How would you expect the reativity of the elements to change going across from group 1 to 2 in the same period

Answer 1

The difference in electro negativity gives some indication. The products from group 2 will have a lower electro negativity difference, than the atom next to it in Group 1.

Example Calcium chloride has a lower electro negativity difference than sodium chloride. This difference in electro negativity can be used as general tool to indicate reactivity.

Of course you could also draw upon observation. Drop a piece of sodium in water watch it fizz away to nothing. Drop a piece of calcium in water not nearly as reactive as the sodium.