Question

What is the molecular formula of the alkane?

What is the molecular formula of the alkane?  Replace the subscript letters with numbers. Formatting counts.

Answer 1

Concepts and reason

The concept used to solve this problem is C-13 rule.

To determine the molecular formula of a compound, C-13 rule is used. Firstly, a base formula is generated by dividing the molar mass of substance by 13. The numerator $\left( n \right)$ or quotient obtained is equal to the number of carbon atoms and the sum of numerator and remainder $\left( r \right)$ is equal to the number of hydrogen atoms in the base formula. The base formula comes out to be ${{\rm{C}}_n}{{\rm{H}}_{n + r}}$ .

Fundamentals

A mass spectrum is a plot of relative abundance of ion vs $m/Z$ (mass to charge ratio).

According to C-13 rule, the molecular formula of a compound is a multiple, $n$ of 13 with a remainder $r$ . The rule is named C-13 because the molar mass of ${\rm{CH}}$ is 13. So, the molecular formula used for interpreting the mass spectra is ${{\rm{C}}_n}{{\rm{H}}_{n + r}}$ . The formula is adjusted in case of heteroatoms. For instance, if the heteroatom ${\rm{O}}$ is present in the compound, ${\rm{O}}$ is added and ${\rm{C}}{{\rm{H}}_{\rm{4}}}$ is subtracted.

The molecular ion mass is 100.

The molecular formula of the compound can be calculated using C-13 rule as follows:

$\frac{{100}}{{13}} = 7r9$

That is,

$\begin{array}{l}\\n = 7\\\\r = 9\\\end{array}$

The base formula is ${{\rm{C}}_n}{{\rm{H}}_{n + r}}$ .

Substitute 7 for $n$ and 9 for $r$ in the base formula to obtain the molecular formula.

$\begin{array}{c}\\{\rm{Molecular formula}} = {{\rm{C}}_{\rm{7}}}{{\rm{H}}_{{\rm{7 + 9}}}}\\\\ = {{\rm{C}}_{\rm{7}}}{{\rm{H}}_{{\rm{16}}}}\\\end{array}$

Therefore, the molecular formula of the alkane is ${{\rm{C}}_{\rm{7}}}{{\rm{H}}_{{\rm{16}}}}$ . The compound is n-heptane.

The mass fragmentation of the compound is as follows:

This explains the signal at $m/Z = 29$ , $m/Z = 43$ , $m/Z = 57$ and $m/Z = 71$ .

The peak at $m/Z = 85$ is due to the removal of ${\rm{C}}{{\rm{H}}_{\rm{2}}}$ group from the parent ion.

Ans:

The molecular formula of the alkane is ${{\rm{C}}_{\rm{7}}}{{\rm{H}}_{{\rm{16}}}}$ .