Question

How can I determine the equivalence with a mirror plane in the molecule?

Answer 1

I take it you are asking this on the basis of an NMR experiment?

Explanation:

Protons and carbon nuclei exchanged (only) by a mirror plane, are said to be enantiotopic (i.e. interchanged by an improper axis of rotation). Enantiotopic nuclei are equivalent (i.e. isochronous), and should give rise to the same chemical shifts in all achiral NMR experiments. Should a homochiral NMR solvent be used (i.e. an optically active NMR solvent, which do exist), their interaction with the enantiotopic nuclei is diastereotopic, and the enantiotopic nuclei may be differentiated and become non-equivalent.