Please explain why molten magnesium chloride conducts electricity whereas solid magnesium chloride does not.
In order for a substance to conduct electricity charge must be able to move through it. An ionic solid has a rigid structure in which ions and their electrons remain in fixed positions so charges are unable to move through the substance. This also explains the brittleness of ionic solids. They tend to shatter when a force is applied because of the rigid structure. Particles within the crystal lattice are unable to move in response to the force while maintaining the structure of the lattice.
An ionic solid begins to melt when heated because the increased vibration of the ions overcomes the electrostatic force holding them in the crystal lattice and they begin to move around. An ionic substance conducts electricity in the liquid or molten state because these mobile ions are able to carry charge throughout the material.
The same thing happens when ionic solids dissolve in water. The hydrated ions are free to move and the solution conducts electricity.
Metals, unlike ionic solids, conduct electricity in the solid state because their shared valence electrons are free to move around and carry charge.