Force intermolecular 326

Intermolecular forces are also referred to as noncovalent interactions or nonbonded interactions. 

Intermolecular forces are the interactions that exist between molecules. A functional group determines the type and strength of these interactions. 

Ionic compounds contain oppositely charged particles held together by extremely strong electrostatic interactions. TThese ionic interactions are much stronger than the intermolecular forces present between covalent molecules, so it takes a great deal of energy to separate oppositely charged ions from each other. 

Covalent compounds are composed of discrete molecules. The nature of the forces between the molecules depends on the functional group present. There are three different types of interactions, presented here in order of increasing strength  

Although any single van der Waals interaction is weak, a large number of van der Waals interactions creates a strong force. For example, geckos stick to walls and ceilings by van der Waals interactions of the surfaces with the 500,000 tiny hairs on each foot. 

Intermolecular forces were introduced in Chapter 5 to expiain nonideai gas behavior. 

Remember that temperature is a measure of the random motions of the particles in a substance. 

In Chapters 8 and 9 we saw that atoms can form stabie units caiied molecules by sharing eiectrons. This is caiied intramolecular (within the moiecuie) bonding. In this chapter we consider the properties of the condensed states of matter (iiquids and soiids) and the forces that cause the aggregation of the components of a substance to form a iiquid or a soiid. These forces may invoive covaient or ionic bonding, or they may invoive weaker interactions usuaiiy caiied intermolecular forces (because they occur between, rather than within, moiecuies). 

Dipole-dipole forces are forces that act between polar molecules. 

As we saw in Section 8.3, molecules with polar bonds often behave in an electric field as if they had a center of positive charge and a center of negative charge. That is, they exhibit a dipole moment. Molecules with dipole moments can attract each other electrostatically by lining up so that the positive and negative ends are close to each other, as shown in Fig. 10.2(a). This is called a dipole-dipole attraction. In a condensed state such as a liquid, where many molecules are in close proximity, the dipoles find the best compromise between attraction and repulsion. That is, the molecules orient themselves to maximize the —0 interactions and to minimize — and — interactions, as represented in Fig. 10.2(b). 

We will proceed in our study of liquids and solids by first considering the properties and structures of liquids and solids. Then we will consider the changes in state that occur between solid and liquid, liquid and gas, and solid and gas. 

The strengths of intermoiecuiar forces in different substances vary over a wide range but are generally much weaker than intramolecular forces—ionic, metallic or covalent bonds ( FIGURE 11.3). Less energy, therefore, is required to vaporize a liquid or melt a solid than to break covalent bonds. For example, only 16 kj/mol is required to overcome the intermoiecuiar attractions in liquid HCl in order to vaporize it. In contrast, the energy required to break the covalent bond in HCl is 431 kj/mol. Thus, when a molecular substance such as HCl changes from solid to liquid to gas, the molecules remain intact. 

Three types of intermoiecuiar attractions exist between electrically neutral molecules dispersion forces, dipole—dipole attractions, and hydrogen bonding. The first two are collectively called van der Waab forces after lohannes van der Waals, who developed the equation for predicting the deviation of gases from ideal behavior. (Section 10.9) 

Another kind of attractive force, the ion—dipole force, is important in solutions. 

A FIGURE 11.4 Dispersion forces. Snapshots of the charge distribution for a pair of 

You might think there would be no electrostatic interactions between electrically neutral, nonpolar atoms and/or molecules. Yet some kind of attractive interactions must exist because nonpolar gases like helium, argon, and nitrogen can be liquefied. Fritz London, a German-American physicist, first proposed the origin of this attraction in 1930. London recognized that the motion of electrons in an atom or molecule can create an instantaneous, or momentary, dipole moment. 

CHAPTER 12 Intermolecular Forces and the Physical Properties of Liquids and Solids 

In Chapter 11, we learned that gases consist of rapidly moving particles (molecules or atoms), separated by relatively large distances. Liquids and solids, the condensed phases [W margin note in Section 1.2], consist of particles (molecules, atoms, or ions) that are touching one another. The attractive forces that hold particles together in the condensed phases are called intermolecular forces. The magnitude of intermolecular forces is what determines whether the particles that make up a substance are a gas, liquid, or solid. 

