Ionic compounds will not conduct electricity as they are fixed in a lattice. They vibrate whe he electrides are placed in but they cannot move around, so they don't conduct.
When dissolved NaCl does conduct electricity. The water molecules sperate ions from the lattice, the ions are then free to move around. Therefore, when the electrodes are placed in the solution the protons and electrons are drawn to the oppositely charged electrode.
Molten compounds, the high temperatures provide enough nergy to overcome the many strong attractive forces between ions. They are free to move around withi the compound, this allows it to conduct electricity.
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