In our discussion of valence bond theory we learned that covalent bonds are formed when two atoms share one or more pairs of electrons. We now want to examine the nature of that sharing in greater detail. First, we will consider the question of whether two atoms share a pair of electrons equally, i.e. is the electron density in the inter-nuclear region symmetrically distributed or not? Bonds in which the electron density is symmertically distributed between the nuclei are called non-polar bonds, while those in which the electron density is unsymmetrically distributed are called polar bonds. Figure 1 presents color-coded schematic representations of polar and non-polar bonds.
Imagining Chemical Bonds
The dots in the figure represent the positions of the nuclei. The colored shapes define areas of high electron density, i.e. a covalent bond. In the top panel the left-hand shape indicates that the electron density is symmetrically distributed between the two nuclei. This could represent the situation in a molecule of dihydrogen, for example. The other image implies that the electron density is higher closer to one nucleus than the other. This would be the case for a molecule like hydrogen fluoride where the electron density lies closer to the more electronegative fluorine atom. In the lower panel, the color gradations correspond to variations in electron density; red represents a region of higher electron density than blue. Note, again, the symmetrical nature of the electron distribution in the left-hand image. The picture on the right suggests that the electron density is higher near one nucleus than the other. The distribution of electron density between two nuclei depends on the electronegativies of the atoms that share the electrons. Chemists represent the uneven distribution of electron density between two nuclei as shown in structure 1 for the specific case of hydrogen fluoride.
Here the symbols d- and d+ are read as "partial minus" and "partial plus". This is the symbolism used to describe a bond dipole. Here's what this convention means: if you compare HF to FF, the electron density around the fluorine atom in HF is higher than it is in FF; if you compare HF to HH, the electron density around the hydrogen atom in HF is lower than it is in HH.
Any bond between two identical atoms is non-polar since the electronegativities of the two atoms is identical. The simplest examples are the diatomic molecules such as H2, N2, and F2. The C-C bond in ethane, H3C-CH3, is also non-polar.
Any bond between two non-identical atoms is polar. The bond in HF is polar. So are the C-H bonds in CH4. Both C-C bonds in propane CH3CH2CH3 are polar. This is because the terminal carbon atoms and the central carbon are not identical. The terminal carbon atoms are both bonded to three hydrogen atoms and the central carbon atom. The central carbon, however, is bonded to two hydrogen atoms and two carbon atoms. An alternative way to think about this is to identify the groups that are attached to each carbon in propane. The left-hand carbon is attached to three hydrogen atoms and a CH2CH3 (ethyl) group. The central carbon is attached to two hydrogen atoms and two CH3 (methyl) groups. Since the right-hand carbon is attached to three hydrogen atoms and an ethyl group, it is identical to the left-hand carbon. Looking at propane in this way allows us to introduce the idea of group electronegativities.
In the same way that the electronegativity of an atom is a measure of the tendency of that atom to attract electrons, group electronegativity is a measure of the tendency of a polyatomic group to attract electrons. Propane contains two CH3 groups and one CH2 group (methylene group). Since these two groups are not identical, they have different group electronegativities. Even though the H3C-CH2 bond is a bond between two carbon atoms, the carbons are not identical because they have different atoms attached to them. As far as the pair of electrons that the two carbons share goes, they experience a different Coulombic attraction from the CH3 group than they do from the CH2 group. One way to investigate group electronegativities experimentally involves nuclear magnetic resonance (NMR) spectroscopy. If you want to know more.
Exercise 1 If the four groups attached to the left-hand carbon in CH3CH3 are H, H, H and CH3, what are the four groups attached to the left-hand carbon in CH3CH2OH?
Exercise 2 What are the four groups attached to the the central carbon in CH3CH(Cl)CH2F? Enter your answers in order of increasing formula weight.
Exercise 3 Are the first and second carbon atoms in propane identical? Yes No
Polar and Non-Polar Molecules
Our discussion to this point has focused on the polarity of individual bonds. Now we want to turn our attention to entire molecules. We'll start with methane, CH4. As we have seen, the C-H bonds in methane are polar. However, a molecule of methane is non-polar. Specifically, the dipole moment of methane is zero. A dipole moment of zero means that the "center of negative charge" in the molecule corresponds to the "center of positive charge". In the case of methane, the "center of positive charge" and the "center of negative charge" are focused on the carbon atom. Think of the "center of charge", whether positive or negative, in the same way that you think of the "center of mass". From that perspective, a molecule with a dipole moment of zero is like a perectly balanced see-saw.
Exercise 4 Select those structures which have a dipole moment of zero.
CCl4 CHCl3 CH2Cl2 CH3Cl CH3CH3 CH3CH2CH3
An alternative way to determine the polarity of a molecule is to assess the interaction of all the bond dipoles in the molecule. A dipole is a vector quantity, and methane has a dipole moment of zero because the vector sum of the individual bond dipoles equals zero. Figure 2 illustrates the idea for a molecule of methane where one C-H bond is aligned along the +z axis of a set of Cartesian coordinates. The arrows represent the magnitude of the z component of the bond dipoles. The magnitude of the z component of each of the C-H bond dipoles shown in color is 1/3 that of the bond dipole that is aligned along the +z axis. The sign of the z component of each of the colored bond dipoles is negative.
A Vector Analysis of the Dipole Moment of Methane
This analysis is based upon the assumption that methane is a tetrahedral molecule. In a way, that assumptiuon puts the cart before the horse. The measurement of dipole moments provided chemists with experimental evidence that alowed them to deduce molecular shapes. Consider the case of dichlorodifluoromethane, CF2Cl2, a component of freon gas. This molecule has a dipole moment of 0.51 Debye. While this fact does not prove that dichlorodifluoromethane is tetrahedral, it does distinguish between square planar structures 2 and 3 .
Exercise 5 Which structure is consistent with the experimental fact that CF2Cl2 has a dipole moment of 0.51 Debye? 2 3
The value of understanding the concept of polarity derives from the insights it provides into many physical and chemical properties of molecules. Let's consider one example, the boiling points of liquids.
Coulomb's Law tells us that as the distance between opposite charges decreases, the attractive force between them increases. If those charges are molecular dipoles, then intermolecular attractions cause the molecules to aggregate. When the aggregates become large enough, droplets of liquid are formed. In the gas phase, the distance between molecules ( r in Coulomb's Law) is very large in comparison to the size of the molecules themselves. The intermolecular attractions are essentially zero. In order to go from a state where there are strong intermolecular interactions to one in which they are essentially zero, it is necessary to add energy to the system. The boiling point of a liquid is a measure of the amount of energy that is required. In other words, the boiling point of a liquid provides an indication of the strength of the forces that hold one molecule next to another.
Exeercise 6 Is the relationship between the polarity of a molecule and its boiling point a direct or an inverse correlation? direct inverse
The boiling point of dihydrogen is -251oC. The boiling point of hydrogen fluoride is +20oC, more than 270o higher!! Clearly the intermolecular forces holding HF molecules together are much greater than those between HH molecules. Figure 3 provides a pictorial rationalization of the intermolcular forces that hold hydrogen fluoride molecules together.
Intermolecular Attractions in HF
The dashed red lines in the figure represent the intermolecular Coulombic attractions between the positve end of a bond dipole in one HF molecule and the negative end of a bond dipole in another HF molecule. Note that the separations between molecules are not much greater than the size of the molecules themselves. The dashed red lines do not represent covalent bonds. The interactions they depict are called secondary bonding interactions.
We'll revisit the idea of polarity when we discuss the classification of solvents.