Strontium Chloride is an ionic compound, means it's made up of positively charged strontium ions and negatively charged chloride ions arranged in a giant lattice. In the solid form, strontium chloride will not conduct electricity. This is because in the solid forms, the ions are not mobile, as they are fixed in place, in the lattice structure. Since the ions can't move a current cannot flow therefore it does not conduct.
In the liquid from (either molten or dissolved) strontium chloride will conduct electricity. This is because in the liquid form the ions are free to move. this means a current can flow.
