# Dipole Moments

#### Introduction:

Evaluation and interpretation of dipole moment of covalent molecules provide important tool in the attack of molecular structure. It helps to determine 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 (µ):

The molecules are composed of the 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 positively charge due to coincides with the center of gravity of the negative charge due to electrons, the molecules becomes non polar.
Examples:
 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 are 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 greater electronegativity of Cl-atom, the bonding electron pair is shifted towards Cl- atom and it acquire 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
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.

 + q - q H Cl ← --l - →

The length of the arrow is directly proportional to the magnitude of µ.

### Unit of Dipole Moment:

In C.G.S. system, the charge is expressed as esu and the length is 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 SI system, charge is expresses in coulomb(c) and length is meter(m).
Hence the unit of µ is coulomb × meter (c х m).

How can convert 1 Debye to Coulomb Meter.

 The dipole moment in CGS system is,  µ = 4.8 × 10⁻¹⁰ × 10⁻⁸ esu cm = 4.8 D In SI system,  1.6 ×10⁻¹⁹ × 10⁻¹⁰ coulomb × metre  = 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

### Dimension of µ:

 Unit of µ =  Unit of Charge × Unit of Length.  Thus, the unit of µ  = esu × cm in CGS system. But from the Coulomb’s Low,  F = q1q2/D r² Thus, (esu)² = dyne × cm² = gm cm sec⁻² × cm² Hence, esu = gm½ sec ⁻¹ cm³/₂ Hence the dimension of µ  = M¹/₂ T⁻¹ L⁵/₂

### Induced Polarization- 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 negative plate.
Under this condition there will be 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 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 hyper polarization may occur.
μi = αi F where, αi is proportionality constant, called induced polarisability 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 unit field strength is applied. The polarisibility 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 spherical shape.
For atoms also, distortion occurs when it is placed between the two charged plates. The polarisibility of the atom increases with the atomic size (r), atomic number (Z) and the case of excitation (I.P.). Thus atom behave like dipole and this dipole moment is induced by the applied electric field.
Clausius Mossotti derived from electromagnetic theory, a relation between the polarisibility (αi) and the dielectric constant (D) of the non-polar medium between two plates as,

### Clausius Mossotti Equation for non-polar substance

Where, N₀ denotes Avogadro number, = molar mass and ρ = density of the medium.
The quantity 4/3 π N₀ αi is called molar induced polarization.
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 dimension less quantity and it is unity for vacuum. For other substance, it is grater then unity. Pi of the substance can be calculated by measuring dielectric constant (D) , density (ρ) and knowing the molar mass (M) of the substance.

### Orientation Polarization- 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 effect will occur.
(i) The field will tend to induced polarization in the molecules and the induced polarization in the molecules,
Pi= (4/3)πN₀αi
(ii)The dipolar molecules will be oriented in the field producing a net dipole moment in the direction of the field.
This polarization is called orientation polarization,
P₀ = (4/3)πN₀α0
Where α0 = orientation polarisibility.
Debye calculated the value of α0 = μ2/3KT
Considering the two tendency 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.
 For Non-Polar Molecules
 For Polar 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 inter molecular forces prevent the free rotation of the molecules.
In that case Pt=Pi
Again if 1/T =0 that is temperature is very high tending to infinity 1/T = 0, Pt=0
And Pt=Pi
This is due to the fact that at high temperature, the polar molecules rotate in such high speed that orientation polarization vanishes.

#### Application of Debye equation:

This equation can be used to determine the dipole moment of the polar molecules. If Pt is plotted against 1/T , a straight line is obtained and that verify the Debye equation.
 The graph of polar and non-polar molecules
The intercept, A = 4/3 π N₀αi from which the induced polarization can be calculated.
The slope, B = 4/3 π N₀(μ²/3k) from which the dipole moment (μ) of the polar molecules can be calculated.
 Determination of dipole moment
Pt is determined for the substance at different temperatures by determining dielectric constant (D) and density (ρ) at different temperature.

Dipole Moment and its Determination Unit Dimension

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