Particles in a gas are separated by large distances and free to move entirely independently of one another. 

Particles in a liquid are touching one another but free to move about. 

Particles in a solid are essentially locked in place with respect to one another. 

Student Annotation The term intermolecular is used to refer to attractive forces between moiecuies, atoms, or ions. 

4 Thermodynamic Effects 4.16.2.4.1 Intermolecular forces (i) Melting points and boiling points 

2-Isoxazolines with alkyl substituents are also all liquids (or low melting solids) and incorporation of aryl substituents results in crystallinity. Introduction of carboxy substituents and endocyclic carbonyl or imino groups also has the anticipated effect, with crystalline products being isolated. These trends are illustrated by the data compiled in Table 2. 

2-Benzisoxazole and its simple alkyl derivatives are liquids with b.p. s of 84°C/11 mmHg for the unsubstituted system, 92.5°C/11 mmHg for the 3-methyl compound, and 117 °C/11 mmHg for the 4,6-dimethylbenzisoxazole. 2,1-Benzisoxazole is also a liquid, b.p. 94.4-94.5 °C/11 mmHg, and its 3-methyl derivative has a b.p. of 115.5-116 °C/11 mmHg. Introduction of a 3-phenyl substituent in both systems results in crystallinity, with m.p. s of 83-84 °C and 52-53 °C, respectively. Polar substituents, as anticipated, also impart crystallinity to these systems. 

Isoxazole dissolves in approximately six volumes of water at ordinary temperature and gives an azeotropic mixture, b.p. 88.5 °C. From surface tension and density measurements of isoxazole and its methyl derivatives, isoxazoles with an unsubstituted 3-position behave differently from their isomers. The solubility curves in water for the same compounds also show characteristic differences in connection with the presence of a substituent in the 3-position (62HC(17)1, p. 178). These results have been interpreted in terms of an enhanced capacity for intermolecular association with 3-unsubstituted isoxazoles as represented by (9). Cryoscopic measurements in benzene support this hypothesis and establish the following order for the associative capacity of isoxazoles isoxazole, 5-Me, 4-Me, 4,5-(Me)2 3-Me 3,4-(Me)2 3,5-(Me)2 and 3,4,5-(Me)3 isoxazole are practically devoid of associative capacity. 

No detailed study of the solubility characteristics of more complexly substituted isoxazoles has been made. However, qualitative indications of solubility characteristics may be found associated with their synthesis. 

In the absence of solvent molecules, the intermolecular forces governing the molecular interachons are essentially of an electrostatic nature and depend on the presence of electrical charges and dipoles in the molecules [3, 4]. 

The greater the molecular weight of the molecule, the greater the number of electrons and the greater these forces. 

The greater the intermolecular force, the higher the boiling point. Polarity and molecular weight must be considered. 

Problem 2.16 Account for the following progression in boiling point CH,CL 43 °C. 

The order of polarity is CH,C1 CH,Br CH,I. The order of molecular weight is CH,I CH,Br CH,C1. The two trends oppose each other in affecting the boiling point. The order of molecular weight predominates here. 

Problem 2.17 The boiling points of n-pentane and its isomer neopeniane are 36.2 °C and 9.5 °C, respectively. Account for this difference. (See Problem 1.4 for the structural formulas.)  

It should be noted that it is assumed that the intermolecular forces do not affect the internal degrees of freedom so that is independent of whether these forces are present or not. When they are absent (Zf = 0), the integral Z collapses to and equation (2.2.31) becomes the same as equation (2.2.23). The important task of the statistical thermodynamics of imperfect gases and liquids is to evaluate Z. This subject is discussed in detail later in this chapter. However, the nature of the intermolecular forces which give rise to the potential energy U is considered next. 

