00:00:00 In this lecture, the second of our series on valence and the electron bond, Pauling

00:00:31 of atoms, molecules, and crystals, I shall talk about the covalent bond and the shared

00:00:38 electron pair bond. They are the same thing, two different names.

00:00:43 The covalent bond, covalence, covalence is an aspect of valence that I think comes closer

00:00:51 to the old-fashioned, rather vague concept of valence than do the other, more precise

00:01:00 aspects of valence that we make use of at the present time.

00:01:06 The theory of structural chemistry involving the idea of the covalent bond represented

00:01:12 by a line drawn between two symbols, the symbols for two atoms, this theory is one

00:01:20 of the greatest constructs of the human mind that has ever been formulated, perhaps the

00:01:28 greatest of all.

00:01:30 The theory of structural chemistry was developed about 100 years ago. It was in 1852 that Franklin

00:01:38 suggested that different elements have different combining powers, can combine with different

00:01:47 numbers of atoms of other elements. In 1858, Kalper and Kekulé invented the idea of the

00:01:55 chemical bond and discovered the quadrivalence of carbon.

00:02:02 Then there was great progress in chemistry. With the aid of this relatively simple theory

00:02:10 that had been obtained by induction from the many thousands of facts of chemistry, it was

00:02:17 possible for chemists to make the extraordinary progress that has led to modern technology

00:02:26 and medicine.

00:02:28 The structure theory assisted the imagination of a man in such a way that he was able to

00:02:36 make discoveries that would not have been made otherwise.

00:02:42 I should like to start out by talking about the simple structure theory, the simple idea

00:02:48 of the chemical bond in the substances that we now consider to contain covalent bonds.

00:02:56 As an example, I may take methane, represented by this model, a carbon atom with four hydrogen

00:03:08 atoms attached. We write for this the formula C-H-H-H-H. And, of course, Kalper and Kekulé

00:03:16 recognized that the carbon atoms forming four bonds can also be attached to one another.

00:03:30 I have another model here representing the structure of ethane, the next hydrocarbon

00:03:38 in the aliphatic series, C-2-H-6. Two carbon atoms attached together, six hydrogen atoms.

00:03:49 Each carbon atom is quadrivalent, forms four bonds, one with the other carbon atom and

00:03:55 three with the three hydrogen atoms that in the structural formula are shown connected

00:04:01 to it by the valence bonds.

00:04:05 As a more complicated example, I may show ethanol, ethyl alcohol. Here we have the two

00:04:16 carbon atoms bonded together, three hydrogen atoms, two here, a bond to the oxygen atom,

00:04:22 and then a bond to the hydrogen atom on oxygen, C-2-H-5-O-H, ethanol.

00:04:29 I may mention that these ball-and-stick models are quite illuminating, but they do not give

00:04:36 a really correct idea of the shape of the molecule. The ethanol molecule does not have

00:04:46 a thin portion that connects the carbon atom to the hydrogen atom. Instead, the electron

00:04:53 distribution in space is more satisfactorily represented by this model, a space-filling

00:05:00 model, in which the atoms are shown as spheres with a radius that corresponds approximately

00:05:10 to the effective contact radius when the molecules are piled together in a liquid or in a crystal.

00:05:18 If there were another molecule in solution, say in ethanol, for example, this rather larger

00:05:27 molecule, then the molecules would roll over one another in such a way that they would

00:05:34 not get much closer to one another than the distance corresponding to contact between

00:05:40 the spheres that represent the atoms in these models.

00:05:48 I shall continue to use, in general, these large models. You must remember that they

00:05:54 do not satisfactorily represent the extension in space of the substances.

00:06:02 A very important contribution to structure theory was made in 1874 by the Dutch chemist

00:06:11 Van't Hoff and the French chemist Labelle, independently of one another. This is the

00:06:17 idea that the four bonds formed by the carbon atom are not directed out toward the corners

00:06:25 of a square in one plane, as indicated here on the blackboard, or are not so loose-jointed

00:06:31 that they have no well-defined direction, but instead are directed toward the four corners

00:06:38 of a tetrahedron. All of our models are built in this way. Here we have the methane molecule

00:06:46 with the four bonds shown proceeding toward four corners of a tetrahedron, a regular tetrahedron.

