11.2 Intermolecular Forces

The strengths of intermolecular forces of different substances vary over a wide range. However, they are generally much weaker than ionic or covalent bonds (Figure 11.2). For example, only 16 kJ/mol is required to overcome the intermolecular attractions between HCl molecules in liquid HCl in order to vaporize it. In contrast, the energy required to break the covalent bond to dissociate HCl into H and Cl atoms is 431 kJ/mol. Less energy is required to vaporize a liquid or to melt a solid than to break covalent bonds in molecules. Thus, when a molecular substance like HCl changes from solid to liquid to gas, the molecules themselves remain intact.

Figure 11.2 Comparison of a covalent bond (an intramolecular force) and an intermolecular attraction.

Many properties of liquids, including their boiling points, reflect the strengths of the intermolecular forces. A liquid boils when bubbles of its vapor form within the liquid. The molecules of a liquid must overcome their attractive forces in order to separate and form a vapor. The stronger the attractive forces, the higher is the temperature at which the liquid boils. Similarly, the melting points of solids increase with an increase in the strengths of the intermolecular forces.

Three types of intermolecular attractive forces are known to exist between neutral molecules: dipole-dipole forces, London dispersion forces, and hydrogen-bonding forces. These forces are also called van der Waals forces after Johannes van der Waals, who developed the equation for predicting the deviation of gases from ideal behavior. Another kind of attractive force, the ion-dipole force, is important in solutions. As a group, intermolecular forces tend to be less than 15 percent as strong as covalent or ionic bonds. As we consider these forces, notice that each is electrostatic in nature, involving attractions between positive and negative species.

Ion-Dipole Forces

An ion-dipole force exists between an ion and the partial charge on the end of a polar molecule. Polar molecules are dipoles; they have a positive end and a negative end. Recall, for example, that HCl is a polar molecule because of the difference in the electronegativities of the H and Cl atoms.

Positive ions are attracted to the negative end of a dipole, whereas negative ions are attracted to the positive end, as shown in Figure 11.3. The magnitude of the attraction increases as either the charge of the ion or the magnitude of the dipole moment increases. Ion-dipole forces are especially important for solutions of ionic substances in polar liquids, for example, a solution of NaCl in water. We will say more about such solutions in Section 13.1.

Figure 11.3 Illustration of the preferred orientation of polar molecules toward ions. The negative end of the polar molecule is oriented toward a cation (a), the positive end toward an anion (b).

Dipole-Dipole Forces

A dipole-dipole force exists between neutral polar molecules. Polar molecules attract each other when the positive end of one molecule is near the negative end of another, as in Figure 11.4(a). Dipole-dipole forces are effective only when polar molecules are very close together, and they are generally weaker than ion-dipole forces.

Figure 11.4 (a) The electrostatic interaction of two polar molecules. (b) The interaction of many dipoles in a condensed state.

In liquids polar molecules are free to move with respect to one another. As shown in Figure 11.4(b), they will sometimes be in an orientation that is attractive, and sometimes in an orientation that is repulsive. Two molecules that are attracting each other spend more time near each other than do two that are repelling each other. Thus, the overall effect is a net attraction. When we examine various liquids, we find that for molecules of approximately equal mass and size, the strengths of intermolecular attractions increase with increasing polarity. We can see this trend in Table 11.2, which lists several substances with similar molecular weights but different dipole moments. Notice that the higher the dipole moment, the higher is the boiling point.

London Dispersion Forces

What kind of interparticle forces can exist between nonpolar atoms or molecules? Clearly, there can be no dipole-dipole forces when the particles are nonpolar. Yet the fact that nonpolar gases can be liquefied tells us that there must be some kind of attractive interactions between the particles. The origin of this attraction was first proposed in 1930 by Fritz London, a German-American physicist. London recognized that the motion of electrons in an atom or molecule can create an instantaneous dipole moment. Let's consider helium atoms as an example.

