dell'anello). Un esempio è dato dalla reazione di addizione del biossido di zolfo all'1,3-butadiene, mostrato qui.
ΔHº = –16,5 kcal/mole
Il verso intrapreso da questa reazione dipende dalla temperatura. Al di sotto di 100º C, l'equilibrio favorisce il prodotto di addizione, con un calore di reazione standard di –16,5 kcal/mole. Al di sopra dei 100º C, il solfone ciclico si decompone in 1,3-butadiene. La costante di equilibrio è vicina all'unità, a 100º C. Se accettiamo che ciò sia vero, la variazione di entropia si calcola facilmente con le seguenti equazioni:
ΔGº = – RTlnK = – 2,303RTlogK
ΔGº = ΔHº – TΔSº
Poiché ΔG = 0 quando Keq = 1, ΔSº = – 16,500/373 = – 44,24 cal/ ºK mole. A 25º C il ΔGº = -3,3 kcal/mole, corrispondente a Keq = 270.
The reaction of carboxylic acids and alcohols to form esters is one of the best known transformations in organic chemistry. The preparation of ethyl acetate outlined in the following equation is a typical example. This reaction is modestly exothermic, and the standard enthalpy of reaction has been measured. Calculated values for the fundamental thermodynamic parameters are shown below the equation.
CH3CO2H + C2H5OH CH3CO2C2H5 + H2O
ΔHº = –0.89 kcal/mole
ΔHº = –0.80 kcal/mole
ΔSº = +1.6 cal/ ºK mole
ΔGº = –1.28 kcal/mole kcal/mole
(calculated)
This esterification reaction is very slow unless catalyzed by a strong acid. The calculated free energy change is –1.28 kcal/mole, which corresponds to a Keq = 8.7. In order to push the yield of ester beyond the 90% predicted for equilibrium, water is removed during the reaction.
Compare the ethyl acetate esterification reaction with the lactonization of 4-hydroxybutanoic acid shown below. The experimentally measured enthalpy of reaction is a mildly endothermic +1.08 kcal/mole, which is close to the value calculated from heats of formation. The nearly 2.0 kcal/mole increase in ΔHº reflects ring strain in the lactone, which is presumably a combination of angle, eclipsing and other conformational strains. In general, esters prefer to adopt a Z-conformation of the ester function, and this is not possible for six-membered and smaller rings.
ΔHº = +1.08 kcal/mole
ΔHº = +1.10 kcal/mole
ΔSº = +13.9 cal/ ºK mole
ΔGº = –3.1 kcal/mole kcal/mole
Based on the endothermic shift in the lactonization reaction, one might expect it to be a slower and less complete process than intermolecular esterification. In fact, the opposite is true. Pure 4-hydroxybutyric acid is difficult to make and purify, and it tends to lactonize spontaneously and completely once formed. The intramolecular nature of lactonization explains the increase in rate, but does not account for lactone dominance at equilibrium. For this we must consider the free energy change in this lactonization:
ΔGº = +1.1 – (298 * 13.9/1000) = –3.1 kcal/mole
As shown, a large positive entropy factor opposes the unfavorable enthalpy component, yielding an exergonic ΔGº, which corresponds to a Keq =190. Thus, quantitative lactonization of the 4-hydroxybutyric acid should be expected.
A thermodynamic analysis of the lactonization of 5-hydroxypentanoic acid, n=3 in the formulas written below, leads to similar conclusions. Although the strain in the six-membered lactone is slightly higher than that of the five-membered lactone, the ΔGº for lactonization is still exergonic, and all efforts to prepare the hydroxy acid itself have failed. Analogous lactonization of 3-hydroxypropanoic acid, n=1 in the following equations, forms a highly strained four-membered ring, so it is not surprising that this cyclization does not proceed spontaneously. A ΔHº of +23 to 25 kcal/mole testifies to the increased ring strain, and an estimated ΔSº of 40 to 43 cal/ ºK mole does not reduce the enthalpy term by more than 5.5 kcal/mole. Consequently, the ΔGº for lactonization is strongly endergonic at +17 to +19 kcal/mole, and this hydroxy acid will most likely dimerize if forced to react.
Terminal hydroxy acids having carbon chains longer than six (n > 3 above) may either lactonize or polymerize. With the exception of seven and eight-membered ring compounds, these lactones are not particularly strained, and are able to adopt Z-like ester conformations. The rate of lactonization is small due to the lower probability of conformations in which the hydroxyl and carboxyl groups are near each other in space (a negative entropy factor). If the concentration of hydroxy acid is high, dimerization and polymerization is favored. At low concentrations of hydroxy acid, lactonization becomes competitive.