00:06:53 This has been found in recent years by the determination of the structure of crystals

00:07:00 and of gas molecules, by the x-ray diffraction method, the electron diffraction method, and

00:07:06 various spectroscopic methods, that the angles between single bonds formed by a carbon atom

00:07:13 remain in all substances quite close to the tetrahedral angle, the angle for a regular

00:07:19 tetrahedron, 109 degrees, 28 minutes. The tetrahedral carbon atom is a very important

00:07:26 part of chemistry. I think that the discovery of the tetrahedral carbon atom was a wonderful

00:07:33 thing. It shows the power of man's mind. The facts were that in 1874 it was known, as a

00:07:43 result of the work of Pasteur, that some substances can form crystals that have either a left-handed

00:07:53 appearance or a right-handed appearance. Van't Hoff and LaBelle asked, how is it possible

00:08:00 for substances to be built up of molecules that are right-handed or left-handed, two

00:08:08 different kinds of molecules that are related to one another in the way that the right hand

00:08:13 and the left hand are related. They showed that the tetrahedral carbon atom provides

00:08:21 the explanation of these facts. If the four bonds of the carbon atom are related to each

00:08:30 other, connected to four different kinds of atoms or groups, for example a hydrogen atom,

00:08:37 a methyl group CH3, a chlorine atom, a bromine atom, then this tetrahedral molecule can be

00:08:46 either a right-handed molecule or a left-handed molecule, and the right-handed molecule does

00:08:52 not become left-handed by any translational or rotational motion in space. Only by breaking

00:08:59 the bond and moving it around to the other side can you convert the right-handed molecule

00:09:04 into the left-handed molecule. Recent investigations, recent structure determinations have of course

00:09:13 completely verified this idea of the tetrahedral carbon atom.

00:09:21 The simple chemical structure theory permits one to understand the existence of isomers.

00:09:30 I have here a model. Let me start with this one. I have here a model representing one

00:09:38 of the two forms of butane, C4H10. C4H10. This is normal butane, a straight chain hydrocarbon.

00:09:46 It is called a straight chain even though the bonds are at the tetrahedral angle here

00:09:59 so that the chain is a zigzag chain. Normal butane is one substance. There is another

00:10:07 substance with formula C4H10 that has somewhat different properties. This other substance

00:10:14 called isobutane is represented by this model. Here we have again four carbon atoms and three,

00:10:22 six, nine, ten, ten hydrogen atoms. But the bonding between atoms is different for isobutane

00:10:31 from that for normal butane. These are the only two ways in which four carbon atoms and

00:10:39 ten hydrogen atoms can be attached together with each carbon atom forming four bonds,

00:10:46 each hydrogen atom one. And corresponding to this, there are only two isomers known,

00:10:53 two substances known that have the composition C4H10. This provides an interesting simple

00:11:01 example of the power of chemical structure theory.

00:11:07 Now there are many other sorts of molecules that one can build that are compatible with

00:11:16 the simple principles of structure theory. I have here a model of a new sort in which

00:11:23 there is a ring, a cycle of carbon atoms. This molecule is the molecule of cyclobutane

00:11:31 C5H10. The angle in a pentagon is 108 degrees, so very close to the tetrahedral angle, so

00:11:42 that there is practically no strain in this molecule. On the other hand, a smaller ring

00:11:50 involves some strain. No longer are we able to use half-inch wood dowel rods in representing

00:11:57 the bonds. We have to have springs in this model, which represents cyclopropane, C3H6.

00:12:07 Here we have bent bonds connecting the carbon atoms. If the bonds came directly from carbon

00:12:14 atom to carbon atom, the angle would be 60 degrees instead of the tetrahedral angle,

00:12:19 109 degrees, 28 minutes. We can represent the structure by the use of these bent bonds.

00:12:27 There is some strain associated with the bent bonds, so the cyclopropane is somewhat less

00:12:33 stable than one would expect for a molecule with the same composition and without the

00:12:40 bent bonds. It is interesting that this substance, cyclopropane, is used as a general anesthetic.

00:12:48 It produces anesthesia. I think that this is an illustration of the present situation

00:12:55 in physiology, biochemistry, our lack of understanding of the nature of the human body.

