What is the drawn product drawn here the major product? I thought the radical (intermediate) is more stabilized at a primary carbon than at a tertiary one. 
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Carbon-centered radicals are electron deficient species in general--you have 7 electrons instead of the desired 8. This means that to first order, you can gauge the stability of a series of radicals the same way as you would for a series of carbocations. In this case, the tertiary cation and the tertiary radical would be the most stable in their respective series. So, no, definitely don't make a primary radical when you can make a tertiary radical.
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$\begingroup$ Ah thank you, that makes sense intuitively. I think I got confused because I was reading this website ( masterorganicchemistry.com/2013/04/12/… ) on free radicals and in one of the examples, it says addition of a bromine radical has anti-markovnikov selectivity. Do you know why this might be? $\endgroup$ Commented Feb 6, 2018 at 21:42
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$\begingroup$ The link you provide has to do with the addition of HBr in the presence of peroxides (Kharasch reaction), not the broomination of an alkane. $\endgroup$ Commented Jun 13, 2019 at 18:04