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The chemical reaction takes place in the presence of organic peroxides and light at the room temperature which is a free radical reaction by anti - markonikov’s rule. The crucial step is abstraction of H* free radical from the hydrogen bromide by the organic free radical (alkoxy or alkyl free radicals).
This step is exothermic and hence formation of Br* free radical is feasible. Thus, the reaction can proceed further.
However, HCl and HI do not undergo any free radical additions to alkenes in presence of peroxides.
In case of HCl, the abstraction of H* from HCl is endothermic. Since H-Cl bond is stronger than H-Br, breaking H-Cl bond requires more energy. The energy released in the formation new O-H bond cannot compensate for this as with HBr. Hence the abstraction from H-Cl is endothermic.
and in case of HI , even though the abstraction of H* from HI is exothermic, the addition of I* free radical to alkene is endothermic. Hence addition with HI or HCl , the reactions are less likely to occur.
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