00:13:02 Why is it that this particular molecule produces anesthesia? Why is it that chloroform, CHCl3,

00:13:12 produces anesthesia? Nobody really knows the answer. No one is able to predict what substances

00:13:20 will be anesthetics and what not. Here we have chloroform with a hydrogen atom down

00:13:25 here. I'll hide this chlorine atom to make it into chloroform. No one knows why chloroform

00:13:32 serves as an anesthetic, too. Some light on this question is provided by the fact that

00:13:40 xenon is also a general anesthetic. Now xenon is one of the noble gases, atomic number 54,

00:13:50 it forms no chemical compounds in which it forms chemical bonds. It will in fact form

00:13:56 a hydrate, xenon hydrate, in which the water molecules are arranged together, attached

00:14:03 to one another in such a way as to make cages, little rooms, in which the xenon atoms sit.

00:14:10 It is interesting that cyclopropane forms a similar hydrate and chloroform forms a similar

00:14:17 hydrate. In the case of chloroform, the hydrate is something like CHCl3-17H2O. I think that

00:14:26 it may well be that the effect of these substances in producing general anesthesia is related

00:14:34 to their power to form moderately stable hydrates, stable at temperatures 10 degrees or more

00:14:41 above the freezing point of water. Perhaps somewhere in the tissues in the nervous system

00:14:48 there are little regions where the water is tied down into a sort of pseudo-crystalline

00:14:55 aggregate by the molecules of the general anesthetic and the normal metabolic activities

00:15:03 of the nervous system are not able then to go on. But we really don't know enough about

00:15:10 the chemistry of the human body to be able to give an explanation of this.

00:15:15 Well, let me go on to discuss some things that we do know about. This model, this model

00:15:23 represents the structure of ethylene. It has something new in it, a new structural feature.

00:15:32 Here we have two bonds connecting one carbon atom with another carbon atom. A double bond

00:15:39 represented in the conventional way by two lines between the carbon atoms. Ethylene is

00:15:54 an interesting substance. It causes oranges to ripen. If you have oranges that aren't

00:16:02 very ripe, look sort of yellow in a freight car, and put some ethylene into the freight

00:16:07 car, the oranges develop a beautiful orange color. Nobody knows why that goes on either.

00:16:14 Well, here is the double bond. We can say two bent bonds holding the two carbon atoms

00:16:20 together. Now, if this double bond is described as involving two tetrahedra, two tetrahedra

00:16:28 that are attached together with one edge in common, then we can see that there is restriction

00:16:36 in the rotation. It is not possible to twist the molecule around through one end through

00:16:42 180 degrees relative to the other end. To do that, one would have to break a bond, and

00:16:47 this takes a lot of energy. The result of this is that a new sort of isomer is found

00:16:55 in substituted ethylene. If we replace one of the hydrogen atoms on this end of the molecule

00:17:03 with, say, a chlorine atom, and one on the other end with a chlorine atom, we may do

00:17:08 this in either one of two ways. This hydrogen and this hydrogen may be replaced by chlorine.

00:17:16 That gives one substance. Or this hydrogen and the opposite hydrogen may be replaced.

00:17:21 That gives another substance. These substances have different properties, different chemical

00:17:27 and physical properties. They are represented by the models shown here. This is called cis-dichloroethylene

00:17:38 in which the two chlorine atoms are on the same side of the double bond. This molecule

00:17:44 represented by this model is called trans-dichloroethylene in which the two chlorine atoms are on opposite

00:17:52 sides of the double bond. Well, here again, we have only two isomers with the formula

00:17:59 C2H2Cl2 and with the chlorine atoms on separate carbon atoms. There is also a third isomer

00:18:10 in which there are two hydrogen atoms attached to one carbon atom, two chlorine atoms attached

00:18:16 to the other carbon atom. In addition to the double bond, the triple bond is known.