In a collection of helium atoms the average distribution of the electrons about each nucleus is spherically symmetrical. The atoms are nonpolar and possess no permanent dipole moment. The instantaneous distribution of the electrons, however, can be different from the average distribution. For example, if we could freeze the motion of the electrons in a helium atom at any given instant, both electrons could be on one side of the nucleus. At just that instant, then, the atom would have an instantaneous dipole moment.

Because electrons repel one another, the motions of electrons on one atom influence the motions of electrons on its near neighbors. Thus, the temporary dipole on one atom can induce a similar dipole on an adjacent atom, causing the atoms to be attracted to each other as shown in Figure 11.5. This attractive interaction is called the London dispersion force (or merely the dispersion force). This force, like dipole-dipole forces, is significant only when molecules are very close together. (In 1993 researchers at the University of Minnesota conducted experiments in which He2 was detected at temperatures below 0.001 K. This "molecule" does not contain an electron-pair bond but instead is held together by the London-dispersion force of attraction. The HeHe "bond" is over 50 Å long and the bond enthalpy is less than 0.1 J/mol!)

Figure 11.5 Two schematic representations of the instantaneous dipoles on two adjacent helium atoms, showing the electrostatic attraction between them.

The ease with which the charge distribution in a molecule can be distorted by an external electric field is called its polarizability. We can think of the polarizability of a molecule as a measure of the "squashiness" of its electron cloud; the greater the polarizability of a molecule, the more easily its electron cloud can be distorted to give a momentary dipole. Therefore, more polarizable molecules have stronger London dispersion forces. In general, larger molecules tend to have greater polarizabilities because they have a greater number of electrons and their electrons are farther from the nuclei. Therefore, the strength of the London dispersion forces tends to increase with increasing molecular size. Because molecular size and mass generally parallel each other, dispersion forces tend to increase in strength with increasing molecular weight. Thus, the boiling points of the halogens and the noble gases increase with increasing molecular weight (Table 11.3).

The shapes of molecules can also play a role in the magnitudes of dispersion forces. For example, n-pentane and neopentane, illustrated in Figure 11.6, have the same molecular formula, C5H12, yet the boiling point of n-pentane is 27 K higher than that of neopentane. (The n in n-pentane is an abbreviation for the word normal. A normal hydrocarbon is one in which carbon atoms are arranged in a straight chain.) The difference can be traced to the different shapes of the two molecules. The overall attraction between molecules is greater in the case of n-pentane because the molecules can come in contact over the entire length of the long, somewhat cylindrically shaped molecule. Less contact is possible between the more compact and nearly spherical molecules of neopentane.

Figure 11.6 Molecular shape affects intermolecular attraction. The n-pentane molecules make more contact with each other than do the neopentane molecules. Thus, n-pentane has the greater intermolecular attractive forces and therefore has the higher boiling point (bp).

Dispersion forces operate between all molecules, whether they are polar or nonpolar. In fact, dispersion forces between polar molecules commonly contribute more to intermolecular attractions than do dipole-dipole forces. In the case of HCl, for example, it is estimated that dispersion forces account for more than 80 percent of the total attraction between molecules; dipole-dipole attractions account for the rest.

When comparing the relative strengths of intermolecular attractions, the following generalizations are useful:

  1. When the molecules have comparable molecular weights and shapes, dispersion forces are approximately equal. In this case, differences in the magnitudes of the attractive forces are due to differences in the strengths of dipole-dipole attractions, with the most polar molecules having the strongest attractions.
  2. When molecules differ widely in their molecular weights, dispersion forces tend to be the decisive ones. In this case, differences in the magnitudes of the attractive forces can usually be associated with differences in molecular weights, with the most massive molecule having the strongest attractions.

There is, however, a type of intermolecular attraction that is typically stronger than dispersion forces—the hydrogen bond—which we consider after the next Sample Exercise.

SAMPLE EXERCISE 11.1

The dipole moments of methyl chloride, CH3Cl, and methyl iodide, CH3I, are 1.87 D and 1.62 D, respectively. (a) Which of these substances will have the greater dipole-dipole attractions among its molecules? (b) Which of these substances will have the greater London dispersion attractions? (c) The boiling points of CH3Cl and CH3I are 249.0 K and 315.6 K, respectively. Which substance has the greatest overall attractive forces?

