Application of dipole moment

Application of dipole moment in chemistry

A different application of dipole moment describes the structure of organic and inorganic molecules.

When a covalent bond is formed between two identical atoms, the two electrons forming the covalent bond may be regarded symmetrically disposed between the two atoms. The centers of gravity of the two electrons and nuclei therefore coincide.

Two dissimilar atoms two electrons are not symmetrically disposed. Because each atom has a different attraction for electrons.

When chlorine and hydrogen combine to form covalent hydrogen chloride, the electrons forming the covalent bond displaced two-word the chlorine atom without any separation of the nucleus.

Different Applications of dipole moment taken for different polar molecules in these courses for school, college students.

Percent ionic character using dipole moment

Let us consider compound hydrogen chloride having the dipole moment μobs and the bond length l cm. Hence the ionic character of the bond calculated from the covalent bond formula.

Chlorine is more electronegative than hydrogen. Chlorine and hydrogen will carry a uni-negative charge and uni-positive charged respectively.

Thus the bond between hydrogen and chlorine is polar and dipole moment of hydrogen chloride greater than zero.

∴ μionic = e × ℓ
= (4.8 × 10-10) ℓ esu cm
where l = bond length.

But the original dipole moment differs from this calculation. This data used to calculate the percentage of ionic character of hydrogen chloride.

Thus the percent of ionic character of the bond

=\left ( \frac{\mu _{obs}}{\mu _{ionic}} \right )\times 100

{\color{DarkBlue} =\left ( \frac{\mu _{obs}}{4.8\times 10^{-10}\times l} \right )\times 100}

where l = bond length of the polar bond.

μobs = q × l
or, q = μobs/l

Polarization of covalent bond

The induced polarization

P_{i}=\frac{4}{3}\, \pi\, N_{0}\, \alpha _{i}

For gas molecules,

P_{i}=\left ( \frac{D_{0}-1}{D_{0}+2} \right )\, \frac{M}{\rho }

where D0 close to unity under this condition.

\left ( \frac{D_{0}-1}{3} \right )\times 22400=\frac{4}{3}\, \pi \, N_{0}\, r^{3}

At NTP, M/ρ = molar volume = 22400cc/mole and
for spherical molecule, αi= r3.

\therefore r^{3}=\left ( \frac{22400}{4\, \pi \, N_{0}} \right )\left ( D_{0}-1 \right )=2.94\times 10^{-21}\left ( D_{0}-1 \right )

Thus the radius of the molecule, r determined by measuring D0 of the substance at NTP.

Chemical properties of noble gases

Mono-atomic noble gases are non-polar, and it indicates the symmetrical charge distribution in the molecule.

Bonding in homonuclear diatomic molecules

The homonuclear diatomic molecules have a covalent bond and largely non-polar.

Nitrogen, oxygen, and chlorine are examples of such types of molecules with symmetrical charge distributions. Thus the bonding electron pair equally shared by the two bonding atoms.

Heteronuclear diatomic molecules

Hydrogen bromide and hydrogen iodide have non zero values of dipole moment. This indicates the unsymmetrical charge distribution between two bonding atoms.

H+ — I

Due to the difference in electronegativity of the constituent atoms in heteronuclear diatomic molecules always polar.

Thus the electron pair is not equally shared and shifted to the more electronegative atom.

Hydrogen chloride1.03 Debye
Hydrogen bromide0.79 Debye
Hydrogen iodide0.38 Debye
Hydrogen fluoride2.00 Debye

Question
The difference between the electronegativity of carbon and oxygen large but the dipole moments of carbon monoxide are very low – why?

Answer
The difference in electronegativity between carbon and oxygen in carbon monoxide very large but the dipole moment of carbon monoxide very low.

This suggested that the charge density in the oxygen atom somehow back-donated to the carbon atom.

Which explains by the formation of a coordinate covalent bond directing towards carbon atom.

The dipole moment of polyatomic molecules

Carbon dioxide, barium chloride, stannous chloride have zero dipole moment indicating that the molecules have a symmetrical charge distribution between the bond.

Thus in carbon dioxide electric moment of one carbon-oxygen bond cancels the electric moment of the other carbon-oxygen bond.