00:18:24 There are substances such as acetylene that contain a carbon-carbon triple bond. Here

00:18:31 we have three bent bonds holding the two carbon atoms together. The other two bonds project

00:18:39 out in opposite directions. The molecule acetylene C2H2 is a linear molecule. The conventional

00:18:47 representation of this molecule is C-H-C-H. No quadruple bond is known. Nobody has ever

00:19:01 recognized the quadruple bond, at least so far as I am aware. In reading the chemical

00:19:07 literature I have never seen mention of evidence that a quadruple bond exists. Perhaps we can

00:19:16 understand that, too, in terms of the tetrahedral carbon atom. For carbon, at any rate, the four

00:19:23 bonds come out in these directions. We can have a double bond by bending the bonds, triple

00:19:31 bond by sharing two faces of the two tetrahedra and bending the bonds enough, but the fourth

00:19:37 bond would have to make a terrific bend in order to get around from the back side of

00:19:42 this carbon atom to the back side of the other carbon atom.

00:19:50 Now let us discuss the modern aspects of valence theory, structure theory. First, let me say

00:19:58 that the classical structure theory, the older structure theory, has not been discarded.

00:20:07 There has not been a revolution of such a nature that the old has been thrown out and

00:20:13 the new has come in. Classical structure theory is still valid. There have been some improvements

00:20:21 in structure theory. Some problems of molecular structure and valence that were hard to discuss,

00:20:29 hard to understand before, can now be discussed in a reasonable and sensible way because of

00:20:37 the additions that have been made. Ideas about hybridized bond orbitals, about the theory

00:20:45 of resonance, partial ionic character of covalent bonds have come in and have made chemical

00:20:53 structure theory more powerful. The whole theory, the classical structure theory and

00:21:00 the modern structure theory, has a sound base in experiment. It has been developed largely

00:21:08 by induction from the tens of thousands of chemical facts with, in the case of the modern

00:21:15 development, a little help, considerable help I should say, from ideas that have been suggested

00:21:22 by the theory of quantum mechanics for which we are indebted to the physicists.

00:21:29 The modern theory began in 1916 when Professor Lewis introduced the idea of the shared electron

00:21:37 pair chemical bond. And much contribution was made also by Irving Langmuir.

00:21:46 The principal statements that we can make about a chemical bond now are that in order

00:21:54 to form a chemical bond between two atoms, you need to have an orbital for each atom.

00:22:01 Let's say atom A must have an orbital, atom B must have an orbital, and two electrons

00:22:09 are involved, which I may write in this way, and their spins must be opposed. One orbital

00:22:16 for each of the two atoms and a pair of electrons with opposed spins, which serve to hold the

00:22:22 atoms together. Here I have a drawing representing the structure of the hydrogen molecule, H2O.

00:22:32 The two nuclei, the two protons, are at these positions, 74 hundredths of an angstrom apart,

00:22:39 and the two electrons are distributed in space, roughly as shown here, with a good concentration

00:22:44 right in the region between the two nuclei. It is almost as though there were, the nuclei

00:22:50 were ball bearings, say steel ball bearings, around which some rubber has been vulcanized

00:22:56 that holds these ball bearings firmly at this distance apart, does not permit them

00:23:02 to escape from one another. This is the standard Lewis symbol for the hydrogen molecule, H2.

00:23:08 The two electrons are shown between the symbols for the two hydrogen atoms. We see that we

00:23:15 can say that each of the hydrogen atoms has succeeded in obtaining the helium structure.

00:23:21 This orbital for hydrogen, the 1s orbital, is occupied by the pair of electrons, which

00:23:27 also occupies the 1s orbital for the other hydrogen atom. The idea that you must have

00:23:38 a stable orbital for each atom in order to form a bond and a pair of electrons permits

00:23:45 a considerable addition to the power of chemical structure theory.

00:23:53 Here I have a drawing representing the electronic structure of the water molecule. The water

00:23:59 molecule, H2O, has the Lewis symbol as shown here. The pair of electrons in the helium

00:24:06 shell for oxygen is not indicated, only those in the neon shell. Here is an unshared pair

00:24:13 of electrons occupying one orbital, a second unshared pair occupying a second orbital,

00:24:20 a third shared pair, in this case occupying the third orbital, and a shared pair occupying

00:24:26 the fourth orbital. The oxygen atom now has four electron pairs, eight electrons in its

00:24:33 neon shell. It has achieved the structure of the neon atom by sharing electrons, and

00:24:40 the hydrogen atoms, as before, using their 1s orbitals, have achieved the helium configuration.

