Final answer:
The best method to produce a racemic mixture of (+) and (-)-2,3-dibromobutane is by the addition of Br2 to cis-2-butene, allowing for anti-addition and equal formation of both enantiomers.
Step-by-step explanation:
The best method to make a racemic mixture of (+) and (-)-2,3-dibromobutane would be option C: addition of Br2 to cis-2-butene. This method allows for an anti-addition of bromine across the double bond, leading to a mixture of both enantiomers, or a racemic mixture. This process is stereoselective and will generate both stereoisomers equally due to the planar nature of the sp2-hybridized carbon atoms in the double bond of cis-2-butene.
Options A, B, and D do not produce a racemic mixture. Photochemical bromination may not be selective, and addition of HBr to a racemic alkene would not necessarily lead to a racemic product due to potential regioselectivity, while addition of Br2 to trans-2-butene would lead to a meso compound, which is not optically active.