# Dipole Moments

Dipole moments occur when there is a separation of charge. They can occur between two ions in an ionic bond or between atoms in a covalent bond; dipole moments arise from differences in electronegativity. The larger the difference in electronegativity, the larger the dipole moment. The distance between the charge separation is also a deciding factor into the size of the dipole moment. The dipole moment is a measure of the polarity of the molecule.

### Introduction

When atoms in a molecule share electrons unequally, they create what is called a dipole moment. This occurs when one atom is more electronegative than another, resulting in that atom pulling more tightly on the shared pair of electrons, or when one atom has a lone pair of electrons and the difference of electronegativity vector points in the same way. One of the most common examples is the water molecule, made up of one oxygen atom and two hydrogen atoms. The differences in electronegativity and lone electrons give oxygen a partial negative charge and each hydrogen a partial positive charge.

### Dipole Moment

The equation to figure out the dipole moment of a molecule is given below:

$\mu = q \, r$

where μ is the dipole moment, q is the magnitude of the charge, and r is the distance between the charges. The dipole moment acts in the direction of the vector quantity. The unit used for dipole moments is the debye (D); 1D = 3.34 × 10-30 C × m

Figure 1: Dipole moment of water (3)                                            Figure 2: Electronegativity of common elements

The vector points from positive to negative, on both the molecular (net) dipole moment and the individual bond dipoles. The table above shows the electronegativity of some of the common elements. The larger the difference in electronegativity between the two atoms, the more electronegative that bond is. To be considered a polar bond, the difference in electronegativity must be large. The dipole moment points in the direction of the vector quantity of each of the bond electronegativities added together.

Example 1: Water

The water molecule picture from Figure 1 can be sued to determine the direction and magnitude of the dipole moment. From the electronegativities of water and hydrogen, the difference is 1.2 for each of the hydrogen-oxygen bonds. Next, because the oxygen is the more electronegative atom, it exerts a greater pull on the shared electrons; it also has two lone pairs of electrons. From this, it can be concluded that the dipole moment points from between the two hydrogen atoms toward the oxygen atom. Using the equation above, the dipole moment is calculated to be 1.85 D by multiplying the distance between the oxygen and hydrogen atoms by the charge difference between them and then finding the components of each that point in the direction of the net dipole moment (remember the angle of the molecule is 104.5˚).

The bond moment of O-H bond =1.5 D, so the net dipole moment =2(1.5)×cos(104.5/2)=1.84 D.

### Polarity and Structure of Molecules

The polarity of a molecule is influenced by its structure. If a molecule is completely symmetric, then the dipole moment vectors on each molecule will cancel each other out, making the molecule nonpolar. A molecule can only be polar if the structure of that molecule is not symmetric. A basic example of a nonpolar molecule is CO2. It is linear and completely symmetric, so the dipole moment vectors on both oxygen atoms cancel out. An example of a polar molecule is H2O. Because of the lone pair on oxygen, the structure of H2O is bent, which means it is not symmetric. The vectors do not cancel each other out, making the molecule polar.

Dipole Moment
Molecular compounds are either polar or nonpolar.
Here are some examples:

Polarity observed when a stream of liquid subjected to charged rods.  Nonpolar CCl4 is not deflected; moderately polar acetone deflects slightly; highly polar water deflects strongly.

The measure of molecular polarity is a quantity called the dipole moment (u). Dipole moment is defined as magnitude of charge (Q) times distance (r) between the charges.

u = (Q)(r)       Q charge in coulombs (C)      r distance in meters (m)

Consider a proton & electron 100 pm (10-12 m) apart:
Each particle possess a charge of 1.60x10-19 C.  When proton & electron closetogether, the dipole moment (degree of polarity) decreases. However, as proton & electron get farther apart, the dipole moment increases. In this case, the dipole moment calculated as:
u = (Q)(r) = (1.60x10-19 C)(1.00x10-10 m) = 1.60x10-29 C.m       [1 debye (D) = 3.336x10-30 C.m]

The debye characterizes size of dipole moment. When a proton & electron 100 pm apart, the dipole moment is 4.80 D:
(1.60x10-29 C.m)(1 D/3.336x10-30 C.m) = 4.80 D

4.80 D is a key reference value! It represents a pure charge of +1 & -1 100 pm apart.
The bond is 100% ionic.

Note:  The debye named after Peter Debye (1884-1966)
who was awarded 1936 Nobel Prize in chemistry
for studies of dipole moments.

When proton & electron are separated by 120 pm, u = (120/100)(4.80D) = 5.76 D  (100% ionic)
When proton & electron are separated by 150 pm, u = (150/100)(4.80D) = 7.20 D  (100% ionic)
When proton & electron are separated by 200 pm, u = (200/100)(4.80D) = 9.60 D   (100% ionic)

It is relatively easy to measure dipole moments. Place substance between charged plates--polar molecules increase the charge stored on plates and the dipole moment can be obtained (has to do with capacitance).

CH3Cl:
C-Cl, the key polar bond, is 178 pm. Measurement reveals 1.87 D.
From this data, % ionic character can be computed.
If this bond was 100% ionic (based on proton & electron),
u = 178/100)(4.80 D) = 8.54 D
Since measurement 1.87 D,
% ionic = (1.7/8.54)x100 = 22%

HCl:
u = 1.03 D (measured)     H-Cl bond length 127 pm
If 100% ionic,
u = (127/100)(4.80 D) = 6.09 D
% ionic = (1.03/6.09)x100 = 17%

### References

1. Housecroft, Catherine E. and Alan G. Sharpe. Inorganic Chemistry.  3rd ed.  Harlow: Pearson Education, 2008. Print. (Pages 44-46)
2. Tro, Nivaldo J.  Chemistry: A Molecular Approach.  Upper Saddle River: Pearson Education, 2008. Print. (Pages 379-386)
3. http://www.wiley.com/college/boyer/0470003790/reviews/pH/dipole.gif
4. http://web.fccj.org/~ethall/dipole/dipole.htm
5. http://www.tutor-homework.com/Chemistry_Help/electronegativity_table/electronegativity.html

### Problems

1. What is a dipole moment and how does it effect molecules in solution?
2. How is a dipole moment calculated (equation and what each variable represents)?
3. Calculate the dipole moment of nitrogen trichloride.

1. A dipole moment is an unequal sharing of electrons which causes polar molecules.  It allows for interactions between other polar molecules in solution by the partial positive and partial negative charges on each molecule attracting one another.
2. u=qr where q is the magnitude of the charge and r is the distance between them.
3. 0.6 D

11:37, 14 Jul 2014

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