Molecules exhibit relatively long-range attractive forces between themselves which give rise to the cohesive forces in liquids. These forces arise because the electronic distribution in the molecule or atom making up the liquid is not uniform either on a time-averaged basis or with respect to its instantaneous value. Non-uniformity in the time-averaged electronic distribution in a molecule is a well-known phenomenon, and is discussed in terms of the experimentally measured dipole 

The potential due to an ideal dipole / at a distance r from its center is 

In this case the potential is independent of the direction from the charge at which it is measured. The dipole potential in a given direction falls off as 1/r, whereas that due to a point charge, as 1/r. 

The field due to the ideal dipole is found by taking the gradient of the potential. Thus, 

In our study of gases, we noted that at high pressures and low temperatures, intermolecular forces cause gas behavior to depart from ideality. When these forces are sufficiently strong compared with the thermal energy, a gas condenses to a liquid. That is, the intermolecular forces keep the molecules in such close proximity that they are confined to a definite volume, as expected for the liquid state. 

In this section, we will examine the types of intermolecular forces known collectively as van der Waals forces. The intermolecular forces contributing to the term a(n/17) in the van der Waals equation for nonideal gases (equation 6.26) are of this type. 

Two molecular properties—the dipole moment (see Section 10-7) and polarizability (see Section 9-7)—are essential for describing the physical basis of attractive intermolecular forces. These properties are used to describe the distribution of electron density within a molecule. Before discussing different types of intermolecular interactions, weTl review some of the points we made earlier about these two molecular properties. 

The polarizability, a, of a molecule provides a measure of the extent to which its electron cloud can be distorted from its normal or average shape, for example, by the application of an externally applied electric field or by the approach of another molecule. The polarizability of a molecule depends on how diffuse or spread out its electron cloud is. Polarizability is often expressed in units of volume, which suggests that the polarizability of a molecule is related to the volume of its charge cloud. 

We now turn our attention to different types of interactions that contribute to the attractions between molecules and account for differences in the physical properties of compoimds. 

What kinds of forces hold neutral molecules to each other Like interionic forces, these forces seem to be electrostatic in nature, involving attraction of positive charge for negative charge. There are two kinds of intermolecular forces dipole-dipole interacdons and van der Waals forces. 

Dipole-dipok interaction is the attraction of the positive end of one polar molecule for the negative end of another polar molecule. In hydrogen chloride, for example, the relatively positive hydrogen of one molecule is attracted to the relatively negative chlorine of another  

As a result of dipole-dipole interaction, polar molecules are generally held to each other more strongly than are non-polar molecules of comparable molecular weight this difference in strength of intermolecular forces is reflected in the physical properties of the compounds concerned. 

Although the momentary dipoles and induced dipoles are constantly changing, the net result is attraction between the two molecules. 

These van der Waals forces have a very short range they act only between the portions of different molecules that are in close contact, that is, between the surfaces of molecules. As we shall see, the relationship between the strength of van der Waals forces and the surface areas of molecules (Sec. 3.12) will help us to understand the effect of molecular size and shape on physical properties. 

In a solution of a solute in a solvent there can exist noncovalent intermolecular interactions of solvent-solvent, solvent-solute, and solute—solute pairs. The noncovalent attractive forces are of three types, namely, electrostatic, induction, and dispersion forces. We speak of forces, but physical theories make use of intermolecular energies. Let V(r) be the potential energy of interaction of two particles and F(r) be the force of interaction, where r is the interparticle distance of separation. Then these quantities are related by 

for example, if V(r) were proportional to r , F(r) would be proportional to -g conventional to take as the zero of potential energy the state in which the particles are infinitely separated. A negative V(r) is attractive, a positive value is repulsive. We are interested in the dependence of V(r) on r. The following treatment is drawn from Hirschfelder et al. (13). 

which is Coulomb s law, the charges are to be aeeompanied with their signs. Because of the high-order reciprocal dependence on distance in Eqs. (8-11) and (8-12), these quadrupolar interactions are usually negligible. For uncharged polar molecules the dipole-dipole interaction of Eq. (8-10), which has the dependence, is the most important contributor to the electrostatie potential energy. 

