[dvp331]

For example, if you are given a molecule and asked if it will undergo racemization in base, how do you figure it out?

Thanks

[Cavillus]

Well, my opinion is that you must look if the base/acid condition of the system can cause some reactions that can cause equilibria between enantiomers.

To explain with an example, an aminoacid in a sufficiently basic solution undergoes racemization, because the dissociation equilibrium of the acidic hydrogen near the carboxylic group leads to a double bond, which can then give both the stereoisomers.

[dvp331]

Hm... I'm not sure I understand still... Is there any other way you could explain it?  Is it pretty much if the base causes a mixture of products (stereoisomers)...at the chiral centre

For example, in these molecules (attached picture), I just do not know where to start

[rucik5]

To change the configuration of a chiral centre you need to brake bonds, right? Since your base will not brake any C-C bonds, a hydrogen atom has to be removed. A carbanion is formed and that scrambles the chiral centre.

This is worth reading: http://en.wikipedia.org/wiki/Keto-enol_tautomerism
In your case you will form an enolate: http://en.wikipedia.org/wiki/Enolate
Which of your compounds possess enolisable protons? It's good to be able to draw the structures.

[discodermolide]

Hm... I'm not sure I understand still... Is there any other way you could explain it?  Is it pretty much if the base causes a mixture of products (stereoisomers)...at the chiral centre

For example, in these molecules (attached picture), I just do not know where to start

Only molecule 3 can racemes because of the acidic proton alpha to the carbonyl, this proton can be enolised by acid or base.

[rucik5]

Just to extrapolate on what discodermolide already said:
all four molecules have alfa-protons next to the carbonyl, so you could form an enolate from every single one. However, only one molecule out of four has an alfa-proton next to the carbonyl on a carbon which is chiral.  Molecules 1 and 4 are non-chiral, and molecule 2 doesn't have any enolisable protons on the quaternary carbon. Only molecule 3 could be racemized with base (or acid, enzymes...).