What Determines the Products of Oxide Reactions with Water?

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With the following examples:

Li2O + H2O -> 2OH- + 2Li+ basic
BeO + H2O -> Be(OH)2 basic
F2O + H2O -> 2HFO acidic

How do you know whether oxide reactions with water results in a single product such as HFO or Be(OH)2 and when it results in ions, such as OH- and Li+? I assume it is because Li does not hydrolyze, but I am still a little confused. Do all basic oxides react with water to form a product with (OH) in it? Can anyone help explain this a little better?

I have tried the following examples to see if I know what I am doing:

SO2 + H2O -> H2SO3
Na2O + H2O -> 2Na+ + 2OH-
 
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Fusilli_Jerry89 said:
With the following examples:

Li2O + H2O -> 2OH- + 2Li+ basic
BeO + H2O -> Be(OH)2 basic
F2O + H2O -> 2HFO acidic

How do you know whether oxide reactions with water results in a single product such as HFO or Be(OH)2 and when it results in ions, such as OH- and Li+? I assume it is because Li does not hydrolyze, but I am still a little confused. Do all basic oxides react with water to form a product with (OH) in it? Can anyone help explain this a little better?

I have tried the following examples to see if I know what I am doing:

SO2 + H2O -> H2SO3
Na2O + H2O -> 2Na+ + 2OH-

From my recollection, acidic and basic oxides with water becomes two products. You may want to read upon this topic a bit more in your standard chemistry text.