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In the example comparing the pH of HClO, HBrO, and HIO, why is the halogen the atom that receives the electrons and makes the anion more stable if Oxygen is more electronegative? Wouldn't oxygen have a stronger pull on the electrons than the halogens?
The oxygen atom is common across all three compounds, so you wouldn't use it to compare them to each other. Instead, we use the halogens because they are different in each compound and therefore comparable.
While oxygen is the most electronegative of the atoms shown, it is not what is being compared in this example. Each compound includes oxygen, so instead you compare the anions by the presence of Cl, Br, and I. Since Cl has the highest electronegativity of the three, it stabilizes the negatively charged oxygen by withdrawing electron density and therefore is the strongest acid.
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