The induction (polarization) forces arise from the effeet of a moment in a polar molecule inducing a charge separation in an adjaeent molecule. The average potential energy funetions are 

The dispersion (London) force is a quantum mechanieal phenomenon. At any instant the electronic distribution in molecule 1 may result in an instantaneous dipole moment, even if 1 is a spherieal nonpolar moleeule. This instantaneous dipole induces a moment in 2, which interacts with the moment in 1. For nonpolar spheres the induced dipole-induced dipole dispersion energy function is 

Dipole-dipole forces are typically only about 1% as strong as covalent or ionic bonds, and they rapidly become weaker as the distance between the dipoles increases. At low pressures in the gas phase, where the molecules are far apart, these forces are relatively unimportant. 

The boiling points of the covalent hydrides of elements in Groups 4A, 5A, 6A, and 7A. 

All chiral separation methods involve an intermediate diastereoisomeric complex formed between the enantiomers to be separated and a chiral selector. All molecular interactions can play a role in the enantiomer-chiral selector-binding process. Table 1 lists these forces along with their strength, direction, and range. 

7t-Tt interactions are observed when tt-electron molecular assemblies, mainly aromatic rings, interact with each other. Aromatic structures are said to be r-acceptor or r-acid where the ring has electron-rich substituents, mainly -NO2 

Type of interaction Strength Direction Working distance 

Coulomb or electric Very strong Attractive (+/-) or repulsive (same charges) Medium range (1/d ) 

Hydrogen bond Very strong Attractive Long range 

In an ideal gas, individual molecules are so far apart on average that we assume they do not attract or repel each other. This description works well at temperatures significantly far from a phase boundary however, in the case of other phases of matter (solids, liquids, or other condensed states), the forces between molecules become critically important and drive the structure of the phase. To discuss and understand the factors that determine the stability of different types of soft matter, we must have a good understanding of the different forces that can act between molecules. There are only a few fundamental forces in the universe, and in materials science, electromagnetism dominates. Essentially all of the intermolecu-lar forces described here result from the electromagnetic force, but this interaction can manifest in a variety of interesting ways. 

We have concluded, thus far, the discussion of the first objective of chemical engineering thermodynamics the evaluation of the feasibility of processes and the efficient energy utilization in them. Before we proceed with the second one, the evaluation of thermophysical properties of fluids, we consider next intermolecularforces because they are useful in understanding the behavior of fluids as well as phase equilibrium, which is part of the third objective. 

Intermolecular forces are present everywhere. If it were not for the attractive forces to hold the molecules together, there would be no solids and liquids the kinetic energy of the molecules would spread them all over the available space. Everything, including ourselves, would be in the gaseous state. And if it were not for the repulsive forces, solids and liquids would not resist compression. 

The importance of intermolecular forces in explaining the thermodynamic behavior of fluids will be evident in the ensuing Chapters. We have already used them, however, in Example 1.5, to explain the observation that the deviation of steam from ideal gas behavior  

You have metal bonds when the metal atoms are placed in a three-dimensional lattice. In such a lattice the bond electrons flow around in all directions in the lattice which results in a very high electrical conductance in all directions. We have now been talking a little bit about intramolecular forces. The different bond types will be described in the following sections but first we are going to look at the intermolecular forces that interact between the molecules and not inside molecules. 

It is very important not to confuse the two terms intramolecular forces and intermolecular forces. Intramolecular forces are forces that act inside the molecules and thus constitute the bonds between the atoms. Intermolecular forces on the other hand are forces that act outside the molecules between molecules. The energies of chemical bonds (intramolecular forces) are much larger than the energies related to the intermolecular forces. Three different types of intermolecular forces can be distinguished  

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The existence of liquid crystals was first observed by Reinitzer [19] in 1888, but they were first classified and examined in a systematic way by Friedel [20] in 1922. Liquid crystals and their application to the formation of ordered thin films are discussed in Chapter 7. 

The basic physics of intermolecular forces is treated by Isrealachvili [21] and the reader is referred to this book for more detailed discussion of some aspects of this topic. 

