If you have an aqueous solution that contains 1.5 moles of hcl, how many moles of ions are in the solution?

There will be three moles of ions.
Because in an aqueous solution, HCl will break apart into  H+ and Cl- ions. 
HCl -> H+ + Cl−
1.5 HCl -> 1.5 H+ + 1.5 Cl−
So the aqueous solution will have 1.5 moles of hydrated hydrogen ions and 1.5 moles of hydrated chloride ions. So, a total of 3 moles of ions are present in the aqueous solution of 1.5 moles of HCl. 

No. an alpha particle is a pair of protons and a pair of neutrons, i.e. a helium