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I understand how the nitrite $\ce{NO2}$ ion can be formed and have a negative charge, but the nitrate $\ce{NO3}$ ion is confusing me. I made some simple drawings to try to explain what I don't understand:

enter image description here

Does the "electron from outside" that the oxygen receives, as indicated in the drawing, comes from the nitrogen atom? If so, then the N atom would be left with only 4 valence electrons instead of 5, thus being able to form another covalent bond with the extra oxygen, forming $\ce{NO3}$. Is this the correct line of thinking?

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An organiker would look at it this way.

Nitrate resonance forms

An inorganiker might look at it as literal N(+5) with two double-bonded oxygens. It does redox as N(+5). Coordination structures are varied,

Nirate coordination

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  • $\begingroup$ I was under the impression that organic chemists have a much greater tendency to expand octets than inorganic ones … $\endgroup$ – Jan Dec 12 '16 at 16:41
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If you are thinking about it like literally adding O to the nitrite ion then yes, the two electrons the oxygen receives are from nitrogen. Imagine moving the nitrogen lone pair to the oxygen to give it a full octet and forming a single bond in the process. You will notice that the Lewis structures will match the "organiker" structures of Uncle Al.

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your NO2- structure is correct , the 3rd Oxygen which is trying to be added in NO2- has 6 electrons in valence shell , that means it needs 2 more. N has 1 lp means 2 unused electrons. N will share its lone pair with Oxygen (oxygen will not use its 6 e, only 2 e of N will be shared by both O and N) , this type of bonding is known as coordinate bond. As Nitrogen is sharing its electron it will get +ve charge , and O is taking Nitrogen's electrons it will get -ve charge. Both -ve and +ve neutralize each other and the resulting compound is NO3-. If any confusion left, you can check some videos of coordinate bonding , then you will surely understand.

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