# Dipole Moments

Evaluation and interpretation of the dipole moment of covalent molecules provide an important tool in the attack of molecular structure. It helps to determine the size and shape of the molecules, spatial arrangements of bonds, bonds partial ionic character, residue charge on the atoms of the molecules, etc.

### Dipole Moment

The molecules are composed of partially charged nuclei and negatively charged electrons distributed in space. The structural arrangement of these particles is different in different molecules.
When the center of gravity of the positive charge due to coincides with the center of gravity of the negative charge due to electrons, the molecules become non-polar. Examples are,
H₂, CO₂, BCl₃, CCl₄, PCl₅, SF₆, C₆H₆, etc.
When the center of gravity of the positive charge does not coincide with the center of gravity of the negative charge, polarity arises in the molecules and the molecules are called polar.
HCl, H₂O, NH₃, CH₃Cl, C₆H₅Cl, etc.
The polar character of the molecules has quantified a term, called dipole moment (µ). The molecule is neutral and hence if (+ q) amount of charge separates at the positive charge center, (- q) will be accumulated at the negative charge center of the molecule. If l is the distance between two centers of the polar molecule, then the dipole moment,
 µ = q × l
For the non-polar molecules, l=0 and hence µ=0. Higher the value of µ of a molecule, higher will be its polarity.
Let us take an example of HCl. Due to the greater electronegativity of Cl-atom, the bonding electron pair is shifted towards Cl-atom and it acquires small negative charge (- q) and hydrogen atom acquires small positive charge (+ q). If l is the distance of the charge separation usually taken in bond length, then,
µ = q × l
The dipole moment is a vector quantity and it has both, magnitude and direction. The direction is represented by an arrow pointing towards the negative end. The length of the arrow is directly proportional to the magnitude of µ.
 The dipole moment of Water

### Unit of the dipole moment

In the C.G.S. system, the charge is expressed as esu and the length in cm.
Thus the unit of µ is esu cm
The charge is the order of 10⁻¹⁰ esu and the distance of separation of charge is in the order of 10⁻⁸ cm.
Hence the order of μ is, 10⁻¹⁰ × 10⁻⁸ = 10⁻¹⁸ esu cm.
This magnitude is called one Debye.
That is, 1 Debye = 10⁻¹⁸ esu cm.

For example, µ of HCl is 1.03 D means, µ of HCl is 1.03 х 10⁻¹⁸ esu cm.
In the SI system, the charge is expressed in coulomb(c) and length is a meter(m).
Hence the unit of µ is coulomb × meter (c х m).

### Dimension of the dipole moment

Unit of µ = Unit of Charge × Unit of Length.
Thus, the unit of µ = esu × cm in the CGS system.

But from the Coulomb’s Low, F = q₁q₂/Dr²
Thus, (esu)² = dyne × cm² = gm cm sec⁻² × cm²
Hence, esu = gm1/2 sec ⁻¹ cm3/2
Hence the dimension of µ = M1/2 T-1 L5/2

### Clausius mossotti equation

When a non-polar substance is placed between two parallel plates and an electric field is applied, the field tends to attract the negatively charged electrons towards the positive plate and positive charge towards a negative plate.
Under this condition, there will be the electrical distortion of the molecule and an electric dipole is created. Such distortion in a molecule is called the electric polarization.
Polarization, however, disappears as soon as the field is withdrawn and the molecule comes back to its original state.
It is thus the induced polarization (Pi) and the electric dipole is created in the molecule due to the presence of the electric field is called induced dipole moment (μi).
The induced dipole moment or simply the induced moment is directly proportional to the strength of the electric field applied(F).
That is, μi ∝ F When F is low, otherwise, hyperpolarization may occur.
μi = αi F
where αi is proportionality constant called induced polarizability of the molecule.
αi measures the case with which the electronic configuration of the molecule can be distorted by an applied electric field. It may also be defined as the amount of induced moment in the molecule when the unit field strength is applied. The polarizability has the dimension of the volume (L³).
αi = μi/F
= (esu × cm)/(esu × cm⁻²)
= cm³
It can also be shown that, αi = r³ where r = radius of the molecule assuming it to have a spherical shape.
For atoms also, distortion occurs when it is placed between the two charged plates. The polarizability of the atom increases with the atomic size (r), atomic number (Z) and the case of excitation (I.P.). Thus atom behaves like a dipole and this dipole moment is induced by the applied electric field.
Clausius Mossotti derived from electromagnetic theory, a relation between the polarizability (αi) and the dielectric constant (D) of the non-polar medium between two plates as,
 Clausius mossotti equation in dipole moment
It gives the distortion produced in the 1 mole of the substance by a unit electric field. αi is constant for the molecule and independent of temperature. Hence Pi is also constant for the molecule and independent of temperature.
D = dielectric constant of the medium = C/C₀ where C = capacitance of the condenser containing the substance and C₀ is the vacuum.
D is the dimensionless quantity and it is unity for vacuum. For other substances, it is greater than unity.
Pi of the substance can be calculated by measuring dielectric constant (D), density (ρ) and knowing the molar mass (M) of the substance.

### Debye modification of Clausius Mossotti equation

For polar molecules like CH₃Cl, H₂O, HF, etc, molar polarization is not constant but decreases with temperature.
Thus, Clausius Mossotti Equation fails very badly for polar molecules. The reason for the failure was put forward by P Debye. According to him, when an electric field is applied between two parallel plates containing polar molecules (gaseous state), two effects will occur.
• Induced polarization
• Orientation polarization

#### Induced polarization

The field will tend to induced polarization in the molecules and the induced polarization in the molecules,
Pi= (4/3) π N₀ αi

#### Orientation polarization

The dipolar molecules will be oriented in the field producing a net dipole moment in the direction of the field.
The orientation polarization,
P₀ = (4/3) π N₀ α₀

Where α₀ = orientation polarisability.
Debye calculated the value of α₀ = μ²/3KT
Considering the two tendencies that polar molecules tend to orient in the direction of the applied field (applied) and thermal orientation tends to destroy the alignment of the molecules.
 Polarization of molecules
Therefore, for the polar molecules, the total polarization,
Pt = Pi + P₀

And the total polarization for polar molecules
Pt = (D-1)/(D+2) M/ ρ
 Debye equation
However the polar molecules in the substance are fixed and unable to orient in the fixed direction, the orientation polarization is taken zero.
This is true for the condensed system where strong intermolecular forces prevent the free rotation of the molecules.
Again if 1/T =0 that is temperature is very high tending to infinity.
Thus 1/T = 0 and Pt=0
∴ Pt=Pi
This is due to the fact that at high temperatures, the polar molecules rotate at such high speed that orientation polarization vanishes.

### Problems solutions

Problem
How can convert 1 Debye to the coulomb meter?
The dipole moment in CGS system is µ = 4.8 × 10⁻¹⁰ × 10⁻⁸ esu cm
= 4.8 D
In the SI system, 1.6 ×10⁻¹⁹ × 10⁻¹⁰ coulombs × meter
= 1.6 × 10⁻³⁰ C × m
Thus, 4.8 Debye = 1.6 ×10⁻³⁰ C × m

or, 1 Debye = (1.6 × 10⁻³⁰)/4.8 C × m
or, 1 Debye = 3.336 × 10⁻³⁰ C × m

Problem
(i)P-F, (ii)S-F, (iii)Cl-F, (iv)F-F which of the following compound has the lowest dipole moment?
The electronegativity difference between two F atoms is zero. Thus the dipole moment of F-F compound is zero.

Dipole Moment and its Determination Unit Dimension

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