Why Does Light Induce the Chlorination of Methane?

First, we should make clear that the light does more than provide energy merely to lift the molecules of methane and chlorine over the barrier of Figure 4-4. This is evident from the fact that very little light is needed, far less than one light photon per molecule of chloromethane produced. The light could activate either methane or chlorine, or both. However, methane is colorless and chlorine is yellow-green. This indicates that chlorine, not methane, interacts with visible light. A photon of near-ultraviolet light, such as is absorbed by chlorine gas, provides more than enough energy to split the molecule into two chlorine atoms:

Once produced, a chlorine atom can remove a hydrogen atom from a methane molecule and form a methyl radical and a hydrogen chloride molecule. The bond-dissociation energies of CH4 (104 kcal) and HCl (103.1kcal) suggest that this reaction is endothermic by about 1kcal:

Figure 4-8). The methyl radical resulting from the attack of atomic chlorine on a hydrogen of methane then can remove a chlorine atom from molecular chlorine and form chloromethane and a new chlorine atom:

Use of bond-dissociation energies gives a calculated ΔH0ΔH0 of −26kcal for this reaction, which is certainly large enough, by our rule of thumb, to predict that KeqKeq will be greater than 1. Attack of a methyl radical on molecular chlorine is expected to require somewhat more oriented collision than for a chlorine atom reacting with methane (the chlorine molecule probably should be endwise, not sidewise, to the radical) but the interatomic repulsion probably should not be much different.

The net result of CH4+Cl⋅⟶CH3⋅+HCl and CH3⋅+Cl2⟶CH3Cl+Cl⋅ is formation of chloromethane and hydrogen chloride from methane and chlorine. Notice that the chlorine atom consumed in the first step is replaced by another one in the second step. This kind of sequence of reactions is called a chain reaction because, in principle, one atom can induce the reaction of an infinite number of molecules through operation of a "chain" or cycle of reactions. In our example, chlorine atoms formed by the action of light on

Figure 4-7. Cl2 can induce the chlorination of methane by the chain-propagating steps:

In practice, chain reactions are limited by so-called termination processes. In our example, chlorine atoms or methyl radicals are destroyed by reacting with one another, as shown in the following equations:

Chain reactions may be considered to involve three phases: First, chain initiation must occur, which for methane chlorination is activation and conversion of chlorine molecules to chlorine atoms by light. Second, 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. Putting everything together, we can write:

The chain-termination reactions are expected to be exceedingly fast because atoms and radicals have electrons in unfilled shells that normally are bonding. As a result, bond formation can begin as soon as the atoms or radicals approach one another closely, without need for other bonds to begin to break. The evidence is strong that bond-forming reactions between atoms and radicals usually are diffusion-controlled, that there is almost no barrier or activation energy required, and the rates of combination are simply the rates at which encounters between radicals or atoms occur.

If the rates of combination of radicals or atoms are so fast, you might well wonder how chain propagation ever could compete. Of course, competition will be possible if the propagation reactions themselves are fast, but another important consideration is the fact that the atom or radical concentrations are very low. Suppose that the concentration of Cl⋅ is 10⁻¹¹ M and the CH4 concentration 1M. The probability of encounters between two Cl⋅ atoms will be proportional to 10⁻¹¹×10⁻¹¹, and between CH4 and Cl⋅ atoms it will be 10⁻¹¹×1. Thus, other things being the same, CH4+Cl⋅⟶CH3⋅+HCl (propagation) would be favored over 2Cl⋅⟶Cl2 (termination) by a factor of 1011. Under favorable conditions, the methane-chlorination chain may go through 100 to 10,000 cycles before termination occurs by radical or atom combination. Consequently the efficiency (or quantum yield) of the reaction is very high in terms of the amount of chlorination that occurs relative to the amount of the light absorbed.

The overall rates of chain reactions usually are slowed very much by substances that can combine with atoms or radicals and convert them into species incapable of participating in the chain-propagation steps. Such substances are 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, CH3OO⋅. This effectively terminates the chain: