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Sorry if the question is silly but this is troubling me more than enough. Here's what I know about chemical formula: Reverse the valencies of the combining elements. But in this case, $\ce{NO2}$ is the formula for nitrogen dioxide while N valency is 3. Please explain it to me if I am wrong somewhere.

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    $\begingroup$ N2O3 - this should be the formula $\endgroup$ Dec 30, 2015 at 13:56
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    $\begingroup$ Your rule of swapping the valencies only works for a very specific set of compounds. In general there are a huge number of compounds where this is not the case and indeed the rule is merely a coincidence and has no real theoretical basis. $\endgroup$
    – bon
    Dec 30, 2015 at 14:02
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    $\begingroup$ Because it is useful for quickly getting the formulae of many compounds that you are likely to meet at that level. $\endgroup$
    – bon
    Dec 30, 2015 at 14:10
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    $\begingroup$ @SujithSizon $\ce{N2O3}$ is a separate compound. It is formed from the reaction of $\ce{NO}$ and $\ce{NO2}$ but it is not a mixture of them. $\endgroup$
    – bon
    Dec 30, 2015 at 14:25
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    $\begingroup$ @SujithSizon $\ce{NO2}$ exists in equilbrium with $\ce{N2O4}$. The position of equilibrium varies with temperature, pressure etc. $\endgroup$
    – bon
    Dec 30, 2015 at 14:34

2 Answers 2

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The rule of swapping the valencies of the atoms to get their ratios only works for a very specific set of compounds and is more of a convenient trick than a rule based on any sort of hard theory.

In particular, it works for binary 'ionic' compounds such as $\ce{NaCl}$, $\ce{CuCl2}$, $\ce{Al2O3}$ etc. because the valencies of the atoms correspond to the charges on the ions and the net charge has to be zero.

However, it obviously doesn't work for a huge range of other compounds where there is more complicated bonding. For example there are a whole range of covalent nitrogen oxides of varying degrees of stability which do not fit the rule ($\ce{N2O}$, $\ce{NO}$, $\ce{NO2}$, $\ce{N2O3}$, $\ce{N2O4}$ etc).

Ultimately the only way to determine the formula of any arbitrary substance is through experiment, typically with a mass spectrometer.

If you are interested in finding out more about the different types of substances that are possible I suggest that you start reading about different types of bonding, in particular ionic versus covalent, to begin to understand the different types of compounds that exist.

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Well. Here is an explanation which is valid at the secondary level. At the university level, it is more correct to speak of bonding and anti-bonding molecular orbitals.

Let's go ! $\ce{NO2}$ is a unusual molecule that has one lonely electron on the $\ce{N}$. This should not happen. But look ! It also contains $4$ $\ce{N-O}$ bonds, with a negative partial charge on the oxygen side. As a consequence, there are $4$ partial positive charges on the central $\ce{N }$ atom. This is much ! Now, experience shows that $\ce{NO2}$ exists only at high temperatures. When cooling it at low temperatures ($T < 0°C$), it gets dimerized and becomes $\ce{N2O4}$. Unfortunately this molecule $\ce{N2O4}$ has a drawback. It contains a bond $\ce{N-N}$ between two atoms holding both $4$ partial positive charges. Similar electric charges are repelling one another. So the bond $\ce{N-N}$ is rather weak in $\ce{N2O4}$, and does not resist at absolute temperatures higher than $\pu{270 K}$. At room temperature for example, $\ce{N2O4}$ is dissociated into $\ce{2 NO2}$, at least partially (as it is an equilibrium).

As a consequence, $\ce{NO2}$ can be considered as a half-molecule ! Exactly like $\ce{H2}$ or $\ce{Cl2}$ which produce $\ce{H}$ or $\ce{Cl}$ atoms when heated to rather high temperatures.

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