When comparing O with S you are looking within the same column. When comparing in the same column it is the size of the atom that is bonded to the hydrogen that will dictate the acidity. For example, S is bigger than O so the hydrogen is much farther out from the nucleus of the S than it is from the O and therefore can be removed more easily. This is the same reason why H-I is more acidic than H-F or H-Cl even though the latter are more electronegative.
Acidity (when bound to hydrogen) and atomic radius increase with the arrows:
When it comes to acidity compare electronegativity within the row as you pointed out with nitrogen < oxygen. When comparing within a column, the atomic radius is more important.
At this point, there is so many neat tricks and mmneomics to remember that I am forgetting which trick goes with which. Do you know of any mnemonic to help me remember other mnemonics
Honestly, no mneumnoic will help you much here. I've been slapped so many times by practice questions that you basically force yourself to think: same row (electronegativity, more stable conjugate base), same column (bigger anion, more polarizable conjugate base). But Chad from coursesaver gives the mneumnic: C.A.R.DI.O, which can take a while to explain but if you googled it up, you might find some helpful explanations on studentdoctor.
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