00:24:47 Many structures, many molecules have structures such that each atom achieves the electronic

00:24:55 structure of the nearest noble gas, with 2, 10, 18, 36, 54, and so on, electrons. The

00:25:03 oxygen-hydrogen distance is known, 0.965 angstroms. The angle between the two OH bonds is known

00:25:14 experimentally, 104 degrees, 30 minutes.

00:25:24 These distances are interesting in that they, the distances of the oxygen atom and the hydrogen

00:25:32 atom are known as determined by spectroscopic or diffraction measurements, in that they

00:25:38 give us an idea about the significance of the chemical bond. The carbon-carbon distance,

00:25:45 well, let me look at this, the chlorine-chlorine distance in the chlorine molecule, Cl2, is

00:25:53 1.98 angstroms. We can write the Lewis formula, ClCl, and the number of atoms in the oxygen

00:26:02 atom. And I shall show also the electrons in the valence shell, the argon shell, of

00:26:09 each chlorine atom. I have written here a line like this to represent the two electrons

00:26:17 that are shared between the chlorine atoms. Chlorine has only 17 electrons, that is 7

00:26:24 in the argon shell, but by sharing a pair, each chlorine atom succeeds in achieving the

00:26:32 argon structure with 18 electrons. The distance between the two chlorine atoms is 1.98 angstroms,

00:26:43 as determined spectroscopically and by electron diffraction. The distance between the two

00:26:50 carbon atoms in the S-plane, the carbon-carbon distance in S-plane is 1.98 angstroms.

00:27:01 I'll change this to ethane, CH3, is 1.54 angstroms. 1.54 angstroms. Now, when we examine carbon-tetrachloride

00:27:20 by spectroscopic methods or electron diffraction, we find that the carbon-chlorine distance

00:27:27 in carbon-tetrachloride is 1.76 angstroms. Carbon, four bonds to chlorine. I might as

00:27:38 well continue to give the example. Well, for this chlorine atom, here again, by forming

00:27:45 the bond, chlorine has achieved the argon structure and the carbon atom has achieved

00:27:52 the neon structure. This distance is found to be 1.76 angstroms. 1.76 angstroms, 1.98

00:28:04 angstrom in chlorine plus 1.54 angstrom in ethane, that is to 3.52, half of that is 1.76.

00:28:11 So the carbon-carbon bond has a length just midway between the lengths of the carbon.

00:28:21 The carbon-chlorine bond has a length just midway between the lengths of the carbon-carbon

00:28:27 single bond in ethane and the carbon, the chlorine-chlorine bond in the chlorine molecule.

00:28:34 While I'm on the subject, I might mention diamond. Here is a model, not built on such

00:28:41 a large scale, so small enough so that I'm able to lift it, a model of diamond. Each

00:28:47 carbon atom is attached by carbon-carbon single bonds to four others that surround it tetrahedrally.

00:28:55 And the distance found experimentally between the carbon atoms is 1.54 angstroms, just the

00:29:05 distance that is found in ethane and in many other substances in which there are carbon-carbon

00:29:14 single bonds. We can understand, too, why diamond is so hard. Here are these chemical

00:29:20 bonds, strong bonds, which connect all of the atoms in the crystal together into a single

00:29:27 molecule. In order to break a crystal of diamond, as, for example, if you tried to scratch it

00:29:33 with some other substance, it would be necessary to carry out a chemical reaction, the reaction

00:29:40 of breaking carbon-carbon bonds. This is so hard to do, the bonds are so strong, that

00:29:46 the substance is very hard, the hardest substance known. I may mention also that the double

00:29:53 bond, which is the stronger bond, has length 1.33 angstrom. The triple bond, still stronger,

00:30:01 has length 1.20 angstrom. As the bond between the carbon atoms gets stronger, the atoms

00:30:08 are pulled more and more closely together.

