What is the reason the group 13 metals have a typical charge of 3+?
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for starters, do metals like to gain or lose electrons?
also, take a look at this interactive periodic table http://www.ptable.com
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Remember metals like to always lose electrons, that's one of their properties.
all elements will either lose or gain electrons depending on their reactivity. if you look at that periodic table I posted in the link at the column starting with Helium and down group 18 those are the noble gases. all elements ideally want to have a configuration like the ideal gases because they don't react and are stable.
Remember, groups are organized based on how many valence electrons the elements have. Group 1 have 1 valence electron, group 2 elements have 2 valence electrons.
let's look at aluminum, it has 13 electrons, that's in group 13. if it has a charge of +3 it means that it looses 3 electrons; the if that's the case it has 10 electrons, what element does it's configuration resemble now?
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Aluminum 3+ means that it loses three electrons to have 10 electrons; this is a noble gas configuration. The groups are organized based on the amount of valence electrons so I believe the metals in group 13 have 3 valence electrons and hence +3 would mean that they would have achieved octet.