SOLUTION (a) Dipole-dipole attractions increase in magnitude as the dipole moment of the molecule increases. Thus, CH3Cl molecules attract each other by stronger dipole-dipole forces than CH3I molecules do. (b) When molecules differ in their molecular weights, the more massive molecule generally has the stronger dispersion attractions. In this case CH3I (142.0 amu) is much more massive than CH3Cl (50.5 amu). Thus, the dispersion forces will be stronger for CH3I. (c) Because CH3I has the higher boiling point, we can conclude that more energy is required to overcome attractive forces between CH3I molecules. Thus, the total intermolecular attractions are stronger for CH3I, suggesting that the dispersion forces are the decisive ones in comparing these two substances.

PRACTICE EXERCISE

Of Br2, Ne, HCl, HBr, and N2, which is likely to have (a) the largest intermolecular dispersion forces; (b) the largest dipole-dipole attractive forces? Answers: (a) Br2; (b) HCl

Hydrogen Bonding

Figure 11.7 shows the boiling points of the simple hydrogen compounds of group 4A and 6A elements. In general, the boiling point increases with increasing molecular weight, owing to increased dispersion forces. The notable exception to this trend is H2O, whose boiling point is much higher than we would expect on the basis of its molecular weight. The compounds NH3 and HF also have abnormally high boiling points. These compounds also have many other characteristics that distinguish them from other substances of similar molecular weight and polarity. For example, water has a high melting point, a high specific heat, and a high heat of vaporization. Each of these properties indicates that the intermolecular forces between H2O molecules are abnormally strong.

Figure 11.7 Boiling points of the group 4A (bottom) and 6A (top) hydrides as a function of molecular weight.

These strong intermolecular attractions in H2O result from hydrogen bonding. Hydrogen bonding is a special type of intermolecular attraction that exists between the hydrogen atom in a polar bond (particularly an H F, H O, or H N bond) and an unshared electron pair on a nearby small electronegative ion or atom (usually an F, O, or N atom on another molecule). For example, a hydrogen bond exists between the H atom in an HF molecule and the F atom of an adjacent HF molecule, F H F H (where the dots represent the hydrogen bond between the molecules). Several additional examples are shown in Figure 11.8.

Figure 11.8 Examples of hydrogen bonding. The solid lines represent covalent bonds; the red dotted lines represent hydrogen bonds.

Hydrogen bonds can be considered unique dipole-dipole attractions. Because F, N, and O are so electronegative, a bond between hydrogen and any of these three elements is quite polar, with hydrogen at the positive end:

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The hydrogen atom has no inner core of electrons. Thus, the positive side of the bond dipole has the concentrated charge of the partially exposed, nearly bare proton of the hydrogen nucleus. This positive charge is attracted to the negative charge of an electronegative atom in a nearby molecule. Because the electron-poor hydrogen is so small, it can approach an electronegative atom very closely and thus interact strongly with it.

The energies of hydrogen bonds vary from about 4 kJ/mol to 25 kJ/mol or so. Thus, they are much weaker than ordinary chemical bonds (see Table 8.3). Nevertheless, because hydrogen bonds are generally stronger than dipole-dipole or dispersion forces, they play important roles in many chemical systems, including those of biological significance. For example, hydrogen bonds are important in stabilizing the structures of proteins, which are key parts of skin, muscles, and other structural components of animal tissues (see Section 25.7). They are also responsible for the way that DNA is able to carry genetic information (Section 25.9).

One of the remarkable consequences of hydrogen bonding is found in comparing the density of ice to that of liquid water. In most substances the molecules in the solid are more densely packed than in the liquid. Thus, the solid phase is denser than the liquid phase (Figure 11.9). By contrast, the density of ice at 0°C (0.917 g/mL) is less than that of liquid water at 0°C (1.00 g/mL).

The low density of ice compared to that of water can be understood in terms of hydrogen-bonding interactions between water molecules. The interactions in the liquid are random. However, when water freezes, the molecules assume the ordered, open arrangement shown in Figure 11.10, which leads to a less dense structure for ice compared to that of water: A given mass of ice occupies a greater volume than does the same mass of liquid water. The structure of ice permits the maximum number of hydrogen-bonding interactions between the H2O molecules.