Reactions which involve the formation of charged atoms and molecules are usually extremely endothermic in the gas phase, but may become spontaneous in certain solvents. If ions are formed from a neutral compound, as when NaCl is dissolved in water, the oppositely charged cations and anions naturally attract each other, so formation of a dispersed homogeneous solution might appear to be energetically unfavorable. To achieve charge separation of ions in solution, two solvent characteristics are particularly important. The first is the ability of solvent molecules to orient themselves between ions so as to attenuate the electrostatic force one ion exerts on the other. This characteristic is a function of the polarity of the solvent. Solvent polarity has been defined and measured in several different ways, one of the most common being the dielectric constant, ε. High dielectric constant solvents such as water (ε=80), dimethyl sulfoxide (ε=48) & N,N-dimethylformamide (ε=39), usually have polar functional groups, and often high dipole moments. When subject to the electric field of an ion, such polar molecules orient themselves to oppose the field, and in so doing they limit its reach. Because of electrostatic attraction between these polar groups, the boiling points of these solvents are generally higher than those of similarly sized nonpolar solvents, such as diethyl ether (ε=4.3) and hexane (ε=1.9). Solvents that have relatively acidic hydrogen atoms (e.g. O-H & N-H) are called protic. Because their functional groups are made up of polar covalent bonds, protic solvents are often polar as well. A list of common protic and aprotic solvents is provided here. The dielectric constants provide a measure of solvent polarity.
Protic Solvents
Aprotic Solvents
Compound
Boiling Pt.
Dielectric Const.
The second factor important in the stabilization of ions, which also resists their intimate recombination, is called solvation. This refers to the ability of solvent molecules to stabilize ions by encasing them in a sheath of weakly bonded solvent molecules, thus somewhat dispersing the electrical charge. Anions are best solvated by hydrogen-bonding solvents; cations are generally solvated by binding to nucleophilic sites on a solvent molecule Two dimensional diagrams illustrating the primary solvation shell about Na(+) and Cl(–) are shown here. The water dipoles are drawn as red arrows, and partial charges are noted. Additional water molecules are oriented in secondary and tertiary layers about the ions.
From this description of ion formation in solution, it should be clear that both enthalpy and entropy factors will be important to the outcome of an ionization process. Thus solvation stabilizes and insulates an ion, helping the enthalpic change, whereas the same solvation adds order and structure to the ionic species at the cost of lowering entropy. The outcome of these interactions is discussed below for two typical salts.
NaCl + H2O Na(+) + Cl(-)
ΔHº = +1.3 kcal/mole ΔSº = +10.3 cal/cal/ ºK mole ΔGº = –1.3 kcal/mole
CaF2 + H2O Ca(2+) + 2 F(-)
ΔHº = +1.5 kcal/mole ΔSº = –36.3 cal/cal/ ºK mole ΔGº = +12.3 kcal/mole
Although these two inorganic salts have similar standard enthalpies of solution in water, their standard entropies are quite different. One might expect this entropy change to be positive, since a single molecule in the solid state produces two or more ionic species, accompanied by an increase in system disorder. However this argument fails to consider the ordering of solvent molecules taking place in the solvation of these ions. Because of their greater charge density, small ions and highly charged ions, such as F– and Ca2+, require greater solvation than large or singly charged ions, such as Na+ or Cl–. The overall entropy change for solution of NaCl is positive, reflecting the increased disorder of ionization, but the entropy change for CaF2 solution is strongly negative thanks to the solvation shell structure required by the resulting ions. These different entropy changes are incorporated in the free energy of solution, which is exergonic for NaCl, but endergonic for CaF2. The result is dramatic. Sodium chloride is quite soluble in water at room temperature (36g per 100g water), but calcium fluoride is nearly insoluble (0.0016g per 100g water).
Among the most commonly observed characteristics of reactions are their rates and their equilibrium constants (if observable). In this respect, the influence of substituents on reactivity often provides information about a reaction mechanism , and has been the subject of extensive study. For example, the acidity constants for some substituted benzoic acids range from 3.4 * 10–5 for the para-methoxy compound to 6.7 * 10–3 for the ortho-nitro compound. A similar, but not identical, increase in the rate of base catalyzed ester hydrolysis has been noted, with the para-nitro compound reacting over 103 times faster than the para-methoxy compound.
