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First, it is not strictly true, but it may be because covalent bonds are between two non-metals and ionic bonds are between a non-metal and a metal. Most non-metals are in the top right of the Periodic Table, and so have lighter atomic weights, whereas metals take up most of the periodic table and so in general are heavier than non-metals (with obvious exceptions such as the very light metal lithium for instance). Also ionic compounds tend to have a long range bonding structure and because of the nature of ionic bonds tend to be tightly packed. Covalent molecules, while the atoms are tightly "packed" in the molecule, the molecules are not so tightly packed against one another, leaving more empty space, and thus reducing the density.

Also, what may cause the added space between the covalently bonded molecules is that fact that the molecular bonds are highly directional (which in many instances causes assymetric molecules) where ionic and metallic bonds are non-directional. This can reduce intermolecular attractions to only weak van der waals forces

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