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I understand the fact that ionic compounds are good conductors of electricity in molten state. But why aren't they good conductors in solid state. Cannot ions vibrate about their mean position and transfer electricity in the same way as they transfer heat?

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Electric charge is transferred by physically moving charged particles around. In the case of an electric current moving through a wire (for example), the electrons are moving.

In an ionic compound, the ions are locked in place. They can move around a little bit, but there is not much translational motion - the ions stay in their places on the crystal lattice. In addition, the ions are "happy" with the number of electrons that they have. The ions formed in the first place by giving up or accepting electrons in order to minimize the overall potential energy of the system. If an anion were to transfer an electron back to a cation (for example) the energy of the system would increase, and so in general, transfer of electrons after the compound has formed is not favorable.

In solution or in a molten state, the ions themselves can move around - they become the charge carriers. In a solid, the ions can't move, and so electricity cannot be easily transferred.

You mentioned heat transfer - heat is the transfer of the kinetic energy of atoms and molecules. Heat can still be transferred (in some cases quite easily) in an ionic solid because, as you said, ions can vibrate about a mean position. When this happens they bump into their neighbors, which spreads the kinetic energy around.

In summary, ionic compounds don't conduct electricity very well because the charge carriers can't move through the crystal. They can conduct heat because the kinetic energy itself is the "heat carrier" - it can be transferred without moving ions too far from their mean positions.

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    $\begingroup$ While generally true, this isn't always true for ionic compounds. Some do have mobile ions that can carry significant quantities of electricity. These are used in some fuel cell and battery technologies, though the compounds are not that common. See the Wikipedia article on fast ion conductors. $\endgroup$ – matt_black Feb 25 '16 at 12:00
  • $\begingroup$ I didn't know about that, @matt_black - thanks for the info! $\endgroup$ – thomij Feb 25 '16 at 16:17
  • $\begingroup$ There are also ionic compounds where you have a mixture of charges in the cations or in the anions, and electrons can "hop" between the mixed-charge ions. This occuus for instance in FeO, which has a fairly large percentage of Fe(III) and cation vacancies; electrons move between the Fe(II) and Fe(III) ions. $\endgroup$ – Oscar Lanzi Oct 8 '17 at 13:42
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Ionic compounds do not conduct electricity in solid state because electron motion results in electricity being conducted but in solid state the constitutive particles are strongly bonded or in fixed positions; thus, they can't move from one part to another. In molten state, the ionic compound is split into ions, and ions are charged particles that are free to move so ionic compounds in water or in molten state conduct electricity.

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As we know that particles in solid state are held by stronger interparticle force.Hence the particles in solid donot possess translatory motion,they can only vibrate about their mean position where as in molten state particles are held by not very strong interparticle force.Hence,the particles in molten state possess translatory motion,they are free to move and they didnot vibrate about their mean position.That`s why Ionic solid conduct electricity in molten state but not in solid state.

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  • $\begingroup$ This just explains why ionic solids conduct electricity in molten state. This also repeats what had already been said by the OP about the solid state of ionic solids. Hence I downvoted this post because this does not answer the question. $\endgroup$ – Gaurang Tandon Feb 18 '18 at 6:19

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