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To my understanding, if the H atom is bonded to the central Cl atom, the Cl atom would have a formal charge of +1, while the O atom would have a formal charge of -1 if it had another lone pair instead of bonding with the H atom. So, the structure in which one O atom is bonded to the H atom and Cl has a lone pair (the Lewis structure pictured) is the structure in which all the atoms have a formal charge of zero. It is the Lewis structure with the lowest energy, and is thus the more stable and more favorable structure!
The H atom would actually be bonded to one of the oxygen atoms that is connected to the chlorine atoms. One of the patterns for acidic molecules is that if there is an hydrogen it usually will want to form an O-H bond with one of the oxygens. For example, for the molecule HCLO4 the hydrogen is attached not to the chlorine but one of the oxygens due to the molecules acidic property.
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