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The Nitrogen Rule in mass spectrometry states that (organic) molecules containing no or an even number of nitrogen atoms will have even masses, and molecules containing an odd number of nitrogen atoms will have odd masses.

Examples (all monoisotopic masses):
No nitrogen, even mass:
H2, 2 Da
HBr, 80 Da
C2H6, 30 Da
One nitrogen, odd mass:
NH3, 17 Da
C5H5N, 79 Da
etc.

Often there is a little disclaimer saying that the nitrogen rule is only valid for molecules that do not contain "exotic atoms." What are some examples for molecules do not follow the nitrogen rule?

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  • $\begingroup$ Just look at periodic table. P and Cl have odd masses. $\endgroup$ – MaxW Nov 5 '18 at 23:30
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    $\begingroup$ @MaxW - Yes, but P tends to be tri or pentavalent, so that cancels out. Consider phosphoramide $\ce{H6N3OP}$, mass 95 Likewise with Cl - its monovalent. Chloramine $\ce{H2NCl}$, mass 51 (and 53). What you need is an even valent atom with an odd mass or an odd valent atom with an even mass (like N). $\endgroup$ – Ben Norris Nov 6 '18 at 3:26
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Vanadocene, Manganocene and Cobaltocene all seem good bets, taking advantage the fact that all the first series transition metals have a +2 valence state, and then picking the odd massed ones. Europium II is another place to look.

In main group chemistry it's harder.

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The reason for the rule is that, outside of transition metal complexes, stable free radicals are relatively rare. If all electrons are paired and we are talking about molecules, not ions, there must also be an even number of protons. Thus an odd number of neutrons must be present to arrive at an odd molecular weight, and the only elements with the most abundant isotope having an odd number of neutrons are beryllium and nitrogen, although dysprosium is kinda close.

In an undergraduate lab you wouldn't be given an unknown with beryllium in it because it's so dangerously toxic, so that leaves you with nitrogen unless you have a deuterated sample.

But there are stable free radicals like nitric oxide (neurotransmitter) or chlorine dioxide (fumigant) that violate the rule. Molecular oxygen doesn't count because it's a diradical and so has an even number of electrons.

EDIT: I spoke too soon about abundances of nuclides with an odd number of neutrons. Here is a table of such nuclides with abundance $> 20\%$ taken from http://atom.kaeri.re.kr/nuchart/ : $$\begin{array}{rl} \text{Nuclide} & \text{Abundance} \\ \hline \sideset{^{9}}\ {Be}& 100\%\\ \sideset{^{14}}\ {N}& 99.636\%\\ \sideset{^{105}}\ {Pd}& 22.33\%\\ \sideset{^{129}}\ {Xe}& 26.4006\%\\ \sideset{^{131}}\ {Xe}& 21.232\%\\ \sideset{^{163}}\ {Dy}& 24.896\%\\ \sideset{^{167}}\ {Er}& 22.869\%\\ \sideset{^{195}}\ {Pt}& 33.78\%\\ \sideset{^{207}}\ {Pb}& 22.1\% \end{array} $$ Of these $\sideset{^{195}}\ {Pt}$ is the most abundant isotope of $Pt$ in addition to $\sideset{^{9}}\ {Be}$ and $\sideset{^{14}}\ N$ previously mentioned.

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