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As we know, water is a covalently bonded molecule. However, the hydroxides - such as sodium hydroxide - are ionic compounds. Both of these are similar, although the difference between both is a sodium atom instead of a hydrogen atom.

Now, both hydrogen and sodium have one outer electron, which makes me come onto my question:

Could sodium share its outer electron with the OH group, like hydrogen does in water molecules, to form a normal covalent bond? Or, could hydrogen lose its outer electron to form a cation, and ionically bond to OH-, like what happens in sodium hydroxide?

Long story short: why is water covalent, whilst the hydroxides are ionic, if the difference is just another atom instead of hydrogen?

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Although I’m not to proficient in this chapter. I believe it’s because sodium and the other group 1 and group 2 elements in particular are electropositive in nature .it is due to this that they form ionic compounds .Hydrogen isn’t electropositive enough to form an ionic bond like you have stated .Just read up on Fajan’s rule and you’ll get the idea

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