3.3 Dipole Moments, Electronegativity, and Polarizability

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3.3.1 Polarity

I All molecules can be viewed as resonance hybrids of purely covalent and ionic characters

1. homonuclear diatomic molecules: both atoms have the same electron-withdrawing power and therefore the covalent resonance structure makes the biggest contribution.

   

2. heteronuclear diatomic molecules: one element has a greater electron-withdrawing power than the other and the ionic resonance structure makes a significant contribution.

   

II As a molecule has greater partial charge, it is said to have considerable ionic character.

III polar: when two atoms have different electron-withdrawing powers and electrons are drawn closer towards the more electronegative atom

1. When a bond is polar, it is said to have an electric dipole moment

   1. it is important to include 'electric' as there are other types as well (magnetic)

2. For a X-Y diatomic molecule, the electric dipole moment is calculated by: $\mu = q \times e \times d$ (Eq.24)

   1. Frequently reported in Debye (D); $1 D = 3.336 \times 10^{-30} C ⋅ m$

3. The more electronegative element of a polar bond has the negative partial charge.

4. A dipole moment is a vector quantity; it has a direction and by SI convention, the arrow points from $\sigma -$ end of the bond to $\sigma +$ end.

   

IV polarity is a molecular property; the net dipole moment is the sum of all vector quantities of the individual dipoles

1. Note: The molecular dipole moment cannot be accurately calculated with a simple addition of vectors; there are discrepancies between vector additions and experimental

2. lone pairs significantly affect the value of $\mu$; if the resultant dipole moment acts in a direction that is reinforced by the lone pair, $\mu$ increases.

3. If the resultant dipole moment opposes the effects of the lone pair, $\mu$ decreases.

   1. Compare $NH_{3}$ and $NF_{3}$. Although $\delta\chi$ is greater for N-F bond, net dipole moment is greater for $NH_{3}$ because N-H dipoles point towards lone pair.

3.3.2 Electronegativity

X electronegativity, Pauling ($\chi^{P}$) difference of experimental bond enthalpy and bond enthalpy calculated from additive rules $\delta\chi = \chi^{P}(Y)-\chi^{P}(X) = \sqrt{\delta D}$ (Eq. 25)

1. bond dissociation enthalpy (D, energy required to break a bond) can be roughly estimated using additive rules as shown in Eq. 7: $D(X-Y) = \frac{1}{2} \times [D(X-X) + D(Y-Y)]$ (Eq. 26)

   1. Eq. 7 is relatively accurate for nonpolar molecules (e.g. ClBr) but horrible for molecules with significant ionic character (e.g. HCl)

   2. Pauling assumed that this was because of the ionic contribution of the bond, as atoms had different electron-withdrawing powers.

2. $\sqrt{\delta D} = D_{experimental} - D_{calculated}$; kJ is converted to eV to obtain a small numeric value

3. Different oxidation states have different electron attracting powers; elements may have more than one $\chi^{P}$ value

XI electronegativity, Mulliken ($\chi^{M}$): the average of ionization energy ($I$) and electron affinity ($EA_{1}$)

1. An electronegativity value that is based on atomic properties

XII electronegativity, Allred-Rochow ($\chi^{AR}$): A measure of the electrostatic force exerted by $Z_{eff}$ on the valence electron (basically, based on $Z_{eff}$)

$\chi^{AR} = (3590 \times \frac{Z_{eff}}{r^{2}_{cov}} + 0.744)$ (Eq. 27)

3.3.3 Polarizability

XIII polarizability ($\alpha$): A measure of the ease with which the electron cloud of a molecule can be distorted

1. species that are electron rich and heavy tend to be more polarizable

XIV polarizing power: A measure of the ease with which an atom can distort the electron cloud of another atom.

1. species that are small with high charge tends to have greater polarizing power

2. A compound composed of small, highly charged cation (strong polarizing power) and large, polarizable anion tends to have bonds with considerable covalent character.

3.3.4 Bond Strengths and Bond Lengths

I dissociation energy (D): the energy required to separate the bonded atoms completely

1. it is the energy required to acquire a homolytic cleavage of a bond like shown below: $H-Cl = \cdot H(g) + \cdot Cl(g)$

II Dissociation energy is representative of the strength of each bond

1. The dissociation energy for C≡C bonds is a lot less than 3 C-C bonds (Ref. Figure 23)

2. the repulsion between lone pairs can also weaken the bonding (e.g. F2)

III bond length: distance between the centers of two atoms joined by a covalent bond

1. the length of the bond is the distance when the potential energy of the molecule is minimum (Ref. Figure 23)

2. bond length correlates to bond strength; the stronger the bond, the shorter the bond.

3. multiple bonds (with additional bonding electrons) attracts the nuclei more strongly and pulls the atoms closer together