The treatment which follows is of a largely qualitative nature as it seems likely that readers will fall into two classes. On the one hand there will be those who have already, at some point in their careers, familiarised themselves with the basic mathematical arguments which lead to the results quoted here. On the other hand are those who do not wish to be encumbered with lengthy algebraic manipulations but who wish to understand the basic physical mechanisms which are responsible for these results. 

True covalent forces are responsible for the bonding of atoms within molecules and are usually sufficiently stable so that energies in excess of 5 eV are required to disrupt them. This energy corresponds to photons having a wavelength of less than 2S0 nm. In this book we are concerned with the interactions between molecules and will thus not be concerned with covalence. 

Here a and a2 are the polarisabilities of the two atoms measured in C2 m2 J 1, /, and I2 are the ionisation potentials of the two atoms in joules, r is the distance between the two nuclei and the other symbols have their usual meanings. This expression is approximately correct but a number of simplifications are used in its derivation. They are as follows. 

Isoxazole itself is a colorless liquid with a strong, pyridine-like odor and has the following physical properties b.p. 94.8 °C/769 mmHg m.p. -80°C D20, 1.0763 critical temperature, 552.04 K ATbat25 °C, 2x 1(T12 dipole moment at 25 °C in benzene 2.75 0.01 D, in dioxane 3.01 0.03 D. 

The most significant contribution to this section comes from studies of partition coefficients made necessary by QSAR modeling. 

The log P of 3-hydroxy-4-amino-5-trifluoromethylpyrazole has been determined 89JMC2il6 . The log P values of l-(l-adamantyl)pyrazole, 3.05 ( ), l-(l-adamantyl)indazole, 4.33 (59), and 2-(l-adamantyl)indazole, 3.68 (60) were determined by HPLC. From these values, the n value of the 

1-adamantyl substituent was calculated as an aromatic substituent Ad = 3.49 87FES915 . 

If a diatomic molecule is composed of two atoms having different electronegativities, the molecule will be polar. The shared electrons will spend a greater fraction of time in the vicinity of the atom having the higher electronegativity (CO is an exception). A measure of this charge separation is fi, the dipok moment, which is defined by the relationship 

If the energy per mole is considered, k is replaced by R since k is R/Nq where Nq is Avogadro s number and R is the molar gas constant. 

In solutions containing solutes consisting of polar molecules, the solvent strongly affects the association of the dipoles. In general, if the solvent has low polarity and/or dielectric constant, the dipoles will be more strongly associated. If the solvent is also polar, it is likely that the solvation of each polar solute molecule will be strong enough that solute molecules will be 

A permanent dipole, = qx r can induce a charge separation in a neighboring nonpolar molecule that is proportional to the polarizability of the molecule. If the polarizabhity of the molecule is represented as a, the energy of the interaction between the permanent dipole and the nonpolar molecule with an induced dipole moment can be expressed as 

These forces between polar molecules and those having a dipole induced in them are called dipole-induced dipole forces, and they are essentially temperature independent. 

Spectacular small molecule activation has been achieved with FLPs, including with 1 2 and N20. The chanistry enabled by frustrated Lewis pairs is being exploited to develop non-transition-metal catalysts that promise to substitute for catalysts that contain toxic and expensive heavy metals.  

Which is a nonpolar molecule with polar covalent bonds  

Even nonpolar molecules can have momentary unequal distribution of their electrons, which results in weak intermolecular forces. For example, why would nitrogen—composed of nonpolar molecules—hquefy Why would carbon dioxide— also composed of nonpolar molecules—form a solid When the molecules get close enough, one molecule will cause an uneven distribution of charge in its neighbor. The two molecules become momentarily polar and are attracted to each other. These induced attractive forces are weak but become more pronounced when the molecules are larger and contain more electrons. 

FIGURE 5.8 Polar sulfur dioxide molecules attracted to one another (oxygen atoms attract electrons more than do sulfur atoms). 

