Chapter 16, Problem 36P

A diol ( ${\text{C}}_8{\text{H}}_{18}{\text{O}}_2$) does not react with periodic acid. Its $\text{H}\text{ NMR}$ spectrum is shown in

Figure 16.6. What is the structure of this diol?

Interpretation Introduction

Interpretation:

The structure for the diol having molecular formula ${\text{(C}}_{\text{8}}{\text{H}}_{\text{18}}{\text{O}}_{\text{2}}\text{)}$ that does not react with periodic acid is to be determined from the given ${}^{\text{1}}\text{H NMR}$ spectrum.

Concept introduction:

The vicinal diols on treatment with periodic acid $\left({\text{HIO}}_{\text{4}}\right)$ undergo cleavage of carbon-carbon bond, where the hydroxyl groups attached and results in two carbonyl compounds.

The oxygen atoms do not show any effect on the index of hydrogen deficiency.

The index of hydrogen deficiency (IHD) represents the presence of number of multiple bonds or a ring in a molecule which can be calculated from the following formula,

$\text{IHD = }\frac{1}{2}\left({\text{C}}_{\text{n}}{\text{H}}_{\text{2n+2}}{\text{ - C}}_{\text{n}}{\text{H}}_{\text{x}}\right)$

Here, ${\text{C}}_{\text{n}}{\text{H}}_{\text{x}}$ is the molecular formula of given compound.

The ${}^{\text{1}}\text{H NMR}$ spectrum gives the information about the various hydrogen atoms in a molecule.

The chemical shift for the protons at carbon bonded to electron withdrawing group increases due to de-shielding effect.

Answer to Problem 36P

Solution: The structure for the diol having molecular formula ${\text{(C}}_{\text{8}}{\text{H}}_{\text{18}}{\text{O}}_{\text{2}}\text{)}$ that does not react with periodic acid is as follows:

Explanation of Solution

As it is mentioned that the diol having molecular formula ${\text{(C}}_{\text{8}}{\text{H}}_{\text{18}}{\text{O}}_{\text{2}}\text{)}$ does not react with periodic acid, it must not be a vicinal diol.

As the oxygen atoms have no effect on index of hydrogen deficiency, the molecular formula of the given compound can be written as ${\text{(C}}_{\text{8}}{\text{H}}_{\text{18}}\text{)}$.

Thus, the index of hydrogen deficiency in the given molecule can be calculated as follows:

$\begin{array}{l}\text{Index of hydrogen deficiency = }\frac{1}{2}\left({\text{C}}_{\text{n}}{\text{H}}_{\text{2n+2}}{\text{ - C}}_{\text{n}}{\text{H}}_{\text{x}}\right)\\ =\frac{1}{2}\left({\text{C}}_8{\text{H}}_{\text{2(8)+2}}{\text{ - C}}_8{\text{H}}_{18}\right)\\ =0\end{array}$

This shows that the molecule does not have a ring or multiple bond. It is saturated compound.

The approximate chemical shift values from the given ${}^{\text{1}}\text{H NMR}$ spectrum are written below:

a) $\text{1}\text{.2}\delta \text{(singlet), 12H}$

b) $\text{1}\text{.6}\delta \text{(singlet), 4H}$

c) $2.5\delta \text{(singlet), 2H}$

The arrangement of atoms in a molecule form the given chemical shift values are as follows:

$\text{1}\text{.2}\delta \text{(singlet), 12H}$

The chemical shift at $\text{1}\text{.2}\delta$ is corresponds to singlet twelve protons which describes that there are four methyl groups in a molecule. Four methyl groups cannot be bonded to single carbon, so there must be two ${\text{-C(CH}}_{\text{3}}{\text{)}}_{\text{2}}$ groups. The chemical shift value $\text{1}\text{.2}\delta$ represents the methyl protons are de-shielded, thus the tertiary carbon bonded to methyl groups must be attached to oxygen atom. The possible connectivity is shown below:

$\text{1}\text{.6}\delta \text{(singlet), 4H}$

The peak at $\text{1}\text{.6}\delta$ corresponds to singlet four protons, means there are two methylene groups bonded to tertiary carbon atom as shown below:

$2.5\delta \text{(singlet), 2H}$

The peak at $\text{2}\text{.5}\delta$ corresponds to two hydroxyl groups which are bonded to the carbon having no hydrogen attached. The possible connectivity is shown below:

Hence, the structure of diol having molecular formula ${\text{(C}}_{\text{8}}{\text{H}}_{\text{18}}{\text{O}}_{\text{2}}\text{)}$ is as follows:

Conclusion

The structure of diol having molecular formula ${\text{(C}}_{\text{8}}{\text{H}}_{\text{18}}{\text{O}}_{\text{2}}\text{)}$ is shown.