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I believe that specifically for this case, the hydrogen bonds to oxygen due to the strong covalent bond attraction. Since Cl is larger than O, the dipole-dipole attraction is weaker and thus hydrogen does not like to bond with chlorine.
If I am correct, hydrogen generally tries to bond to N, O, or F as this allows it to take place in hydrogen bonding. Therefore, it did not bond to Cl because then the overall strength of the molecule would be decreased significantly.
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