Imagine a compound such as 1,3-dibromo-1,2,3-trichloropropane. Since the first and third carbons are attached to four different groups, they are both chiral centers. Assuming that both of these stereocenters are mirror images of one another (as in (1$S$-3$R$)-1,3-dibromo-1,2,3-trichloropropane), would the second carbon also be considered a stereocenter? If so, how would you differentiate the two enantiomers around that carbon using IUPAC nomenclature? Also, would such a carbon be optically active?
Yes, carbon-2 is a stereocenter, and by (arbitrarily) giving the R conformation higher priority than the S, we can assign its stereochemistry using s/r notation:
Pseudochirality simply means that a molecule has two substituents of a stereocenter are mirror images of each other, and the other substituents are either achiral or also mirror images of each other. Despite having multiple stereocenters, pseudochiral molecules are ahciral (optically inactive) because the mirror images of both the s and r conformations are identical.