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For your example problem, anything that weakens the O-H bond would cause the molecule to be a stronger acid. So the answer would be HClO<HClO2<HClO3<HClO4 due to the impact the added oxygen atoms have on the O-H bond. This is generally the same idea with bases as molecules that dissociate more easily are stronger acids/bases.
Another thing we learned in class is the stability of the ion when it is broken from the H. So ClO4 is the strongest because it has more oxygens, and hence, more resonance, making the ion stronger than the others.
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