rotational conformations of ethane
In organic chemistry, the word structure has a specific meaning; It designates the order in which the atoms are joined to each other. A structure does not necessarily specify the exact shape of a molecule because rotation about single bonds could lead, even for a molecule as simple as ethane, to an infinite number of different arrangements of the atoms in space. These are called conformations and depend on the angular relationship between the hydrogens on each carbon. Two extreme arrangements are shown in Figure 2.3.
In end-on views of the models, the eclipsed conformation is seen to have the hydrogens on the forward carbon directly in front of those on the back carbon. The staggered conformation has each of the hydrogens on the forward carbon set between each of the hydrogens on the back carbon. It has not been possible to obtain separate samples of ethane which correspond to these or intermediate arrangements because actual ethane molecules appear to have essentially "free rotation" about the single bond joining the carbons.
Free, or at least rapid, rotation is possible around all single bonds, except under special circumstances, as when the groups attached are so large that they cannot pass by one another, or when the attached groups are connected together by chemical bonds (e.g., in ring compounds). For ethane and its derivatives, the staggered conformation is always more stable than the eclip
sed conformation because in the staggered conformation the atoms are as far away from one another as possible and offer the least interaction.
Many problems in organic chemistry require consideration of structures in three dimensions, and it is very helpful to be able to use ball-and-stick models for visualizing the relative positions of the atoms in space. Unfortunately, we are very often forced to communicate three-dimensional concepts with drawings in two dimensions, and not all of us are equally gifted in making or visualizing such drawings. Obviously, communication by means of drawings such as the ones shown in Figure 2.3 would be impractically difficult and time consuming-some form of abbreviation is necessary.
Two styles of abbreviating the eclipsed and staggered conformations of ethane are shown in Figure 2.4. Of these, we strongly favor the " sawhorse " convention because, although it is perhaps the hardest to visualize and the hardest to master, it is the only three-dimensional convention which is suitable for complex compounds, particularly natural products. With the sawhorse drawings, we always consider that we are viewing the molecule slightly from above and from the right, just as we have shown in Figure 2.4.
space-jilling models
Ball-and-stick models of molecules are very useful'for visualizing the relative positions of the atoms in space but are unsatisfactory whenever we also want to show how large the atoms are. Actually, atomic radii are so large relative to the lengths of chemical bonds that when a model of a molecule such as chloromethane is constructed with atomic radii and bond lengths, both to scale, the bonds connecting the atoms are not clearly evident. Nonetheless, this type of "space-filling" model, made with truncated balls held together with snap fasteners, is widely used to determine the possible closeness of approach of groups to each other and the degree of crowding of atoms in various arrangements (see Figure 2.5).
A defect of both the ball-and-stick and space-filling models is their motionless character. The atoms in molecules are in constant motion, even at absolute zero, and the frequencies of these vibrations give valuable information about molecular structure and shape. This subject is considered in greater detail in the section on infrared spectroscopy (Section 7.4).
chemical reactions of the C1 and C2 hydrocarbons
Two of the four simple hydrocarbons we have been considering are saturated (contain only single bonds) and two are unsaturated (contain multiple bonds). All four are rather similar physically, being low-boiling, colorless gases that are insoluble in water, Chemically, however, they are rather different, the unsaturated compounds being much the more reactive. The three kinds of reactions we shall consider in the following sections are combustion (shared by all hydrocarbons), substitution reactions (more important for saturated compounds), and addition reactions (confined to the unsaturated compounds).
combustion
The rapid reaction of a chemical substance with oxygen to give an oxide, usually carbon dioxide, is called combustion. The burning of a candle, the explosion of a gasoline-air mixture in the cylinder of an automobile engine, and the oxidation of glucose in a living cell are all examples of this process. In all of these cases, the result is liberation of energy.
Water and carbon dioxide, the products of complete combustion of organic compounds, are very stable substances, relative to oxygen and hydrocarbons. This means that large amounts of energy are given out when combustion occurs. Most of the energy of combustion shows up as heat, and the heat liberated in a reaction occurring at constant pressure is called the enthalpy change, AH, or simply heat of reaction. By convention, AH is given a negative sign when heat is evolved (exothermic reaction) and a positive sign when heat is absorbed (endothermic reaction). Some examples are given below, with the state of the reactants and products being indicated by subscripts (g) for gas and (s) for solid.
