Question

What is the VSEPR shape of `(SO_4)_2?`

Answer 1

There isn't a good way to describe it. How many central atoms are there?

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You seem to refer to the peroxydisulfate dianion...

...which is `["O"_3"S"-"O"-"O"-"SO"_3]^(2-)`. Clearly, there is more than one central atom. Thus, there is no one molecular shape for the entire molecular ion... there are four shapes.

It is tetrahedral around each sulfur, and bent around each central peroxo oxygen.