What is the rule of 13?

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