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Why does increasing bond polarity affect acid strength? For instance, why is $\ce{HF}$ a stronger acid than $\ce{CH4}$?

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This can be extrapolated to why polar substances ionize more often in water than non-polar substances. This is because water too is polar. Always remember "like dissolves like." Polar dissolves polar. This is because the positive end of the water molecule pulls at the negative end of the solute while the negative end of the water molecules pull at the positive end of the solute. In a non-polar molecule this would obviously not happen. Hence, in the case of acids, polar acids will dissociate more and hence more hydrogen atoms will be released into the solution.

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