Question

Question: How many degrees of unsaturation does each of the following drugs contain?

a.  zolpidem (sleep aid sold as Ambien),${\mathit{C}}_{\mathbf{19}}{\mathit{H}}_{\mathbf{21}}{\mathit{N}}_{\mathbf{3}}\mathit{O}$

b.  mefloquine (antimalarial drug),${\mathit{C}}_{\mathbf{17}}{\mathit{H}}_{\mathbf{16}}{\mathit{F}}_{\mathbf{6}}{\mathit{N}}_{\mathbf{2}}\mathit{O}$

Short answer

Answer

1. Zolpidem has 11 degrees of unsaturation.
2. Mefloquine has eight degrees of unsaturation.

Step-by-step solution

Degree of unsaturation

The degree of unsaturation helps to predict the total number of possible $\mathbf{\pi }$-bonds or any rings present in the structure formed by a given molecular formula.

Calculation of degree of unsaturation

For each nitrogen atom, a hydrogen atom is subtracted, and for each halogen atom present, one hydrogen atom is added to the molecular formula of the compound.

The oxygen atom does not change the total count of the hydrogen atoms in the molecular formula.

Degree of unsaturation in the given compounds

a. For three nitrogen atoms, three hydrogen atoms are subtracted from the given molecular formula.

Hence, the given compound contains 19 carbon and 18 hydrogen atoms.

The maximum number of hydrogens for 19 carbon atoms is $2\left(19\right)+2=40$.

Here, the number of hydrogen atoms lacking is $40-18=22$.

Thus, the number of degrees of freedom is $\frac{22}{2}=11$.

Thus, $C_{19}{H}_{21}{N}_{3}O$ has 11 degrees of unsaturation.

b. For two nitrogen atoms, two hydrogen atoms are subtracted, and for six fluorine atoms, six hydrogen atoms are added to the given molecular formula.

Hence, the given compound contains 17 carbon and 20 hydrogen atoms.

The maximum number of hydrogens for 17 carbon atoms is $2\left(17\right)+2=36$.

Here, the number of hydrogen atoms lacking is$36-20=16$ .

Thus, the number of degrees of freedom is $\frac{16}{2}=8$.

Thus, $C_{17}{H}_{16}{F}_6{N}_{2}O$ has eight degrees of unsaturation.