Why does benzoyl peroxide homolytically cleave to give phenyl radical Benzoyl Peroxide cleavese rapidly to give out $\ce{CO2}$ and phenyl radical.


What I could not understand was why phenyl radical is formed because it is not at all resonance stabilized and nor any electronic effects are acting on it that could help in its stabilization then why is it being formed ?? Wouldn't it be too unstable ??

I mean after first cleavage, (Before $\ce{CO2}$ leaves) it should be more stable due to resonance (and that too equivalent resonating structures)
The mistake you're making (which is an easy one to make) is that you're neglecting to consider the carbon dioxide product. Carbon dioxide is a stable molecule, and its release also increases the entropy of the system. 

So even if the phenyl radical is less stable than the benzoyl radical intermediate, the combination of phenyl radical + $\ce{CO2}$ can still have an overall lower free energy than the benzoyl radical.