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The positive and negative ions, formed by ionic bonding, are held together by strong forces of attraction between the opposite charged ions. These ionic bonds result in a massive structure of ions.
The ions are held very tightly in this massive structure. It takes a lot of energy to break apart all the bonds which results in high melting points and boiling points of ionic compounds.
Ionic compounds possess an equal amount of positive and negative ions which are arranged in a 3D lattice resulting in high melting points.
When ionic compounds are dissolved in water, it forms a solution where ions move freely resulting in conduction of electricity by these solutions.
Likewise, when ionic compounds are heated, they melt the ions resulting in their movement which can also conduct electricity.