Chapter 14, Problem 14A.1ST

Interpretation Introduction

Interpretation:

The magnitude of the electric dipole moment of methanal has to be calculated.

Concept introduction:

The quantity that is used to measure the uneven distribution of electrons around the atoms of a compound that possess the covalent bonds is known as dipole moment. The electric dipole moment is basically a measurement of the separation of negative and positive electrical charges. It is denoted by $\mu$.

Answer to Problem 14A.1ST

The magnitude of the electric dipole moment of methanal is $\underset{\_}{3.21D}$.

Explanation of Solution

The given illustration of methanal or formaldehyde is shown below.

Figure 1

The positions of the given atoms are represented by $\left(x,y,z\right)$ coordinates having distance in picometers.

The value of charge is $e=1.602\times {10}^{-19}\text{C}$.

The equation that s used to calculate the electric dipole is given below.

    $\mu ={\left({\mu }_x^2+{\mu }_y^2+{\mu }_z^2\right)}^{1/2}$        (1)

The value of ${\mu }_x$ is calculated below.

    $\begin{array}{c}{\mu }_x=-0.38e\left(0\text{pm}\right)+0.18e\left(-94\text{pm}\right)+0.18e\left(94\text{pm}\right)+0.02e\left(0\text{pm}\right)\\ =0\end{array}$

The value of ${\mu }_y$ is calculated below.

    $\begin{array}{c}{\mu }_y=-0.38e\left(118\text{pm}\right)+0.18e\left(-61\text{pm}\right)+0.18e\left(-61\text{pm}\right)+0.02e\left(0\text{pm}\right)\\ =-44.84\text{}e\text{pm}-10.98e\text{pm}-10.98e\text{pm}\\ =-66.8\text{}e\text{pm}\end{array}$

Substitute $e=1.602\times {10}^{-19}\text{C}$ and convert picometer into meter in the above equation.

    $\begin{array}{c}{\mu }_y=-66.8\times \text{}1.602\times {10}^{-19}\text{C}\times {\text{10}}^{-12}\text{m}\\ =-1.07\times \text{}{10}^{-29}\text{C}\cdot \text{m}\\ =-\text{3}\text{.21}\text{D}\end{array}$

The structure of methanol is planar, so $z$-coordinate is zero. So, ${\mu }_z=0$

Substitute ${\mu }_y=$$-\text{3}\text{.21}\text{D}$, ${\mu }_x=0$ and ${\mu }_z=0$ in equation (1).

    $\begin{array}{c}\mu ={\left(0+{\left(-3.21\text{D}\right)}^2+0\right)}^{1/2}\\ ={\left(10.3041\text{D}\right)}^{1/2}\\ =\underset{\_}{3.21D}\end{array}$

Therefore, the magnitude of the electric dipole moment of methanal is $\underset{\_}{3.21D}$.