Proton NMR (Enantiomer vs. Diastereomer)

[Helicore]

I am a bit confused with how to determine whether a set of hydrogens are enantiomers or diastereomers (and therefore how many different sets there are).
[In attachment} I understand d, and e, since they both already have a chirality center, and replacing a hydrogen on the CH2 (which is a pro-chirality center) would create another chirality center making it a diastereomer. But I don't quite get the rest when there are no present chirality centers.

I am assuming a is enantiotopic since it would produce a single chirality center (?), but the other two diastereotopic ones don't quite make sense to me (though I think it should..).
For the CH3's that make up the diastereomer in c, and e, the hydrogens on the methyl itself are homotopic correct? And diastereotopic when compared to the other methyl?

* What kind of process should I be going through to determine this?
I think I have only a single step so far that I am somewhat sure on, which is to check for any present chirality centers. What should follow?

 

[siddharth]

To see if the protons are equivalent, imagine the proton to be replaced by some other atom Z. If the replacement of either of the two protons gives enantiomeric products, then the two protons are chemically equivalent.

Enantiomers are mirror-image isomers, which are non-superimposable. They only differ in the way the atoms are oriented in space.

First, let me give you some definitions, which you may already know.
Molecules that are not superimposable on their mirror image are chiral
By superimposable, I mean that, the molecule and it's mirror image coincide completely.
A carbon atom where four different groups is attached is called a chiral center

Now, not all molecules that contain a chiral center are chiral. Such molecules will have more than one chiral center. There are also chiral molecules which do not contain chiral centers. So the presence of chirality centers does not guarantee that the molecule is chiral.

Having said that, however, most chiral molecules have chiral centers. So if you find a chiral center, consider the possibility that the molecule is chiral and exists in enantiomeric forms. To predict if a molecule is chiral or not on paper, draw the wedge diagram and see if you can superimpose the mirror image.

Now what are diastereomers? Stereoisomers that are not mirror images of each other are called diastereomers. This can happen in case of Geometric (cis/trans) isomerism (where there is restricted rotation), or when there is more than one chiral center.

So, in your attached diagram, after replacing the H proton by Z see if the resulting compound is enatiomeric, or diastereomeric. This will tell you if it's enantiotopic or diastereotopic. The last one is pretty simple, because it's easy to see it gives you the same molecule.