Chapter 2, Problem 2.28SP

The C≡N triple bond in acetonitrile has a dipole moment of about 3.6 D and a bond length of about 1.16 A. Calculate the amount of charge separation in this bond. How important is the charge-separated resonance form in the structure of acetonitrile?

Interpretation Introduction

Interpretation: The amount of charge separation in the $\text{C}\equiv \text{N}$ triple bond is to be calculated. The importance of the charge-separated resonance form in the structure of acetonitrile is to be stated.

Concept introduction: The polarity of an individual bond is measured as its bond dipole moment. A quantity that describes two opposite charges separated by a distance is the dipole moment. The dipole moment is calculated by the formula,

$\mu =\delta \times d$

The delocalization of electrons due to the presence of lone pair of electrons and double bond is called resonating structure. The structure is more stable if there are more resonating structures. Resonance helps to explain the structure and reactivity of organic molecules.

To determine: The amount of charge separation in the $\text{C}\equiv \text{N}$ triple bond and the importance of the charge-separated resonance form in the structure of acetonitrile.

Answer to Problem 2.28SP

The amount of charge separation in the $\text{C}\equiv \text{N}$ triple bond is $\underset{\_}{0.646e}$.

The resonance structure suggests high electron density on nitrogen atom.

Explanation of Solution

Given

Dipole moment of $\text{C}\equiv \text{N}$ triple bond is $3.6\text{D}$.

Bond length of $\text{C}\equiv \text{N}$ triple bond is $1.16\stackrel{\text{ο}}{\text{A}}$.

The amount of charge separation is calculated by the formula,

$\mu =4.8\delta \times d$

Where,

• $\mu$ is the bond dipole moment in Debye (D).
• $\delta$ is the amount of charge at either end of the dipole.
• $d$ is the distance between the charges.

Substitute the values of $\mu$ and $d$ in the above formula to calculate the amount of charge separation.

$\begin{array}{c}3.6\text{D}=4.8\delta \times 1.16\stackrel{\text{ο}}{\text{A}}\\ \delta =\frac{3.6\text{D}}{4.8\times 1.16\stackrel{\text{ο}}{\text{A}}}\\ \delta =\frac{3.6\text{D}}{5.568\stackrel{\text{ο}}{\text{A}}}\\ \delta =\underset{\_}{0.646e}\end{array}$

Hence, the amount of charge separation is $\underset{\_}{0.646e}$.

Resonance contributors provide a description of charge and electron density distribution in a molecule. Important resonance contributors have comparable energies. The resonating structures of acetonitrile are shown below.

Figure 1

The additional resonance structure suggests that the electron density is high on nitrogen atom that bears a negative charge. The percentage of extent of charge separation shows that there is a chance for existing two resonating structures for acetonitrile. More the covalent bonds, greater will be the importance. Importance decreases with charge separation. Bond lengths show inverse relation with charge separation.