Question

Question:Propose a structure consistent with each set of data.

a. a compound that contains a benzene ring and has a molecular ion at m/z= 107

b. a hydrocarbon that contains only sp3 hybridized carbons and a molecular ion at m/z= 84

c. a compound that contains a carbonyl group and gives a molecular ion at m/z= 114

d. a compound that contains C, H, N, and O and has an exact mass for the molecular ion at

101.0841

Short answer

Answer

Step-by-step solution

Rule of thirteen

The value of the molecular ion peak is equal to the molecular mass of an organic molecule. The rule of thirteen is based on the determination of the molecular formula of a compound from the molecular ion value.

The formula, which relates the molecular mass M of a compound with the subscripts of C and H, is given below.

$\frac{\text{M}}{\text{13}}\text{\hspace{0.17em}=\hspace{0.17em}n\hspace{0.17em}+\hspace{0.17em}}\frac{\text{r}}{\text{13}}$.

Accordingly, the molecular formula is expressed as ${\text{C}}_{\text{n}}{\text{H}}_{\text{n+r}}$.

Determination of the structure

a.

For the first compound, the molecular ion is at m/z =107.

From the rule of thirteen, the molecular formula of the compound containing only C and H is as follows.

$\frac{107}{\text{13}}\text{\hspace{0.17em}=\hspace{0.17em}}8\text{\hspace{0.17em}+\hspace{0.17em}}\frac{3}{\text{13}}$

Thus, the formula of the compound is ${\text{C}}_{\text{n}}{\text{H}}_{\text{n+r}}{\text{\hspace{0.17em}=\hspace{0.17em}C}}_{\text{8}}{\text{H}}_{\text{11}}$.

As the molecular ion is an odd number, the compound may contain an odd number of nitrogen atoms.

After substituting one group for nitrogen, the formula becomes ${\text{C}}_{\text{7}}{\text{H}}_{\text{9}}\text{N}$.

It is given that it contains a benzene ring. So, the possible structure can be as follows.

Possible structure of compound a

b.

It is given that the compound is a hydrocarbon, thus containing only carbon and hydrogen.

The molecular ion is at m/z=84.

From the rule of thirteen, the subscripts will be

$\frac{84}{\text{13}}\text{\hspace{0.17em}=\hspace{0.17em}}6\text{\hspace{0.17em}+\hspace{0.17em}}\frac{6}{\text{13}}$$\frac{84}{\text{13}}\text{\hspace{0.17em}=\hspace{0.17em}}6\text{\hspace{0.17em}+\hspace{0.17em}}\frac{6}{\text{13}}$.

Thus, the formula will be ${\text{C}}_{\text{n}}{\text{H}}_{\text{n+r}}{\text{\hspace{0.17em}=\hspace{0.17em}C}}_6{\text{H}}_{12}$.

The possible structure of the compound is given below.

Possible structure of compound b

c.

The molecular ion of the compound is at m/z=114, and it contains a carbonyl group.

The molecular formula of the compound, derived from the rule of thirteen, is

$\frac{114}{\text{13}}\text{\hspace{0.17em}=\hspace{0.17em}}8\text{\hspace{0.17em}+\hspace{0.17em}}\frac{10}{\text{13}}$

.${\text{C}}_{\text{n}}{\text{H}}_{\text{n+r}}{\text{\hspace{0.17em}=\hspace{0.17em}C}}_8{\text{H}}_{18}$

As a carbonyl group is present, the compound has one oxygen atom. As the mass of one oxygen atom corresponds to the mass of 1 carbon and 4 hydrogen atoms, the substitution is done, as shown below.

$\frac{\text{+O}}{{\text{-CH}}_{\text{4}}}\to {\text{\hspace{0.17em}C}}_7{\text{H}}_{14}\text{O}$.

A possible structure with such molecular formula is given below.

Possible structure of compound c

d.

The given compound contains C, H, N, and oxygen, and the molecular ion is at m/z=101.0841.

The molecular formula of the compound with respect to carbon and oxygen is

$\frac{101.084}{\text{13}}\text{\hspace{0.17em}=\hspace{0.17em}}7\text{\hspace{0.17em}+\hspace{0.17em}}\frac{10}{\text{13}}$

${\text{C}}_{\text{n}}{\text{H}}_{\text{n+r}}{\text{\hspace{0.17em}=\hspace{0.17em}C}}_7{\text{H}}_{17}$.

The oxygen atom can be substituted, as shown below.

$\frac{\text{+O}}{{\text{-CH}}_{\text{4}}}\to {\text{\hspace{0.17em}C}}_6{\text{H}}_{13}\text{O}$.

As there is also an odd number of nitrogens present in the compound, the substitution occurs, as shown below.

.$\frac{\text{+N}}{{\text{-CH}}_2}\to {\text{\hspace{0.17em}C}}_5{\text{H}}_{11}\text{NO}$

The possible structure is shown below.

Possible structure of compound d