# Bond polarity and dipole moments

### How to determine the polarity of a bond?

Evaluation and interpretation of the polarity of bond and 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, bond polarity, residue charge on the atoms of the molecules.

The molecules are composed of partially charged nuclei and negatively charged electrons distributed in space. The structural arrangement of these bonds is different in different molecules.

#### Nonpolar covalent bond

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.

Hydrogen, carbon dioxide, boron trichloride, phosphorus pentachloride, benzine are the example of non-polar molecules.

#### Polar covalent bond definition

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.

Hydrogen chloride, water, ammonia, methyl chloride, chlorobenzene are examples of polar molecules.

#### What is the dipole moment of a molecule?

The polarity of a bond in a molecule has quantified a term, called dipole moment (µ).

If +q amount of charge separates at the positive charge center, -q will be accumulated at the negative charge center of the molecule and l is the distance between two centers of the molecule.

∴ Dipole moment, µ = q × l
But non-polar molecules, l=0 and hence µ=0.

Higher the value of µ of a molecule, higher will be its polarity.

#### Dipole moment chemistry

In hydrochloric acid, due to the greater electronegativity of a chlorine atom, the bonding electron pair shifted towards chlorine atom.

Thus chlorine atom acquires a small negative charge and hydrogen atom acquires a small positive charge. If l is the distance of the charge separation usually taken in bond length.

∴ µ = q × l

The dipole moment is a vector quantity and it has both, magnitude and direction. The direction represented by an arrow pointing towards the negative end. The length of the arrow directly proportional to the magnitude of µ.

Problem
P – F, S – F, Cl – F, and F – F which of the following compound has the lowest dipole moment?

The electronegativity difference between the two F atoms is zero. Thus the dipole moment of the fluorine molecule is zero.

#### CGS and SI unit of the dipole moment

In the CGS system, the charge expressed as esu and the length in cm.
Thus the unit of dipole moment = esu cm

The charge in order of 10-10 esu and distance of separation of charge in order of 10-8 cm.

Thus the order of dipole moment
= 10-10 × 10-8
= 10-18 esu cm
This magnitude is known as Debye or simply D.

∴ 1 Debye = 10-18 esu cm

The dipole moment of hydrochloric acid
= 1.03 D
= 1.03 × 10-18 esu cm

In the SI system, the charge expressed in coulomb and length = meter.

Thus SI unit of the dipole moment
= coulomb × meter (c × m).

#### What is the value of 1 Debye?

Dipole moment = q × l.

Thus dipole moment in the CGS system
= 4.8 × 10-10 × 10-8 esu cm
= 4.8 D

But dipole moment in the SI system
1.6 × 10-19 × 10-10 coulombs × meter
= 1.6 × 10-30 C × m

∴ 4.8 Debye = 1.6 ×10-30 coulomb meter

$or,&space;1&space;Debye=\frac{1.6\times&space;10^{-30}}{4.8}\,&space;coulomb\,&space;meter$

= 3.336 × 10-30 coulomb meter

#### The dimension of the dipole moment

Unit of dipole moment = unit of charge × unit of length.
∴ CGS unit of µ = esu × cm

Coulomb’s Law,

$F=\frac{q_{1}\,&space;q_{2}}{D\,&space;r^{2}}$

Thus (esu)2 = dyne × cm2
= gm cm sec-2 × cm2

$\therefore&space;esu=gm^{\frac{1}{2}}\,&space;sec^{-1}\,&space;cm^{\frac{3}{2}}$

$unit\,&space;of\,&space;\mu&space;=gm^{\frac{1}{2}}\,&space;sec^{-1}\,&space;cm^{\frac{3}{2}}\times&space;cm$

$=gm^{\frac{1}{2}}\,&space;sec^{-1}\,&space;cm^{\frac{5}{2}}$

$\therefore&space;Dimension\,&space;of\,&space;\mu&space;=M^{\frac{1}{2}}L^{\frac{5}{2}}T^{-1}$

#### What do you mean by polarization?

When a non-polar substance placed between two parallel plates and an electric field 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 called the electric polarization.

Polarization, however, disappears as soon as the field is withdrawn and the molecule comes back to its original state.

#### Induced polarization of polar molecules

Induced polarization (Pi) and the electric dipole created in the molecule due to the presence of the electric field 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).

∴ μi ∝ F
When F is low, otherwise, hyperpolarization may occur.
μi = αi F
where αi is proportionality constant called induced polarizability of the molecule.

Induced dipole moment measures the case with which the electronic configuration of the molecule 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.

αi = μi/F
∴ Dimension of αi = (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 placed between the two charged plates. The polarizability of the atom increases with the atomic size, atomic number and the case of ionization energy. Thus atom behaves like a dipole and this dipole moment induced by the applied electric field.

#### Clausius mossotti equation in chemistry

Mossotti derived from electromagnetic theory, a relation between the polarizability and the dielectric constant of the non-polar medium between two plates.

It gives the distortion produced in the 1 mole of the substance by a unit electric field. Induced polarizability is constant for the molecule and independent of temperature. Hence induced dipole moment 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. Other substances value of D greater than unity.

The induced dipole moment of the substance calculated by measuring dielectric constant, density (ρ) and knowing the molar mass (M) of the substance.

#### Debye equation for molar polarization

Polar bonding molecules like methyl chloride, water, hydrogen fluoride, etc, molar polarization not constant but decreases with temperature.

Clausius Mossotti equation fails very badly for the polarity of bonds in the molecules. The reason for the failure was put forward by P Debye.

According to him, when an electric field applied between two parallel plates containing polar molecules (gas molecules), two effects will occur.

#### 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 definition

The dipolar molecules will be oriented in the field producing a net dipole moment in the direction of the field.

∴ 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.

#### What is Polarisation in chemical bonding?

For the polar bonding molecules, the total polarization,

Pt = Pi + P₀

#### Polarizability temperature dependence

A polar bond is fixed and unable to orient in the fixed direction, the orientation polarization has taken zero. This is true for the condensed system where strong intermolecular forces prevent the free rotation of the molecules.

At very high temperatures tending to infinity.

1/T = 0 and Pt = 0
∴ Pt = Pi

At high temperatures, the polar molecules rotate at such high speed that orientation polarization vanishes.

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