I'll try and interpret the question correctly...
The first question is why nitrogen dioxide is
This comes from the nomenclature of nonmetal compounds; for binary covalent compounds such as nitrogen dioxide, they are named such that prefixes are attached to each element ( except if the first element has only
#1#of it in the compound, then no prefix is present).
"Nitrogen dioxide" thus means there is one nitrogen present and two oxygen atoms (prefix "di-" indicates
#2#), the compound formula is #"NO"_2#.
The next question, I assume, is why the formula is not something else according to the chemical reaction
Here's something worth knowing about chemistry and specifically chemical reactions: reactants can form products that have completely different characteristics than those of the reactants.
The fact that
#"N"_2#seems to lose its diatomic property is just the nature of the reaction; although #"N"_2"O"_2#is a real compound, it is far less common to hear about it or work with it.
Basically, the chemical structure of
#"NO"_2#is thermodynamically more favorable than that of #"N"_2"O"_2#, and thus the reaction will, under certain conditions, yield #"NO"_2#(you'll learn more about the thermodynamics of reactions later!)
As far as balancing goes, we have so far
two nitrogens on the left, one on the right
two oxygens on the left, two on the right
Therefore, nitrogen is the only unbalanced element. To fix this, we simply add a
#color(red)(2)#in front of #"NO"_2#:
#"N"_2(g) + "O"_2(g) rarr color(red)(2)"NO"_2(g)#(unbalanced)
Now you may notice that the oxygen quantities have become unbalanced, and there are
#4#on the right side and #2#on the left. A quick fix is done by placing another #color(blue)(2#in front of #"O"_2#:
#"N"_2(g) + color(blue)(2)"O"_2(g) rarr color(red)(2)"NO"_2(g)#(balanced)
And our equation is balanced!