For each of these examples, AH can be visualized as the total heat given off when a mixture of gaseous hydrocarbon and excess oxygen at 1 atm pressure is exploded in a bomb at 25", the contents allowed to expand or contract by
You can see that the amount of heat liberated per gram of fuel is not greatly different in the case of the four hydrocarbons, but is much lower for the compound C6HI2O6 (glucose), which is already in a partly oxidized state. In the next section, we shall consider how you can estimate heats of reaction, with particular reference to combustion.
A. ESTIMATION OF HEAT OF COMBUSTION OF METHANE
The experimental value for the heat of combustion of methane obtained as described above does not depend on speed of the reaction. Slow oxidation of methane over many years would liberate as much heat as that obtained in an explosion, provided the reaction were complete in both cases, and the initial and final temperatures and pressures are the same. At 25", combustion of each mole of methane to carbon dioxide and water vapor produces 192 kcal of heat.
We can estimate the heat of this and many other reactions by making use of the bond energies given in Table 2.1. Bond energies for diatomic molecules represent the energy required to dissociate completely the gaseous substances to gaseous atoms at 25" or, alternatively, the heat evolved when the bonds are formed from such atoms. For polyatomic molecules the bond energies are average values. They are selected to work with a variety of molecules and reflect the fact that the bond energy of any particular bond is likely to be influenced to some extent by other groups in the molecule.
It turns out that what is called conjugation (alternation of double and single bonds) can have a relatively large effect on bond strengths. We will see in Chapter 6 that this effect normally operates to increase bond energies; that is, the bonds are harder to break and the molecule is made more stable. However, the effects of conjugation are so special that they are not normally averaged into bond energies, but are treated separately instead.
To calculate AHfor the combustion of methane, first we calculate the energy to break the four C-H bonds as follows (using the average value of 99 kcal for the energy of a C-H bond):
Then 119 kcal is used for the energy required to cleave a molecule of oxygen (rounded off from the exact value of 1 19.1) :
The net of these AH changes is 396 f 238 - 384 - 444 = - 194 kcal, which is reasonably close to the value of 191.8 kcal for the heat of combustion of methane determined experimentally.
The same type of procedure can be used to estimate AH values for many other kinds of reactions of organic compounds in the vapor phase at 25'.
Moreover, if appropriate heats of vaporization or solution are available, it is straightforward to compute AH for liquid, solid, or dissolved substances.
The steps shown above are not intended to depict the actual mechanism of methane combustion. The overall heat of reaction is independent of the way that combustion occurs and so the above calculations are just as reliable as (and more convenient than) those based on the actual reaction path. Some of the general questions posed by the reaction mechanism are taken up in Section 2.5B.
substitution reactions of saturated hydrocarbons
Of the four simple hydrocarbons we are considering in this chapter, only ethene and ethyne are unsaturated, meaning they have a multiple bond to which reagents may add. The other two compounds, methane and ethane, have their atoms joined together by the minimum number of electrons and can react only by substitution-replacement of a hydrogen by some other atom or group.
There are only a few reagents which are able to effect the substitution of a hydrogen atom in a saturated hydrocarbon (an alkane). The most important of these are easily the halogens, and the mechanism and energetics of halogen substitution will be discussed in detail later. (Although the hydrogen atoms in alkenes such as ethene and alkynes such as ethyne are also subject to substitution, these reactions under normal conditions tend to be much slower than addition to the multiple bond and are therefore usually not important when compared to addition.)
A complete description of a chemical reaction would include the structures of the reactants and products, the position of equilibrium of the reaction, its rate, and its mechanism. These four characteristics fall nicely into two groups. The equilibrium constant for a reaction depends only on the energies of the reactants and products, not on the rate of reaction nor on the mechanism. The rate of the reaction, on the other hand, is intimately related to the reaction mechanism and, in particular, to the energy of the least stable state along the reaction path. The subjects of equilibrium constants and reaction rates are treated in the next two sections.