Intermolecular forces Attractive forces fhat act between molecules weaker than covalent bonds Hydrogen bonding Attraction between a hydrogen atom bonded to a highly electronegative atom (0. N, F) and the lone pair on an electronegative atom in another or the same molecule 

FIGURE 5.9 Boiling points of simple hydrogen-containing compounds. 

How would you expect the H —Cl distance represented by the red dotted line to compare with the H —Cl distance within the HCI molecule  

When water boils, what are the bubbles composed of  

Force Holding Particles Together Substance Melting Point (K) Boiling Point Kj 

The features of metallic conductors, semiconductors, and insulators that we ve outlined here apply to more than just elemental forms of substances. Alloys are combinations of metallic elements (with an occasional minor component that is a nonmetal), and their bonding resembles what we have just described for metals. Semiconductors are often made from combinations of elements, too. Gallium arsenide is a particularly important example. Insulators, too, are often made from combinations of elements, and many ceramic materials are insulators. 

Not all materials have chemical bonds that are responsible for holding a solid together. Now we will look at other forces that play roles in condensed matter. 

The mutual attraction of neutral molecules or atoms in different molecules is caused by the van der Waals or donor-acceptor interactions, or a formation of hydrogen bonds (H-bonds) which define features of structures and heats of evaporation (sublimation) of molecular substances. In the reviews of Bent [1] and Haaland [2] the reader can find numerous examples of thermodynamic, structural, physical and chemical properties, and features of products of molecular interactions. Many energetic and geometrical characteristics of molecules with the van der Waals (vdW) interaction are presented in the previous chapters of the book. Therefore here the attention will be drawn only to some principal questions and problems of structural chemistry and thermodynamics which have not been considered earlier. 

Obtaining evidence for scientific theories and testing predictions based on them 

The term van der Waals forces includes three types of intermolecular forces London (dispersion) forces, permanent dipole-dipole forces (sometimes referred to as Keesom forces) and permanent-induced dipole interactions (Debye forces). In 1910, van der Waals was awarded the Nohel Prize for his work on the equation of state for gases and liquids concerned with the reasons for non-ideal behaviour in real gases. His equation introduced compensatory terms to account for the non-zero size of the particles and the inter-particle forces between them. This broader definition of van der Waals forces runs contrary to the use of the term in many current textbooks, but is consistent with its use in the IB syllabus. 

The polarization of xenon atoms leads to production of induced dipole forces between atoms 

This atom is not yet poiarized, but its eiectrons wiii be repeiied by the dipoie next to it, 

Factors which influence London (dispersion) forces 

Draw the structure of a compound fitting each description  

Draw structures that fit each description and name the functionai group in each moiecuie  

The fundamental basis for molecular recognition is provided by the potential energy surface that represents the interaction energy of two or more molecules in a cluster as a function of their mutual separation and orientation. 

The six relative translational and orientational degrees of freedom of an interacting pair of non-linear polyatomic molecules generally fluctuate slowly compared to the intramolecular vibrations. For some purposes, such as rotational relaxation, it may be sufficient to average u over the vibrational motion, thereby reducing the number of variables upon which u depends to just six. For vibrational relaxation of a particular mode, it may sometimes be 

Hint Break the process into three steps and then take the sum. 

AIMS To learn about dipole-dipole attraction, hydrogen bonding, and London dispersion forces. To understand the effect of these forces on the properties of liquids. 

We have seen that covalent bonding forces within molecules arise from the sharing of electrons, but how do intermolecular forces arise Actually several types of intermolecular forces exist. To illustrate one type, we will consider the forces that exist among water molecules. 

Hydrogen bonding has a very important effect on various physical properties. For example, the boiling points for the covalent compounds of 

In ammonia and the nitrogen trihalides, there is a non-bonding pair of electrons, leading to a pyramidal molecular shape. 

If a gas is gradually cooled, the average speed of the molecules decreases. Eventually, there comes a temperature when the gas turns into a liquid or solid, which occupies a much smaller volume than the gas did. How do we explain this  

Boiling temperatures are therefore a crude measure of the intermolecular forces if these forces are strong, a high temperature is needed to free the molecules from each other s influence. 

