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You can figure out which would be the central atom due to the formation with the atom that will make the most bonds, or share the most electrons. You can always use the formula charge formula to access and see that placing O as the center atom would give a formal charge closest to or at the optimal formal charge level of 0. Drawing out the structure may help you to visualize why the center atom is the atom that it is.
To start finding the structures of this acid, you should first, according to the book, "choose as the central atom the element with the lowest ionization energy." Here, oxygen has the lowest ionization energy (besides Hydrogen, which shouldn't be considered as the central atom). Oxygen as the central atom is the best option for the Lewis structure, but, keep in mind that Chlorine can also be in the center (even if it isn't the most likely structure). Chlorine as the center atom results in formal charges for Chlorine and Oxygen, and structures with formal charges involved are less likely structures.
Typically, you would choose the element that has the lowest ionization energy as the middle and in this case, it is oxygen. Also, Chlorine typically only forms one bond so it wouldn't make sense to have Chlorine in the middle.
Typically, to draw the Lewis structure, you would need the total number of valence electrons, so what I do is write out each element’s valence electrons and the element with the smallest valence electron number is the center. Not sure how accurate my interpretation is, but that’s what I do for it.
O would be the central atom since it is the least ionization energy and can form more bond than the H and Cl. It would not H since H can only have one bond and it would not be Cl either since can normally only form one bond.
Cl is the least electronegative atom in the molecule, but since it has 7 valence electrons, it only has room left for one electron to complete the shell. It's more stable overall to have oxygen in the middle of the molecule.
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