Final answer:
Ammonium persulfate is the catalyst used for acrylamide polymerization and to decompose persulfate ion, necessary for polyacrylamide gel formation.
Step-by-step explanation:
The catalyst for acrylamide polymerization that also helps to decompose persulfate ion is ammonium persulfate ((NH4)2S2O8). Ammonium persulfate serves as the auxiliary oxidizing agent that initiates the free-radical polymerization necessary to form polyacrylamide gels. These gels are formed by polymerizing acrylamide monomers in the presence of a crosslinker like methylenebisacrylamide, which determines the pore size of the resulting gel structure. Other agents like sodium persulfate and potassium persulfate can also serve similar functions, but in the context of this question, ammonium persulfate is the correct answer.