Why ice is bad conductor of electricity while water is very good conductor of electricity?

Answer 1

Pure water will not conduct electricity to any measurable degree. (Water has about a billion times lower conductivity than a metal.) In tap water and naturally occurring water, it is the impurities in the water that provide conduction. Unlike a metal, the charge that moves through water is the charge associated with the motion of ions, not electrons. Ions, being heavy charged atoms, will interact (collide) with water molecules much more strongly than electrons and therefore move slower making conductivity very small by virtue of their small numbers and slow average (drift) velocity. Testing the purity of water is often done by measuring it's resistance. Water with a higher resistance, is considered purer.

Ice can also conduct electric current and, like water, this is very small when pure. Whatever ionic impurities are captured in the crystalline structure of ice will still contribute to a small conductivity that is much reduced because the ion motion through the solid is thousands of times smaller than the motion of the same ions through the liquid, i.e. ions are effectively frozen in.

The short answer to "why" is that conductivity of water is fundamentally different than conductivity of a metal, the metal allows easy motion of electrons as charge carriers and water (as well as other materials) has predominately charged atoms, ions, as the carriers of moving charge. The solid structure of ice does not provide much in the way of intermolecular spaces for ions to move through while water, with the constant movement of water molecules, provides much more opportunity for ionic motion.