Where does the energy to break the C-H bond in a compound undergoing hyperconjugation come from?

Question

In an organic molecule such as Toluene, one of the C-H bonds in the Methyl group attached to the Benzene ring breaks in order to leave a lone pair of electrons on carbon which causes the Resonance to begin. However, C-H bond dissociation energy if around 104kCal. Where does this energy come from?

Answer 1

Depends.  What reaction are you doing?  How are you breaking the bond?

Toluene is stable.  It doesn't spontaneously generate radicals at room temperature by homolyzing that C-H bond.  The energy doesn't "come from" anywhere, which is why the bond ain't breaking.

Your question implies that you've done something to break the bond, but unless you specify the exact chemical change and the conditions under which it occurs, it's impossible to say what the driving force is.  Maybe you're heating it.  Maybe you're bombarding it with high energy photons.  Maybe you're reacting it with something that wants that H atom more that toluene does.  Dunno.

Your question is also confusing two concepts.  The C-H BDE refers to a very specific chemical process: gas phase toluene turns into a gas phase hydrogen atom (H-dot) and a gas phase toluene radical (C6H5CH2-dot).  Uphill by 104 kcal/mol.  Your mention of a "lone pair of electrons on C" implies not C-H homolysis (bond strength), but H+ dissociation (acidity), which is a different reaction: products of H+ and [C6H5CH2]–.  You can't use bond strength data (alone) to predict acidities or energies of heterolytic bond cleavage: the gas phase loss of H+ to leave a lone pair on C is not an enegy change of 104 kcal.