How can Nitrogen and oxygen form nitrogen dioxide if both nitrogen and oxygen have a negative charge?
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They don't. Oxygen, in the free state, (such as in air that you and I breathe) is zero charged. So is the nitrogen in the air, in the free state. In fact, ALL elements in the free state (uncombined with anything) have a zero charge and a zero oxidation state. One "valence value" of oxygen is -2 and one valence value for nitrogen is +4 and that accounts for NO2. Nitrogen is one of those animals with many different valences (I prefer to call them oxidation states) with +1, +2, +3, +4, + 5, and -3 for starters.
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