State whether the following conduct electricity as solid or molten: Aluminium, Aluminium fluoride, Boron tribromide

We start with aluminium (Al). Al conducts electricity in both solid and molten states, this is because Al has metallic bonding between fixed positive Al^(3+) ions and delocalised electrons. The delocalised electrons are free to move in both states and so can carry charge.

Next we consider aluminium fluoride (AlF3). AlF3 conducts electricity in molten but not solid states, this is because AlF3 has ionic bonding between positive Al^(3+) ions and negative F^(-1) ions. As a solid these ions are fixed in a lattice structure and so are not free to move and carry charge. However, as molten these ions are free to move and carry charge so it is able to conduct electricty as molten.

Finally, boron tribromide (BBr3). BBr3 doesn't conduct electricity in either solid nor molten states, this is because BBr3 has covalent bonding between the central B atom and the 3 surrounding Br atoms. Covalent bonds are formed through a shared pair of electrons and so BBr3 has no charged particles (delocalised electrons or ions) that are free to move, therefore it cannot carry charge at all.