Halogenation of Alkanes. Energies and Rates of Reactions

the economies of the highly industrialized nations of the world are based in large part on energy and chemicals produced from petroleum. Although the most important and versatile intermediates for conversion of petroleum to chemicals are compounds with double or triple bonds, it also is possible to prepare many valuable substances by substitution reactions of alkanes. In such substitutions, a hydrogen is removed from a carbon chain and another atom or group of atoms becomes attached in its place.

A simple example of a substitution reaction is the formation of chloromethane and chlorine

CH4+Cl2→CH3Cl+HCl   (4.5.1)

the e quation for the reaction is simple, the ingredients are cheap, and the product is useful. However, if we want to decide in advance whether such a reaction is actually feasible, we have to know more. Particularly, we have to know whether the reaction proceeds in the direction it is written and, if so, whether conditions can be found under which it proceeds at a convenient rate. Obviously, if one were to mix methane and chlorine and find that, at most, only 1% conversion to the desired product occurred and that the 1% conversion could be achieved only after a day or so of strong heating, this reaction would be both too unfavorable and too slow for an industrial process

One way of visualizing the problems involved is with energy diagrams, which show the energy in terms of some arbitrary reaction coordinate that is a measure of progress between the initial and final states (Figure 4-4). Diagrams such as Figure 4-4 may not be familiar to you, and a mechanical analogy may be helpful to provide better understanding of the very important ideas involved. Consider a two-level box containing a number of tennis balls. An analog to an energetically favorable reaction would be to have all of the balls

Figure 4-4: Schematic energy diagrams for reactions that are energetically favorable and unfavorable when proceeding from left to right along the reaction coordinate on the upper level where any disturbance would cause them to roll down to the lower level under the influence of gravity, thereby losing energy.

If the upper level is modified and a low fence added to hold the balls in place, it will be just as energetically favorable as when the fence is not there for the balls to be at the lower level. The difference is that the process will not occur spontaneously without some major disturbance. We can say there is an energy barrier to occurrence of the favorable process.  

Figure 4-4 where we show an energy barrier to the spontaneous conversion of reactants to products for an energetically favorable chemical reaction

Now, if we shake the box hard enough, the balls on the upper level can acquire enough energy to bounce over the barrier and drop to the lower level. The balls then can be said to acquire enough activation energy to surmount the barrier. At the molecular level, the activation energy must be acquired either by collisions between molecules as the result of their thermal motions, or from some external agency, to permit the reactants to get over the barrier and be transformed into products. We shortly will discuss this more, but first we wish to illustrate another important concept with our mechanical analogy, that of equilibrium and equilibration.

With gentle shaking of our two-level box, all of the balls on the upper level are expected to wind up on the lower level. There will not be enough activation to have them go from the lower to the upper level. In this circumstance, we can say that the balls are not equilibrated between the lower and upper levels. However, if we shake the box vigorously and continuously, no matter whether we start with all of the balls on the lower or upper level, an equilibrium will be set up with, on the average, most of the balls in the energetically more favorable lower level, but some in the upper level as well

To maintain a constant average fraction of the balls at each level with vigorous and continued shaking, the rate at which balls go from the upper to the lower level must be equal to the rate that they go in the opposite direction. The balls now will be equilibrated between the two levels. At equilibrium, the fraction of the balls on each of the two levels is wholly independent of the height of the barrier, just as long as the activation (shaking) is sufficient to permit the balls to go both ways.

The diagrams of Figure 4-4 are to be interpreted in the same general way. If thermal agitation of the molecules is sufficient, then equilibrium can be expected to be established between the reactants and the products, whether the overall reaction is energetically favorable (left side of Figure 4-4) or energetically unfavorable (right side of Figure 4-4). But as with our analogy, when equilibrium is established we expect the major portion of the molecules to be in the more favorable energy state.

What happens when methane is mixed with chlorine? No measurable reaction occurs when the gases are mixed and kept in the dark at room temperature. Clearly, either the reaction is energetically unfavorable or the energy barrier is high. The answer as to which becomes clear when the mixture is heated to temperatures in excess of 300^o or when exposed to strong violet or ultraviolet light, whereby a rapid or even explosive reaction takes place. Therefore the reaction is energetically favorable, but the activation energy is greater than can be attained by thermal agitation alone at room temperature. Heat or light therefore must initiate a pathway for the reactants to be converted to products that has a low barrier or activation energy.

Could we have predicted the results of this experiment ahead of time? First, we must recognize that there really are several questions here. Could we have decided whether the reaction was energetically favorable? That the dark reaction would be slow at room temperature? That light would cause the reaction to be fast? We consider these and some related questions in detail because they are important questions and the answers to them are relevant in one way or another to the study of all reactions in organic chemistry.