Can solid FeBr2 react with Cl2 gas to produce solid FeCl2 and Br2 gas? Why or why not?

Yes

Explanation:

The balanced equation of the reaction is;

FeBr2 (aq) + Cl2 (g) → FeCl2 (aq) + Br2 (aq)

This reaction is possible because chlorine is more electronegative than bromine and can displace it from its salt.

In group seventeen, electro negativity decreases down the group. Hence as we move down the group, elements become less electronegative and can be displaced from their salt by more electronegative elements found earlier in the group.

Hence chlorine can displace bromine in FeBr2 to form FeCl2.