Now these differences in reactivity may be attributed to perturbations of ΔGº and/or ΔG‡ by a combination of inductive, resonance and steric effects. If the same factors are responsible for the substituent effects in various different reactions, the rates and or equilibria should change in a proportional manner. Indeed, the exponential relationship of free energy to rate or equilibrium constants, as shown on the right, suggests that logarithmic plots should demonstrate this proportionality. To investigate this possibility, logarithms of the rate and equilibrium constants noted above for substituted benzoic acids and their ethyl esters were graphed as shown below. The data points are represented by small circles. It is immediately apparent that the rates and equilibria of the meta and para substituted compounds correlate well (the green line), but the ortho substituted compounds do not. This is not entirely unexpected, since the ortho substituents lie close to the reaction site and each may interact with different intermediates or transition states in many different ways. An analysis of factors that influence the acidity of ortho-substituted benzoic acids is presented elsewhere.
Linear free energy plots of the kind shown here are called Hammett Plots in recognition of Louis Hammett (Columbia University), who first employed this analysis of organic reactions. Hammett selected the Ka's of substituted benzoic acids as a reference system, and defined a substituent constant σ:, based on the log of the ratio of a substituted benzoic acid's acidity (K) to that of benzoic acid itself (Ko).
σ = log(K/Ko)
A table of these σ: constants for different substituents at meta and para locations on a benzene ring is provided here. An examination of the sign and magnitude of these substituent constants is instructive, particularly in context with the influence they have on electrophilic aromatic substitution. Electron withdrawing substituents increase the acidity of benzoic acid (K > Ko) and will therefore have positive σ constants. Electron donating substituents will decrease the acidity, resulting in a negative σ. Inductive and resonance effects do not necessarily act in the same direction, so many σ values are small. Many of the substituent groups listed in the section on the left have negative σ constants and are electron donating. The hydroxy and methoxy substituents change sign depending on their location, illustrating the inductive withdrawal of electrons (meta) and strong resonance electron donation (para). The substituent groups listed in the right hand section are all strongly electron withdrawing, both by inductive and resonance influence. When there is strong resonance interaction between a substituent group and the reaction site, deviations from a Hammett equation plot may occur. For example, the acidity of phenols or anilinium cations is enhanced by para-nitro, cyano and carbonyl substituents to a greater degree than predicted by their σ values. Likewise, electron donating para-substituents such as NH2 and OR facilitate benzyl cation formation to an exceptional degree. These deviations have led to the formulation of specialized σ constants ( e.g. σ - and σ+ among others ) for specific applications. These will not be discussed here.
Substituent
meta σ
para σ
Since the substituent constants are a logarithmic function of benzoic acid Kas, the previous log-log plot of ethyl benzoate hydrolysis rates can be reproduced as a plot of rates against σ. Such a plot is shown below, and the slope of the best fitting correlation line is a characteristic of the specific reaction (and its conditions) for which rate or equilibrium data has been determined. Hammett called this slope the reaction constant, ρ.
Reaction constants for a large group of reactions involving substituted benzyl or benzoyl functions have been measured. Since the acidity of benzoic acids serves as a reference, the ρ for this reaction is 1.00. Some additional reaction constants are listed in the following table.
Reaction
Equilibrium or Rate
ρ
The following diagram shows rate or equilibrium plots against σ for three different reactions. The slope of each best-fit line provides the ρ for that reaction. These relationships have been consolidated by a simple mathematical formula, known as the Hammett Equation. If the ρ and Ko (or ko) of a reaction are known, then the K (or k) for a substituted analog is easily calculated from the σ for the substituent.
log(K/Ko) or log(k/ko) = σ ρ
Reaction constants are useful indicators of the electron demands at the reaction site. Anilinium ion acidity, shown by the green line above, has a large positive ρ, indicating enhancement by electron withdrawing substituents. Phenolate anion alkylation, shown by the blue plot has a moderate negative ρ and is retarded by electron withdrawing substituents, but accelerated by electron donation. A ρ near zero, as in the acid-catalyzed benzamide hydrolysis reported in the table, indicates a reaction that is relatively insensitive to meta or para ring substitution. Care must be taken to recognize all reaction variables, since ρ values are sensitive to both solvent and temperature changes. Thus, the ρ for anilinium acidity increases from 2.77 in pure water to 3.57 in 70% aqueous dioxane, both at 25 ºC. Saponification of ethyl benzoate in 85% ethanol at 25 ºC has a ρ = 2.54, which drops to 2.32 at 50 ºC in the same solvent. Interestingly, acid-catalyzed hydrolysis of this ester in 60% acetone at 100 ºC has a rather small ρ = 0.11, similar to that for acid-catalyzed benzamide hydrolysis. Base-catalyzed benzamide hydrolysis in water at 100 ºC has a ρ = 1.1. The near zero ρ for acid-catalyzed ester and amide hydrolysis probably reflects the intermediacy of a conjugate acid species, the concentration of which would be increased by para-electron donating substituents.