In NF3 the dipole moment developed by the non-bonding pair opposes that developed in the N—F bonds in NH3, it reinforces it. The dipole moment of NF3 is therefore much less than that of NH3. 

CI2 has no permanent dipole moment and so these forces cannot be what holds 

As you know well, the most common equation of state is the ideal gas model. It can be written explicitly for pressure in terms of the intensive properties n and T as follows  

The ideal gas model is of the form presented in Equation (4.1) in that it relates the measured variables P, T, and v. The ideal gas equation can be derived directly from the kinetic theory of gases for a gas consisting of molecules that are infinitesimally small, hard round spheres that occupy negligible volume and exert forces upon each other only through collisions. Stated more concisely, the assumptions of the ideal gas model are that molecules  

Exert no intermolecular forces (except when they collide with each other or with the container s walls) 

As we shall see in Section 4.2, the absence of intermolecular forces leads to the internal energy being independent of pressure. It depends only on temperature, that is, the molecular kinetic energy of the molecules. Hence, 

As the pressure goes to zero, all gases approach ideal gas behavior. 

---

Bfi and 022- However, in the second binary, intermolecular forces between unlike molecules are much stronger than those between like molecules chloroform and ethyl acetate can strongly hydrogen bond with each other but only very weakly with them-... 

Boyle s law At constant temperature the volume of a given mass of gas is inversely proportional to the pressure. Although exact at low pressures, the law is not accurately obeyed at high pressures because of the finite size of molecules and the existence of intermolecular forces. See van der Waals equation. 

The next point of interest has to do with the question of how deep the surface region or region of appreciably unbalanced forces is. This depends primarily on the range of intermolecular forces and, except where ions are involved, the principal force between molecules is of the so-called van der Waals type (see Section VI-1). This type of force decreases with about the seventh power of the intermolecular distance and, consequently, it is only the first shell or two of nearest neighbors whose interaction with a given molecule is of importance. In other words, a molecule experiences essentially symmetrical forces once it is a few molecular diameters away from the surface, and the thickness of the surface region is of this order of magnitude (see Ref. 23, for example). (Certain aspects of this conclusion need modification and are discussed in Sections X-6C and XVII-5.)... 

The different kinds of intermolecular forces (dispersion, dipole-dipole, hydrogen bonding, etc. see Section VI-1) may not equally contribute to A-A, B-B, and A-B... 

One fascinating feature of the physical chemistry of surfaces is the direct influence of intermolecular forces on interfacial phenomena. The calculation of surface tension in section III-2B, for example, is based on the Lennard-Jones potential function illustrated in Fig. III-6. The wide use of this model potential is based in physical analysis of intermolecular forces that we summarize in this chapter. In this chapter, we briefly discuss the fundamental electromagnetic forces. The electrostatic forces between charged species are covered in Chapter V. 

Generally speaking, intermolecular forces act over a short range. Were this not the case, the specific energy of a portion of matter would depend on its size quantities such as molar enthalpies of formation would be extensive variables On the other hand, the cumulative effects of these forces between macroscopic bodies extend over a rather long range and the discussion of such situations constitutes the chief subject of this chapter. 

As also noted in the preceding chapter, it is customary to divide adsorption into two broad classes, namely, physical adsorption and chemisorption. Physical adsorption equilibrium is very rapid in attainment (except when limited by mass transport rates in the gas phase or within a porous adsorbent) and is reversible, the adsorbate being removable without change by lowering the pressure (there may be hysteresis in the case of a porous solid). It is supposed that this type of adsorption occurs as a result of the same type of relatively nonspecific intermolecular forces that are responsible for the condensation of a vapor to a liquid, and in physical adsorption the heat of adsorption should be in the range of heats of condensation. Physical adsorption is usually important only for gases below their critical temperature, that is, for vapors. 

Buckingham A D 1967 Permanent and induced molecular moments and long-range intermolecular forces Adv. Chem. Phys. 12 107... 

Brooks F C 1952 Convergence of intermolecular force series Phys. Rev. 86 92... 

