What is the rule of 13?

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Answer 1 · 2015-03-27T18:22:04

The rule of 13 states that the formula of a compound is a multiple $n$ of 13 (the molar mass of $"CH"$ ) plus a remainder $r$ .

The formula is used in interpreting mass spectra.

$"Molecular formula" = "C"_n"H"_(n+r)$

If you have heteroatoms, you adjust the formula. For example:

For example, benzamide has a molecular ion at 121, which is an odd number.

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$121/13 = 9r4$

The rule of 13 predicts a formula of $"C"_9"H"_(9+4) = "C"_9"H"_13$ .

The odd mass and the odd number of $"H"$ atoms make it reasonable to add an $"N"$ atom and subtract $"CH"_2$ :

$"N-15" = "N - (CH+H) = N-CH"_2$

This gives a formula $"C"_8"H"_11"N"$ .

The peak at 77 suggests $"C"_6"H"5$ , so the peak at 44 is the other fragment.

$44/13 = 3r5$ , which gives a formula of $"C"_3"H"_(3+5) = "C"_3"H"_8$ .

We know this contains $"N"$ , so the formula becomes $"C"_2"H"_6"N"$ .

The infrared spectrum may give further information.

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If it shows a strong peak at $"1640-1690 cm"^"-1"$ .

This shows the presence of an O atom.

$"O - 16" = 16 -("CH + 2") = "16 - CH"_4$

The formula becomes $"CH"_2"NO"$ .

The two absorptions in the region $"3100-3500 cm"^"-1"$ suggest a primary amide $"CONH"_2 (m//z = 44)$ .

The structure becomes

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