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My book says:

As single ions of a metal are not associated in the solid with single ions of a non metal, separate units of ionic compounds do not exist. It is, therefore, wrong to talk of a molecule of an ionic compound.

I know ionic solids exist in form of crystal lattice but why can't we isolate a single molecule of ionic compound?

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    $\begingroup$ Actually compounds considered ionic in solid state are molecular in gas phase. $\endgroup$ – Mithoron Aug 8 '15 at 17:56
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Ions are electrostatically bound. One need only separate them with inegrated inverse squared distance work. If you mix multiple ionic compounds in solvent, a melt, gas phase, the original paired associations are spontaneously scrambled. Benzene plus xylene does not give you toluene. "Separating" benzene is not electrostatic attraction.

Quaternized glycine, $\ce{^{+}N(CH3)3-CH2-C(=O)O^{-}}$, is betaine. It is ionic, but the ions are covalently bound into a molecule. Where are the discrete formula units in alumina? You can draw lines to connect closest atoms, but those are not bonds. (Note fractional atom counts for atoms embedded in planes, edges, and corners.)

Alumina crystal structure

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  • $\begingroup$ How is this unit cell $\ce{Al2O3}$? It seems to have six aluminum and six oxygen atoms. $\endgroup$ – Oscar Lanzi Nov 21 '17 at 22:31

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