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If something is a hard acid, it tends to form ionic bonds as it is polarizing. So why is the aluminium ion a hard acid when it forms bonds with covalent character. A similar argument follows for why carbon dioxide is considered a hard acid?

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    $\begingroup$ The hydrogen proton is the hardest acid, yet I can't think of any ionic compounds with the hydrogen proton as a component. Perhaps you may need to reexamine your rule of thumb. $\endgroup$ – Dissenter Dec 17 '14 at 22:27
  • $\begingroup$ what is the rule of thumb then? $\endgroup$ – RobChem Dec 18 '14 at 14:14
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Short summary - HSAB theory has it's limits of applicability, and this is a good example.

More recent discussion of acid-base theory center on the frontier orbital concept, e.g. W. B. Jensen, The Lewis Acid-Base Concepts (1980) pp. 112-155.

In this concept, an "acid-base" reaction creates new HOMO-LUMO orbitals of the product. So it's about energy matching between the acid (empty LUMO) and base (filled HOMO) (and also symmetry and orbital overlap). It's still very much a Lewis picture, since you have the electron pair on the base and an electron acceptor on the acid.

For example, if we react $\ce{NH3 + H+ -> NH4+}$ we combine the HOMO of $\ce{NH3}$ (i.e., a lone pair) with an empty LUMO on $\ce{H+}$ to create the adduct.

IMHO, this is a nice concept, since the orbital energy match between Al and O is good, you get covalent character to the resulting product. (Now you also get ionic character, but that's a different question.)

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The Orbital Molecular Theory explains it very well; the symmetry and orbital overlap defined by the wave functions gives a complete approach. I add some thoughts to the question qualitatively:

The concept of covalent and ionic bonds must be taken carefully when talking of acidity, a property normally refereed to aqueous solution where other interactions (hydration enthalpy) take place.

The $\ce{Al^3+}$ ion is very polarizing, and has a high charge and low ionic radius leading to high effective nuclear charge. In solution the cation must have many shells of hydration, coordinating or polarizing water molecules and attaching $\ce{OH-}$ groups in order to compensate the positive charge, thus increasing the net amount of available $\ce{H+}$.

Similarly, carbon dioxide is a gas and it can be seen as a separated phase on a soda drink (bubbles); so first it must be dissolved in water. The dissolution of a $\ce{CO2 (g)}$ molecule in water increases the acidity, $\ce{[H+]}$, as can be tasted when leaving a glass of soda open in equilibrium with air for a while. I copy here the equations found at this link which explains why carbon dioxide is acidic. If you follow the link, it has a brief explanation:

$\ce{CO2 (g) <=> CO2 (aq)}$

$\ce{CO2 (aq) + H2O (l) <=> H2CO3 (aq)}$

$\ce{H2CO3 (aq) <=> HCO3- (aq) + H+ (aq)}$

$\ce{HCO3- (aq) <=> CO3^2- (aq) + H+ (aq)}$

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