Achiral molecules halogenation

Now we understand why the halogenation of an achiral molecule gives a racemic halide. What products can we expect from the halogenation of a chiral, enantiomerically pure molecule Or, to put it differently, how does the presence of a stereocenter in the structure affect its function in a reaction ... 

We have seen that a chemical reaction, such as the halogenation of an alkane, can introduce chirality into a molecule. How exactly does this occur To find the answer, we need to look more closely at the conversion of achiral butane into chiral 2-bromobutane, which gives racemic material. Once we have done so, we shall be able to understand the halogenation of 2-bromobutane and the effect of the chiral environment of a stereocenter already present in a molecule on the stereochemistry of the reaction. 

Proceed In E, the molecule is symmetrical, and the rate of attack from the top is equal to that from the bottom. If the halogenation were to be executed by using F2 or CI2, Cj would remain a stereocenter, the R and S enantiomers having been formed in equal amounts (racemate Section 5-7, Figure 5-13). However, in our case, bromination at C2 removes the asymmetry of this carbon Compound G is achiral and hence not optically active. 

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