Dipole Moment

Dipole Moment Definition

Let's start by looking at the definition of dipole moment.

While temporary dipoles can be formed in an atom or a molecule, it is only molecules that can have a permanent dipole (these are called polar molecules).

In a molecule, a dipole is established when there is an uneven distribution of electrons, caused by a difference in electronegativity.

The most electronegative atom is fluorine, so the closer an atom is to the top right of the periodic table (i.e. the closer to fluorine), the more electronegative it is. The closer an atom is to the bottom left of the periodic table, the less electronegative it is.

When an atom is more electronegative, it will pull electron density towards itself, so that side of the molecule will be partially negative (δ-). The other side of the molecule will then be partially positive (δ+).Below is an example of a polar molecule (HF):

Fig.1-The polar molecule HF

Fluorine is more electronegative (3.98), so it has a δ- charge, while hydrogen is less electronegative (2.2), so it has a δ+ charge.There are two important things to remember when it comes to dipoles:1) Symmetrical molecules "cancel" any polar bonds, so they do not have a dipole. Essentially, the dipoles are equal and opposite, so they cancel (see Figure 4 for details).2) Atoms must have at least a 0.5 difference in electronegativity to be considered polar/have a dipole.

Dipole Moment Direction

A key fact about a dipole moment is that it is a vector, meaning it has both a magnitude and direction. The dipole moment shows the net direction of the charge.

For example, here is the dipole moment for HF:

Fig.2-The dipole moment of HF points toward fluorine

The dipole moment points towards the area of the molecule where there is the greatest amount of electron density (i.e. the more electronegative atom). The "crossed" portion of the arrow marks where there is a lack of electron density (i.e. the less electronegative atom).

In this case, the arrow is pointing towards fluorine (most EN element) and the crossed portion is at hydrogen.

Dipole Moment of Water

When a molecule has more than one bond, the net dipole moment is the total value of all the bond dipole moments. For example, here is the dipole moment of water:

Fig.3 Water has a net dipole moment facing downwards

Individual bond dipole moments are always parallel to their bonds, while the net dipole moment doesn't have to follow a bond, but will always point towards the more electronegative atom.

The magnitude of the net dipole moment is not simply the sum of the individual bond dipole moments. As we'll see later when we look at the formula, the net dipole is the sum of the dipoles in each coordinate direction (i.e. the x and y directions).

As an example, the individual dipole moment of the O-H bond is 1.5 D, while the net dipole moment of water is 1.84 D.

Dipole Moment for Symmetrical Molecules

As mentioned previously, molecules that have symmetrical/opposite dipoles don't have a dipole/dipole moment. This is because the bond polarities cancel each other, so there is no net dipole.

As an example, let's look at BeCl₂:

There is a significant difference between the electronegativity of beryllium and chlorine (it is 1.5), so the individual bonds do have a dipole moment. However, since the bond dipole moments have equal magnitude but point in exactly opposite directions, there is no net dipole moment.

This is why molecules like BeCl₂ are considered non-polar, even though the difference in electronegativity is large.

Dipole Moment Formula

The formula for dipole moment is as follows:

$$\vec{\mu}=\Sigma_{i} q_{i} \vec{r_i}$$

Where,

• \(\vec{\mu}\) is the dipole moment vector.

• q_i is the magnitude of the i^th charge.

• \(\vec{r_i}\) is the position vector of the i^th charge.

This is the more complex version of the formula used for molecules that have more than two atoms. Since dipole moment is a vector quantity, you need to calculate it for each coordinate axis (x, y).

There is a simpler form of this formula that we use just for diatomic molecules:

$$\mu_{diatomic}=Q*r$$

Where,

• Q is the magnitude of the charge
• r is the bond length (distance) between charges.

While you won't need to use this formula for calculations at the AP level, it's helpful to know the formula, so you can understand the trends in dipole moment.

Trends in Dipole Moment

There are three factors affecting dipole moment. These are:

1. Distance

   • The greater the bond length, the greater the dipole moment

     • Shown by the formula, μ = q*r

2. Polarity

   • The greater the difference in polarity, the greater the dipole moment

     • The difference in polarity is what influences the magnitude of the charges (Q)

3. Geometry of the molecule

   • If a molecule has opposing dipoles, it will have no dipole moment (Ex: BeCl₂)

It's important to note that these factors are working in tandem, i.e. all of these factors need to be taken into account. Just because the bond distance is greater, it doesn't automatically mean it has a greater dipole moment. For example, here is the trend in dipole moment as you move down the halogens (group 17)

As you can see, even though the bond length is increasing, the polarity is decreasing. The decrease in polarity is greater than the increase in bond length, so the dipole moment decreases.

Knowing the dipole moment can be very important for determining different chemical properties. For example, here are some properties that dipole moment can affect:

1. Solubility

   • The greater the dipole moment, the more likely that molecule can dissolve in a polar solvent.

     • "like dissolves like" so polar dissolves polar.

2. Boiling/Melting point

   • The greater the dipole moment, the larger the boiling/melting point

     • Greater dipole → stronger forces between molecules → forces are harder to break

3. Stability/Reactivity

   • The greater the dipole moment, the greater the reactivity (i.e. low dipole moment=more stable).