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A polar bond will be stronger than a relatively less polar bond. So how does increasing polarity of O-H bond ever increase acidity. Shoudn't it make it harder to release H+ and become less acidic.

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A polar bond is formed by the exchange of electrons between atoms to form a cation and an anion. Thus the bond between the cation and anion is due to electrostatic attraction. When such compounds(ionic) are dissolved in polar solvents(water, ammonia) these cations and anions exist as independent ions(hydrated ions to be precise). You can take the example of how hydrochloric acid releases protons in water. So here, as the polarity of the OH bond increases, there is a greater tendency for the oxygen and hydrogen atoms to form anion and cation respectively and hence when the compound is dissolved in water, they tend to ionize releasing protons into the solution.

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