predict which three of the following five aqueous solutions should react with solid aluminum metal (the elemental form of aluminum): AgNO3, Na2CO3, CuSO4, CaCl2, Pb(NO3)2

Answer 1

The Ag, Cu, and xx salts.
See the activity series chart here.
http://www.files.chem.vt.edu/RVGS/ACT/notes/activity_series.html

Here is how you do it. A metal in the activity series will displace any ION BELOW it in the activity series. Al is above Ag so it will displace Ag from AgNO3.
Al + 3AgNO3 ==> Al(NO3)3 + 3Ag

Also it will displace Cu ion.
2Al + 3CuSO4 ==> Al2(SO4)3 + 3Cu

Note that it will NOT displace Ca ion since Ca is ABOVE Al in the activity series.
Al + Ca ==> No reaction.

You should be able to pick out the remaining ion Al will displace from the above information.
Al +