Why is aluminium(III) considered a hard acid if it forms covalently bonded compounds like aluminium oxide?

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?




**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.](https://books.google.com/books?id=RrREAAAAIAAJ&q=The+Lewis+Acid-Base+Concepts&dq=The+Lewis+Acid-Base+Concepts&hl=en&sa=X&ei=l2mTVO23GqHbsAT12ICgBw&ved=0CB8Q6AEwAA)


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](http://ion.chem.usu.edu/~sbialkow/Classes/3600/Overheads/Carbonate/CO2.html) 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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