[bobjam]

Hello,

A problem in my chemistry book asks whether NO₃^- or CO₃^2- has a greater charge density.

The solution manual simply says "CO₃^2- has both a smaller volume and a larger ionic charge, so it has the greater charge density."

I understand the reasoning behind the greater charge bit, but I don't understand why it would have a smaller volume.  Nitrogen is a smaller atom than carbon, and has a greater effective nuclear charge.  I would think that the two extra electrons on the carbonate ion would spread out more due to the lesser nuclear charge of the carbon, relative to the nitrate ion.

Any thoughts on this to help me conceptualize it better?

Thanks

[magician4]

it depends on what the authors of the original problem would understand to be the "volume" of those very ions...

i am always uncomfortable with those values, as they more often than not are derived form ion mobility experiments in solution, i.e. with a complete hull of water around them and thatlike

those data might be useful, if I considered HSAB (which deals with ions in solution) as the topic of the hour [which to me seems to be the background of your thread ?] , but could be completely meaningless in other experiments

so. maybe the relative volumes mentioned are valid with respect to HSAB-discussions
in this case, the relative diameters of the ions (here: calculated as "ball shaped") might have been recalculated from their respective λ-values

with respect to a completely different approach, i.e discussing bond length, you would result in a completely different picture (i.e.: you were right): carbonate and nitrate being isoelectronic and isosymmetric (sp² at the central atom, 3 identical ligands due to mesomeric effects) , we could take a look at the bondlength N-O and C-O , respectively
and, surprise, surprise: N-O in nitrate is reported as 127,3 pm , C-O in carbonate as 131 pm
so, from this analysis, carbonate in fact should be larger than nitrate


as I said: it depends


regards

Ingo