You must be more specific on what you mean with "persulfate". There are multiple ions, which could pass as "persulfate" ion:
- S2O8(2-), peroxodisulfate. This is available in pure form as the sodium salt, potassium salt (which is only sparingly soluble) and the ammonium salt
(which only has limited shelf life).
- SO5(2-), monoperoxosulfate. This is one of the ions in "oxone", which is a triple salt of KHSO4, K2SO4 and K2SO5. Oxone is much more soluble than
potassium peroxodisulfate, and approximately as soluble as Na2S2O8 and (NH4)2S2O8.
Both oxone and peroxodisulfates are capable of oxidizing bromide to bromine. Peroxodisulfate, however, is sluggish at room temperature and for a
decent reaction speed you either need to heat this to 60 C or so, or you need to add a catalyst, being Ag(+) ion. Oxone reacts quickly. If you add
solid oxone to hydrochloric acid, then it bubbles, releasing chlorine gas. So, I expect oxidation of bromide to occur even faster.
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