A. EQUILIBRIUM CONSTANTS In Section 2.4A we considered bond energies and showed how heats of reaction could be calculated. Reactions which give out large amounts of heat (highly exothermic processes) usually proceed to completion. Consequently it is reasonable to ask if the equilibrium constant, K, for a reaction is determined only by the heat of reaction, AH. The study of thermodynamics tells us that the answer to this question is no. The equilibrium constant is, in fact, a function of the quantity free energy (AG), which is made up of AH and a second quantity called entropy (AS). These relations are
AG = - RTln K
AG=AH-TAS
AG = Free energy change for the reaction
R = The gas constant (1.986 cal/deg mole)
T = Temperature in degrees Kelvin
K = Equilibrium constant
AH = Heat of reaction
AS = Entropy of reaction
The heat of reaction term, AH, is readily understood but the meaning of the entropy term, AS, is more elusive. It is related to the difference in the numbers of vibrational, rotational, and translational states available to reactants and products (see Sections 7.3 and 7.4). As we have seen, molecules are not lifeless objects but are in constant motion, each undergoing vibrational, rotational, and translational motions. These states of motion are quantizedthat is, they can have certain energies only. The more of these states or degrees of freedom available to a molecule, the higher its entropy and the more favorable the equilibrium constant for its formation. Thus, a positive entropy change in a reaction tends to make the free energy change more negative and increase the equilibrium constant, hence moving the reaction toward completion.
In simple terms, a negative entropy change (a AS that is unfavorable for the reaction as written) means that the freedom of the atoms in the products (including the environment) is restricted more than in the reactants. A positive entropy change (favorable for the reaction as written) means a greater freedom in the products.
In practice, reactions which are fairly exothermic (-AH > 15 kcal/mole) almost always proceed far to the right; that is, K is large. An unfavorable entropy term will seldom overcome such a AH value at ordinary temperatures because a AG that is negative by only a few kilocalories per mole will still have a large K. This follows from the logarithmic relation between AG and K. The thermodynamic values for the chlorination of methane are
(calculated from above value of AG and the equation AG = - RT ln K).
In some cases, you can experimentally check an equilibrium constant calculated as above by measuring the concentrations of reactants and products when the system has come to equilibrium. Here, however, K is so large that no trace of the reactants can be detected at equilibrium, a situation often encountered in organic chemistry.
Suppose bond energy calculations for a certain reaction indicate that the equilibrium strongly favors the desired products. Can we be assured that the reaction is a practical one to perform in the laboratory? Unfortunately, no, because first, side reactions may occur (other reactions which also have favorable equilibrium constants); and second, the rate of the desired reaction may be far too low for the reaction to be a practical one.
In the chlorination of methane, whose equilibrium constant we have seen overwhelmingly favors the products, the first of these two matters of concern is whether the substitution process may proceed further to give dichloromethane, CH2C12.
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In fact, given sufficient chlorine, complete substitution may occur to give tetrachloromethane (carbon tetrachloride), CCI, . Indeed, if the rate of chlorination of chloromethane greatly exceeds that of the first step, methane chlorination, there will be only traces of the monosubstituted product in the mixture at any time. Using an excess of methane will help encourage monosubstitution only if the rates of the first two chlorination steps are comparable.
With compounds and reagents that are more complex than methane and chlorine, you can imagine side reactions taking other forms. When devising synthetic schemes you must always consider possible side reactions that may make the proposed route an impractical one.
The second question about the chlorination of methane that is left unanswered by the calculation of the equilibrium constant is whether or not the reaction will proceed at a reasonable rate. The subject of reaction rates is bound up intimately with the question of reaction mechanism and this subject is explored in the next section.
B. REACTION RATES AND MECHANISM
Despite the enormously favorable equilibrium constant for the formation of chloromethane and hydrogen chloride from methane and chlorine, this reaction does not occur at a measurable rate at room temperature in the dark. An explosive reaction may occur, however, if such a mixture is irradiated with strong violet or ultraviolet light. Evidently, light makes possible a very effective reaction path by which chlorine may react with methane.
Any kind of a theoretical prediction or rationalization of the rate of this or other reactions must inevitably take into account the details of how the reactants are converted to the products-in other words, the reaction mechanism. One possible path for methane to react with chlorine would have a chlorine molecule collide with a methane molecule in such a way that hydrogen chloride and chloromethane are formed directly (see Figure 2-6). The failure of methane to react with chlorine in the dark at moderate temperatures is strong evidence against this path, and indeed four-center reactions of this type are rather rare.