The density of ice compared to water profoundly affects life on Earth. Because ice is less dense than water, ice floats (Figure 11.9). When ice forms in cold weather, it covers the top of the water, thereby insulating the water below. If ice were more dense than water, ice forming at the top of a lake would sink to the bottom, and the lake could freeze solid. Most aquatic life could not survive under these conditions. The expansion of water upon freezing (Figure 11.11) is also what causes water pipes to break in freezing weather.

SAMPLE EXERCISE 11.2

In which of the following substances is hydrogen bonding possible: methane (CH4), hydrazine (H2NNH2), methyl fluoride (CH3F), or hydrogen sulfide (H2S)?

SOLUTION All of these compounds contain hydrogen, but hydrogen bonding normally requires that the hydrogen be directly bonded to N, O, or F atom. There also needs to be an unshared pair of electrons on an electronegative atom (usually N, O or F) in a nearby molecule. These criteria clearly eliminate CH4 and H2S, which do not contain H bonded to N, O, or F. They also eliminate CH3F whose Lewis structure shows a central C atom surrounded by three H atoms and a F atom. (Carbon always forms four bonds, whereas hydrogen and fluorine form one each.) Because the molecule contains a C F bond and not a H F one, it does not form hydrogen bonds. In the case of H2NNH2, however, we find N H bonds, and therefore hydrogen bonds exist between the molecules.

PRACTICE EXERCISE

In which of the following substances is significant hydrogen bonding possible: methylene chloride (CH2Cl2), phosphine (PH3), hydrogen peroxide (HOOH), or acetone (CH3COCH3)? Answer: HOOH

Comparing Intermolecular Forces

Let's put the intermolecular forces in perspective. To summarize, we can identify the intermolecular forces that are operative in a substance by considering its composition and structure. Dispersion forces are found in all substances. The strengths of these forces increase with increased molecular weight and also depend on molecular shapes. Dipole-dipole forces add to the effect of dispersion forces and are found in polar molecules. Hydrogen bonds, which are recognized by the presence of H atoms bonded to F, O, or N, also add to the effect of dispersion forces. Hydrogen bonds tend to be the strongest type of intermolecular force. None of these intermolecular forces, however, is as strong as ordinary ionic or covalent bonds. Figure 11.12 presents a systematic way of identifying the kinds of intermolecular forces in a particular system, including ion-dipole and ion-ion forces.

Figure 11.12 Flowchart for recognizing the major types of intermolecular forces. London dispersion forces occur in all instances. The strengths of the other forces generally increase proceeding from left to right.

SAMPLE EXERCISE 11.3

List the substances BaCl2, H2, CO, HF, and Ne in order of increasing boiling points.

SOLUTION The boiling point depends in part on the attractive forces in the liquid. These are stronger for ionic substances than for molecular ones, so BaCl2 has the highest boiling point. The intermolecular forces of the remaining substances depend on molecular weight, polarity, and hydrogen bonding. The other molecular weights are H2 (2), CO (28), HF (20), and Ne (20). The boiling point of H2 should be the lowest because it is nonpolar and has the lowest molecular weight. The molecular weights of CO, HF, and Ne are roughly the same. Because HF can hydrogen bond, it has the highest boiling point of the three. Next is CO, which is slightly polar and has the highest molecular weight. Finally, Ne, which is nonpolar, should have the lowest boiling point of these three. The predicted order of boiling points are therefore

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The actual normal boiling points are H2 (20 K), Ne (27 K), CO (83 K), HF (293 K), and BaCl2 (1813 K), in agreement with our predictions.

PRACTICE EXERCISE

(a) Identify the intermolecular forces present in the following substances, and (b) select the substance with the highest boiling point: CH3CH3, CH3OH, CH3CH2OH. Answers: (a) CH3CH3 has only dispersion forces, whereas the other two substances have both dispersion forces and hydrogen bonds; (b) CH3CH2OH