Teaching stereochemistry of Tartrat(e)

Question

(I'm a German, thus no end e - otherwise the main gag wouldn't work.)

Stereoisomeres are not 100% intuitive; it is telling that chemists came on the idea relative late (IMHO). The first compound separated was tartrat, which is even worse to intuition due to two stereocenters. It is tempting to present this to one's pupils using one dimension less (| denotes the mirror):

TARTRAT | TAЯTЯAT D/L

TARTЯAT | TARTЯAT meso

This works exactly so long until the valedictorian asks: OK, but what about

TAЯTRAT | TAЯTRAT meso

so aren't there four stereoisomers?!

The short answer is, of course: 2D and 3D point symmetries are not the same (and in 4D you could even rotate D into L, but there are still other kinds of stereoisomeres). Could you give me a more satisfying answer (other than: Go to Math SE) where the analogy falls flat?

(p.s. at mods: it seems we have a "teaching-lab" tag but none for "general" teaching?!)

Answer 1

Here is a different representation in two dimensions: Up arrows represent R configuration and down arrows represent S configuration. A horizontal mirror changes the molecule to its enantiomer. Reversing the order of the symbols represents renumbering the parts of the molecule.

In this representation,

$$\frac{\ \ \ce{^ ^}\ \ }{\ce{v v}}$$ shows the R/R stereoisomer (above the mirror plane) and its S/S enantiomer (below). Renumbering the first and the second part doesn't make those two the same.

On the other hand (haha),

$$\frac{\ \ \ce{^ v}\ \ }{\ce{v ^}}$$ shows the R/S stereoisomer (above the mirror plane) and its S/R enantiomer (below). Renumbering the first and the second part shows that they are the same.

In the amusing TARTRAT tractate,

TARTЯAT | TARTЯAT

does double duty. It flips the stereocenters and renumbers at the same time. If the mirror had been placed horizontally, it would just flip the stereocenters without renumbering (of course, this doesn't work with the shape of the letter "R", so I switched to the arrows). What is missing here is the drama of thinking you have a new molecule, and then realizing you don't upon renumbering (or if you have access to a 3-D model, rotating the mirror image you just built to see it is the same as the original).

So you have to convince the valedictorian that TAЯTRAT and TARTЯAT are the same as an afterthought, whereas showing that $\ce{^ v}$ and $\ce{v ^}$ are the same is part of the main argument.