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Bromine addition to trans-cinnamic acid

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During bromine addition to trans-cinnamic acid, why is it necessary to maintain excess bromine in the reaction mixture and how can you tell there is an excess of bromine?

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https://brainmass.com/chemistry/acid-and-base-organic-chemistry/bromine-addition-trans-cinnamic-acid-59405

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You will want an excess of bromine to push the reaction forward to completion. Having your substrate ...

Solution Summary

It explains the reason why that excess bromine is required in the reaction with trans-cinnamic acid.

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Bromination of trans-cinnamic acid

I recently did an experiment where the addition of bromine to trans-cinnamic acid gives a dibromide with two stereocenters (chiral centers). Thus, there were four stereoisomers possible (see figures on page 136 on attachment).

According to the melting points of my product, I ended up with the racemic mixture (2R,3S) and (2S,3R), erythro diastereomer (see attachment). EVERYTHING I have read points to the idea that this should be an anti addition, but the teaching assistant has just told me, no, this is a syn addition since we have ended up with the erythro diastereomer. How can this be? All the literature says that when a bromonium ion is formed in the bromination of an alkene, this is anti addition.

(1) Showing a lot of detail, please draw out the mechanism of the reaction of bromine with trans-cinnamic acid step-by-step for me. How does each bromine enter?
(2) Is it syn or anti addition or both?
(3) Isn't the erythro diastereomer a meso compound?

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