The electric moment or bond moment associated with the bond arising from the difference of electronegativity.

In molecules, the vectorial addition of the bond moments gives the resultant dipole moment of the molecule.

∴ μ2 = m12 + m22 + 2m1m2Cosθ
where m1 and m2 are the bond moments.

Bond moments help to calculate the bond angle of carbon dioxide molecule, where dipole moment = 0 and m1 = m2 = m.

∴ 0 = 2m2(1 + cosθ)
or, θ = 180°

The dipole moment of hydrogen sulfide and water

Water and hydrogen sulfide non-polar because they have non-linear structures. The bond angle can be calculated from the polarity of the molecules.

The polarity of the water molecule

Due to the non-linear structure of water molecules, the net dipole moment ≠ 0.

Polarity of water molecules
Structure of water molecules

If the dipole moment of water
μ = 1.84 D and bond moment = 1.60 D.

∴ μ2 = 2 m2 (1+ cosθ )
or, (1.84)2 = 2 (1.60)2 (1+ cosθ )
∴ θ = 105°

Thus the contribution of non-bonding electrons towards the total dipole moment included within the bond moment.

The polarity of boron trifluoride

Boron trichloride, boron trifluoride are the tetratomic molecules having dipole moment zero, indicating that they have regular planar structure.

Polarity boron trichloride
The geometry of boron trifluoride

Their halogen atoms are on a plane at the corner of the equilateral triangle and boron atom at the intersection of the molecules. Thus the bond moment of the above molecules is zero.

The polarity of ammonia and phosphine

Other types of the molecule such as ammonia and phosphine are polar, where μ≠0 indicated that the molecule has a pyramidal structure.

Hence three hydrogen atoms on a plane and nitrogen atom at the apex of the pyramid in ammonia and phosphine.

But NF3 shows a very small dipole moment although there is a great difference of electronegativity between nitrogen and fluorine atoms and similar structure of NH3.

Thus this low value of dipole moment in NF3 explained by the fact that the resultant bond moment of the three nitrogen – fluorine bonds are acting in the opposite direction to that of the lone pair placed at the nitrogen-atom.

But in NH3, the resultant bond moment is acting in the same direction as that of the lone pair electrons.

Penta atomic molecule

Methane, carbon tetrachloride, platinum chloride are examples of Penta-atomic molecules having zero dipole moment.

This suggests that the molecules either regular tetrahedral or square planer structure. But polar molecules of this type have pyramidal structures.

The bond polarity of methane

For calculating bond polarity, let us discuss the structure of methane that has regular tetrahedral structure and the angle of each H-C-H = 109°28ˊ.

Thus the group moment of methane depends on the arrangement of the bonds in the group and the difference of the electronegativity of the constituent atoms forming the bonds in the group.

Dipole moment of methane
Bond moment of methane

But it can be shown that the group moment of methyl group identical to the bond moment of a carbon-hydrogen bond.

Thus the two bond moments cancel each other and the resulting dipole moment of methane is zero.

∴ mCH3 = 3 mCH × Cos(180° -109°28՛)
= 3 mCH Cos 70°32՛
= 3 mCH × (1/3)
So, mCH3 = mCH

Thus the dipole moment of methane
= mCH (1 + 3 Cos 109°28՛)
= 0

Dipole moment of CH3Cl and CHCl3

μ2 = m12 + m22 + 2 m1m2 Cosθ
But here θ = 0° hence Cosθ = 1

Thus μ2 = m12 + m22 + 2 m1m2
= (m1 + m2)2

∴ μ = (m1 + m2)
= (mCH3 + mCl)
= (1.5 D + 0.4 D)
Thus μCH3Cl = 1.9 D

But for CHCl3

μ = (m1 + m2)
= (mCCl3 + mCH)
= (1.5 D + 0.4 D)
Hence μCHCl3 = 1.9 D

A similar calculation done for the group moment of C2H4, C3H7, C4H9, etc. Thus the bond moment equal to the bond moment of carbon-hydrogen.

But the application of dipole moment gives identical and homologous alcohols and saturated hydrocarbons.