# What is the rule of 13?

Mar 27, 2015

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

#### Explanation:

The formula is used in interpreting mass spectra.

${\text{Molecular formula" = "C"_n"H}}_{n + r}$

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

• For $\text{O}$, add $\text{O}$ and subtract ${\text{CH}}_{4}$.
• For $\text{N}$, add $\text{N}$ and subtract ${\text{CH}}_{2}$.
• For $\text{^35"Cl}$, add $\text{Cl}$ and subtract $\text{C"_2"H"_11}$.

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

$\frac{121}{13} = 9 r 4$

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

The odd mass and the odd number of $\text{H}$ atoms make it reasonable to add an $\text{N}$ atom and subtract ${\text{CH}}_{2}$:

${\text{N-15" = "N - (CH+H) = N-CH}}_{2}$

This gives a formula $\text{C"_8"H"_11"N}$.

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

$\frac{44}{13} = 3 r 5$, which gives a formula of ${\text{C"_3"H"_(3+5) = "C"_3"H}}_{8}$.

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

The infrared spectrum may give further information.

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

This shows the presence of an O atom.

${\text{O - 16" = 16 -("CH + 2") = "16 - CH}}_{4}$

The formula becomes $\text{CH"_2"NO}$.

The two absorptions in the region $\text{3100-3500 cm"^"-1}$ suggest a primary amide ${\text{CONH}}_{2} \left(m / z = 44\right)$.

The structure becomes