Based on the chemical formula, you know that each formula unit of #"Cu"("NO"_3)2# will dissociate into 3 ions when dissolved in water (one #"Cu"^(2+)# ion and two #"NO"_3^(-)# ions). The polyatomic ion does not dissociate.

So if we multiply #2.5 xx 3# we get #7.5# moles of ions. Then, multiply by Avogadro’s constant, #6.02 x 10^23#, and we get the final result #4.5 xx 10^24# ions.