Ahlrichs R 1976 Convergence properties of the intermolecular force series (l/r expansion) Theor. Chim. Acta 41 7... 

Stone A J 1996 The Theory of Intermolecular Forces (New York Oxford)... 

Kutzelnigg W and Maeder F 1978 Natural states of interacting systems and their use for the calculation of intermolecular forces. III. One-term approximations of oscillator strength sums and dynamic polarizabilities Chem. Phys. 35 397... 

Claverie P 1971 Theory of intermolecular forces. I. On the inadequacy of the usual Rayleigh-Schrddinger perturbation method for the treatment of intermolecular forces Int. J. Quantum Chem. 5 273... 

Elrod M J and Saykally R J 1994 Many-body effects in intermolecular forces Chem. Rev. 94 1975... 

Hutson J M 1990 Intermolecular forces from the spectroscopy of van der Waals molecules Ann. Rev. Phys. Chem. 41 123... 

Maitland G C, Rigby M, Smith E B and Wakeham W A 1981 Intermolecular Forces Their Origin and Determination (Oxford Clarendon)... 

Douketis C, Socles G, Marchetti S, Zen M and Thakkar A J 1982 Intermolecular forces via hybrid Hartree-Fock SCF plus damped dispersion (HFD) energy calculations. An improved spherical model J. Chem. Phys. 76 3057... 

Stone A J 1979 Intermolecular forces The Moiecuiar Physics of Liquid Crystais ed G R Luckhurst and G W Gray (New York Academic) pp 31-50... 

Margenau H and KesPierN R 1971 Theory of Intermolecular Forces 2nd edn (New York Pergamon)... 

Weeks J D, Vollmayr K and Katsov K 1997 Intermolecular forces and the structure of uniform and non uniform fluids Physice A 244 461... 

Stillinger F 1973 Structure in aqueous solutions from the standpoint of scaled particle theory J. Solution Chem. 2 141 Widom B 1967 Intermolecular forces and the nature of the liquid state Sc/e/ ce 375 157 Longuet-Higgins H C and Widom B 1964 A rigid sphere model for the melting of argon Mol. Phys. 8 549... 

Hutson J M 1990 Intermolecular forces from the spectroscopy of Van der Waals molecules Ann. Rev. Phys. Chem. 41 123-54 Huston J M 1991 An introduction to the dynamics of Van der Waals molecules Adv. Mol. Vibrat. Coll. Dyn. 1A 1-45... 

In most covalent compounds, the strong covalent bonds link the atoms together into molecules, but the molecules themselves are held together by much weaker forces, hence the low melting points of molecular crystals and their inability to conduct electricity. These weak intermolecular forces are called van der WaaFs forces in general, they increase with increase in size of the molecule. Only... 

The dotted lines represent hydrogen bonds. The high boiling point and viscosity of the pure acid indicate strong intermolecular forces of this kind. 

From the standpoint of thermodynamics, the dissolving process is the estabHsh-ment of an equilibrium between the phase of the solute and its saturated aqueous solution. Aqueous solubility is almost exclusively dependent on the intermolecular forces that exist between the solute molecules and the water molecules. The solute-solute, solute-water, and water-water adhesive interactions determine the amount of compound dissolving in water. Additional solute-solute interactions are associated with the lattice energy in the crystalline state. 

Rigby M, E B Smith, W A Wakeham and G C Maitland 1981. Intermolecular Forces Their Origin an, Determination. Oxford, Clarendon FYess. 

Z1, P Cieplak, W D Cornell and P A Kolhnan 1993. A Well-Behaved Electrostatic Potential Based 5thod for Deriving Atomic Charges - The RESP Model. Journal of Physical Chemistry 97 10269-10280. sen H C, J P M Postma, W F van Gunsteren and J Hermans 1981. Interaction Models for Water in lation to Protein Hydration. In Pullman B (Editor). Intermolecular Forces. Dordrecht, Reidel, I. 331-342. 

If the gas particles interact through a pairwise potential, then the contribution to the viriai from the intermolecular forces can be derived as follows. Consider two atoms i and j separated by a distcmce r. ... 

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