Question

What is the rule of 13?

Answer 1

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`.

Explanation:

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 `"O"`, add `"O"` and subtract `"CH"_4`.
• For `"N"`, add `"N"` and subtract `"CH"_2`.
• For `""^35"Cl"`, add `"Cl"` and subtract `"C"_2"H"_11"`.

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

`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.

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