Why is basic character inversely proportional to oxidation number?

Since you have not specified Lewis or Bronsted basic character, this question is too broad to focus on only one of them.

First of all, "inversely proportional to oxidation number" is a poorly-worded statement. It does not specify whether the oxidation state is positive or negative.

It makes a lot more sense to talk about negative oxidation states, because #"H"^(+)# are positively charged, so the question should have been worded:

"Why might basic character be inversely proportional for negative oxidation numbers?"

LEWIS BASIC CHARACTER

If we are talking about Lewis bases, let us compare #"O"^(-)# with #"O"^(2-)#.

The greater the overall negative charge, the greater the attraction of the ion's valence electrons to a positively-charged Lewis acid's nucleus, and the greater the tendency to donate a valence electron pair.

That would demonstrate greater Lewis basicity.

Therefore, the more negative the oxidation state, the greater the Lewis basic character, and we have a direct proportionality.

(If you really wanted to push it, you could say that the Lewis basicity increases when the oxidation state decreases from #0#, but that's harder to keep straight.)

BRONSTED BASIC CHARACTER

If we are talking about Bronsted bases, let us again compare #"O"^(-)# with #"O"^(2-)#.

• The conjugate acid of #"O"^(-)# is #"OH"#, which is neutral.
• The conjugate acid of #"O"^(2-)# is #"OH"^(-)#, which is the normal polyatomic ion.

Since the conjugate acid of #"O"^(2-)# can still accept another proton, #"OH"^(-)# is the stronger Bronsted base or weaker Bronsted acid---it is more likely to hold onto its #"H"^(+)#.

The conjugate base of the weaker Bronsted acid (#"OH"^(-)#) is a stronger Bronsted base, so #"O"^(2-)# is the stronger Bronsted base.

Therefore, a more negative oxidation state is directly proportional to the strength of Bronsted basicity.

(If you really wanted to push it, you could say that the Bronsted basicity increases when the oxidation state decreases from #0#, but that's harder to keep straight.)