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In the second chapter, Methane Energy of activation and Transition state in the textbook Organic Chemistry by Morrison and Boyd, Energy of activation is given the following definition:

The minimum amount of energy that must be provided by a collision for a reaction to occur is called the energy of activation, Eact.

The Eact for the reaction:

Cl(free radical) + CH3-H ---------> H-Cl + CH3(free radical)

is 4 kcal/mol. Therefore, on an average, it is 4/NA kcal per individual collision (where NA is the Avogadro number).

However, the bond energy of the carbon-hydrogen bond in methane is 104 kcal/mol. Therefore, on an average, it would be 104/ NA kcal for a single molecule of methane. In other words, 104/ NA kcal should be the energy provided by a collision that involves a methane molecule in order to break the carbon-hydrogen bond. Why does this not agree with the statement above which says 4/NA kcal per individual collision is what is required?

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The bond dissociation energy is the energy needed for the reaction leading to the rupture the $\ce{C-H}$ bond. I.e. it is the enthalpy of the reaction:

$$\ce{CH_3-H \rightarrow CH_3^{\bullet} + H^{\bullet}}$$

In the case of the reaction in the question, formation of the $\ce{H-Cl}$ bond will counterbalance the energy cost for breaking the $\ce{C-H}$ bond.

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  • $\begingroup$ So, bond-making and bond-breaking are perfectly synchronized? $\endgroup$ – AVU May 11 '18 at 11:39
  • $\begingroup$ The minimum energy pathway (i.e. the one which for which the activation energy is defined in the question) is the pathway for which bond breaking and bond formation balance as best as possible. $\endgroup$ – PLD May 11 '18 at 11:44
  • $\begingroup$ I assume that by "balance each other" you mean take energy from bond making process and use it in bond breaking process. So, if the balance is to be as best as possible then shouldn't activation energy simply be equal to enthalpy of reaction, i.e, 1 kcal/mol (given that HCl bond energy is 103 : so 104 -103 = 1)? $\endgroup$ – AVU May 11 '18 at 11:53
  • $\begingroup$ In the general case this is not the case: at some stage in the elongation of the bond (and shortening of the other one) there is some imbalance even on the minimal pathway. At some stage the H atom will be shared between the CH3 group and the Cl atom, and some repulsion between the electrons on the bond orbitals on both sides will rise the energy on the potential energy surface with no other way then go through this minimum. (Think of is as a pass in the moutain: its the lowest path to go but not lower than the valleys on both sides.) $\endgroup$ – PLD May 11 '18 at 16:00
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In this reaction the C-H bond is not broken then the Cl reacts with the H to form the products, but rather as the Cl atom approaches its electrons and those in methane interact and a combined transient species called a transition state is formed. This species lasts only a very few picoseconds and has the nature of long Cl-H and H-C bonds, in a picturesque way something like Cl--H--CH3. As the reaction proceeds the Cl-H bond forms and the H-C bond breaks and the CH3 radical and HCl then depart from one another. The activation energy is that needed to reach the transition state and involves using some of the kinetic and vibrational energy of the reacting species. The transition state is at a far lower energy than direct CH bond breaking although it is at the highest point on the reaction path, i.e at the top of the barrier.

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