If concerted four-center mechanisms for formation of chloromethane and hydrogen chloride from chlorine and methane are discarded, the remaining possibilities are all stepwise mechanisms. A slow stepwise reaction is dynamically analogous to the flow of sand through a succession of funnels with different stem diameters. The funnel with the smallest stem will be the most important bottleneck, and if its stem diameter is much smaller than the others, it alone will determine the flow rate. Generally, a multistep chemical reaction will have a slow rate-determining step (analogous to the funnel with the small stem) and other, relatively fast steps which may occur either before or after the slow step. The prediction of the rate of a reaction proceeding by a stepwise mechanism then involves, as the central problem, a decision as to which step is rate determining and an analysis of the factors which determine the rate of that step.
A possible set of steps for the chlorination of methane follows:
Reactions (1) and (2) involve dissociation of chlorine into chlorine atoms, and the breaking of a C-H bond of methane to give a methyl radical and a hydrogen atom. The methyl radical, like chlorine and hydrogen atoms, has one odd electron not involved in bond formation. Atoms and free radicals are usually highly reactive, so that formation of chloromethane and hydrogen chloride should proceed readily by (3) and (4). The crux then will be whether steps (1) and (2) are reasonable under the reaction conditions.
Our plan in evaluating the reasonableness of these steps is to determine how much energy is required to break the bonds. This will be helpful because, in the absence of some external stimulus, only collisions due to the usual thermal motions of the molecules can provide the energy needed to break the bonds. Below 10Q°C, it is very rare indeed that thermal agitation alone can supply sufficient energy to break any significant number of bonds stronger than 30 to 35 kcal/mole. Therefore, we can discard as unreasonable any step, such as the dissociation reactions (1) and (2), if the AH'S for breaking the bonds are greater than 30 to 35 kcal.
In most reactions, new bonds form as old bonds break and it is usually incorrect to consider bond strengths alone in evaluating reaction rates. (The appropriate parameters, the heat of activation, AHx, and the entropy of activation, ASS, are discussed in Section 8.9.) However, the above rule of thumb of 30 to 35 kcal is a useful one for thermal dissociation reactions such as (1) and (2), and we can discard these as unreasonable if their heats of dissociation are greater than this amount.
For reaction (1) we can reach a decision on the basis of the CI-C1 bond energy from Table 2.1, which is 58.0 kcal and clearly too large to lead to bond breaking as the result of thermal agitation at or below 100". The C-H bonds of methane are also too strong to break at 100" or less.
The promotion of the chlorination reaction by light must be due to light being absorbed by one or the other of the reacting molecules to produce a highly reactive species. Since a Cl-C1 bond is much weaker than a C-H bond, it is reasonable to suppose that the former is split by light to give two chlorine atoms. We shall see in Section 7.3 that the energy which can be supplied by ultraviolet light is high enough to do this; photolytic rupture of the more stable C-H bonds requires radiation with much higher energy. It should now be clear why a mixture of methane and chlorine does not react in the dark at moderate temperatures.
Once produced, a chlorine atom can remove a hydrogen atom from a methane molecule and form a methyl radical and a hydrogen chloride molecule (as will be seen from Table 2.1, the strengths of C-H and C1-H bonds are quite close) :
The methyl radical resulting from the attack of atomic chlorine on a hydrogen of methane can then remove a chlorine atom from molecular chlorine and form chloromethane and a new chlorine atom:
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An important feature of the mechanistic sequence postulated for the chlorination of methane is that the chlorine atom consumed in the first step is replaced by another chlorine atom in the second step. This type of process is
called a chain reaction since, in principle, one chlorine atom can induce the chlorination of an infinite number of methane molecules through operation of a "chain " or cycle of reactions. In practice, chain reactions are limited by so-called termination processes, where chlorine atoms or methyl radicals are destroyed by reacting with one another, as shown in these equations:
Chain reactions may be considered to involve three phases. First, chain initiation must occur, which for chlorination of methane is activation and conversion of chlorine molecules to chlorine atoms by light. In the second phase, the chain-propagation steps convert reactants to products with no net consumption of atoms or radicals. The propagation reactions occur in competition with chain-terminating steps, which result in destruction of atoms or radicals.
