[solipse]

For example, consider the successive chlorates: HClO, HClO2, HClO3, HClO4. Chlorine increases its oxidation state from +1, to +3, +5 and +7. Does this correlate with how powerful an oxidant the chlorate is, or its chemical reactivity? If so, why?

(Highly oxidized compounds like K2Cr2O7 and KMnO4 are very strong oxidizers, and are also highly oxidized themselves, so it got me wondering.)

[Schrödinger]

Yes, indeed there is a relationship. Usually, when an element exhibits many oxidation states, the highest state is more powerful an oxidizing agent when compared to the lower states, simply because it has many more options to get reduced to, in contrast to the lower states, which have a lesser number of options.

Ex : Cl exhibits states -1,0,+1,+3,+5, and +7... +7 has many more options available when compared to +3 and hence is much more powerful an oxidizer.

[Borek]

simply because it has many more options to get reduced to, in contrast to the lower states, which have a lesser number of options.

I would rather link it with the fact higher oxidation states are - in a way - related to higher ionization levels. These always require more energy, and more energy means higher potential.

[Schrödinger]

Yeah, now that I think along those lines, I might as well have written that...