The two chain-termination reactions for methane chlorination as shown might be expected to be exceedingly fast, because they involve combination of unstable atoms or radicals to give stable molecules. Actually, combination of chlorine atoms does not occur readily in the gas phase because there is almost no way for the resulting molecule to lose the energy of reaction except by redissociating or colliding with some third body, including the container wall. The products in the other termination steps shown above, by contrast, can take care of this energy by redistributing it as vibrational excitation of their C-H bonds. Collisions with other molecules then disperse the excess vibrational energy throughout the system in the form of heat.
If much chain propagation is to occur before the termination steps destroy the active intermediates the propagation steps must themselves be very fast. However, propagation is favored over termination when the concentrations of radicals (or atoms) are low because then the chance of two radicals meeting (termination) is much less likely than encounters of radicals with molecules which are present at relatively high concentrations (propagation).
The overall rates of chain reactions are usually slowed significantly by substances which can combine with atoms or radicals and convert then into species incapable of participating in the chain-propagation steps. Such substances are often called radical traps, or inhibitors. Oxygen acts as an inhibitor in the chlorination of methane by rapidly combining with a methyl radical to form the comparatively stable (less reactive) peroxymethyl radical, CH300.. This effectively terminates the chain. Under favorable conditions, the methane-chlorination chain may go through 100 to 10,000 cycles before termination occurs by free-radical or atom combination. The efficiency (or quantum yield) of the reaction is thus very high in terms of the amount of chlorination that occurs relative to the amount of the light absorbed.
C. REACTIVE INTERMEDIATES
We have seen that the chlorination of methane proceeds stepwise via highly unstable intermediate species such as chlorine atoms (C1.) and methyl radicals (CH, .). Are there other molecules or ions which are too unstable for isolation but which might exist as transient intermediates in organic reactions? If we examine simple C, species we find the possibilities:
Each of these C, entities possesses some serious structural defect that makes it much less stable than methane itself. The methyl radical is unstable because it has only seven electrons in its valence shell. It exists for only brief periods of time at low concentrations before dimerizing to ethane:
The methyl cation, CH3,@, is an example of a carbonium ion. This species has only six valence electrons; moreover, it carries a positive charge. Methyl cations react with most species that contain an unshared pair of electronsfor example, a chloride ion, CH,@ + Cl° + CH3-Cl. We shall see later, however, that the replacement of the hydrogens of the methyl with other groups, such as CH3- or C6,H5,-, can'provide sufficient stability to make carbonium ions important reaction intermediates. In fact, they can sometimes be isolated as stable salts (Section 24.5). Having only three pairs of electrons about the central carbon atom, carbonium ions tend toward planarity with bond angles of 120". This gives the maximum separation of the three pairs of electrons.
The methyl anion, CH3,@, does possess an octet of electrons but bears a negative charge, for which it is ill suited by virtue of carbon's low electronegativity. Such carbanions react rapidly with any species that will accept a share in an electron pair-any proton donor, CH3,@% CH4, , for example. We shall see later that carbanions can be stabilized and rendered less reactive by having strongly electron-withdrawing groups, such as nitro (-NO2), attached to them, and we shall encounter such carbanions as reaction intermediates in subsequent chapters. Carbanions have four pairs of electrons about the central carbon atom. The mutual repulsion of the electrons gives the ion a pyramidal shape. The methyl anion, for example, is isoelectronic with ammonia and is believed to have a similar shape:
The nonbonding electron pairs in each of the above molecules are expected to repel the bonding pairs more than the bonding pairs repel each other (see pp. 8-9 and Exercise 1.1 1). This accounts for the fact that the H-N-H bond angles in ammonia (Section 1.2A) are slightly less than the tetrahedral value
Methylene, :CH2, like a carbonium ion, possesses only a sextet of electrons in its valence shell and tends to react rapidly with electron donors(Section9.7). It is important to be able to deduce the overall charge of a species from its
negatively charged because the carbon has an unshared electron pair in addition to its half-share of the six bonding electrons, giving it effective possession of five valence electrons, one more than that of a neutral carbon atom.