00:30:13 There is one aspect of the carbon atom, the bonds formed by the carbon atom, that I should

00:30:21 mention. The question is this. You remember that the orbitals for the carbon atom are

00:30:28 the 1s orbital, the 2s orbital, and the 3,2p orbital. Now, these are the orbitals in the

00:30:36 valence shell, and one might well ask, is not one bond formed by the carbon atom different

00:30:44 from the other three? The answer to this is a simple one. No, the four bonds are equivalent,

00:30:51 and we can describe these bonds in terms of four equivalent orbitals. Instead of the s

00:30:58 orbitals and the p orbitals, we can formulate, as hybrid orbitals, four that are directed

00:31:06 toward the four corners of a regular tetrahedron, and these orbitals are perfectly satisfactory

00:31:13 in providing an explanation of the four equivalent tetrahedral bonds. I think that it is interesting

00:31:21 that if it happened, as it might well have happened, that chemists discovered quantum

00:31:27 theory, wave mechanics, rather than the physicists, then we would be saying that the s orbital

00:31:34 and the p orbital that the chemists are interested in are hybrid orbitals formed of the four

00:31:41 equivalent tetrahedral orbitals of the carbon atom.

00:31:48 Let us consider now some substances, some molecules, for which the classical valence

00:31:54 theory was not satisfactory. An example is benzene. The benzene molecule C6H6 may be

00:32:03 represented, according to classical theory, by this structure, a six-membered carbon ring.

00:32:10 In order that the carbon atoms be quadrivalent, we must have in this six-membered carbon ring

00:32:18 not only the bonds from carbon to hydrogen and carbon to carbon, but also double bonds.

00:32:34 But chemists found a hundred years ago that if two of these hydrogen atoms were replaced

00:32:42 by, say, chlorine atoms, one did not obtain two substances, a substance in which the chlorine

00:32:52 atoms were on carbon atoms held together by a single bond and another substance in which

00:32:57 chlorine atoms were on carbon atoms held together by a double bond. Instead, only one substance

00:33:03 could be obtained of this sort.

00:33:06 The explanation of this is given by the theory of resonance. This theory states that sometimes

00:33:14 instead of writing a single valence bond structure to represent a molecule, one must write two

00:33:21 or more valence bond structures and lump them together. Benzene is described now as being

00:33:29 a resonance hybrid of these two. Those are identical. I'll have to draw the double bonds

00:33:36 differently. There's the second one with the chlorine atoms here for dichlorobenzene.

00:33:45 We write these two Kekulé structures. A single structure of this sort was first written by

00:33:51 Kekulé nearly a hundred years ago. We write these two Kekulé structures and say that

00:33:56 the two structures together provide a satisfactory description of the benzene molecule.

00:34:04 A similar sort of structure can be written for graphite. This represents a portion of

00:34:12 the graphite crystal, a very soft substance. The molecule is to be thought of as being

00:34:20 infinite in size, a very large layer consisting of hexagonal rings. If I start to represent

00:34:27 this structure, I can show carbon atoms attached together in rings. Now, I need to have a double

00:34:36 bond on this carbon atom in order that there will be a quadrivalent carbon atom. But the

00:34:42 double bond does not need to be here. It may be there or here or here. There are a great

00:34:47 many structures that I can draw to represent the molecule of graphite.

00:34:51 The physical properties of graphite are nicely explained by this structure. On this scale,

00:34:57 the scale of this model, the layers, these giant two-dimensional molecules, are about

00:35:04 this far away from one another and very loosely attached to one another so that they can slide

00:35:09 back and forth relative to one another. There are many other substances for which a double

00:35:17 bond, a satisfactory structure, cannot be written, a single satisfactory structure,

00:35:25 and instead two or more structures must be written.

00:35:31 Ozone is an example. The ozone molecule consists of three oxygen atoms with about a 120 degree

00:35:39 angle in this region. If we try to assign a structure in which each of the stable orbitals,

00:35:50 too many there, each of the stable orbitals is used in forming a bond or for occupancy

00:35:57 by unshared pairs, then we find that this is the best that we can do. Each oxygen atom

00:36:04 has now achieved the neon structure, two unshared pairs and two shared pairs, three unshared

00:36:10 pairs and one shared pair, one unshared pair and three shared pairs. But this makes this

00:36:17 oxygen-oxygen bond different from this, whereas it is known that these oxygen-oxygen bonds

00:36:23 are equivalent.

00:36:24 The solution to this difficulty is that there is another way of introducing the valence

00:36:31 bonds in which the single bond and the double bond have changed places. Ozone has a resonating

00:36:37 structure. Each of these bonds can be described as being a hybrid of a single bond and a double

00:36:43 bond, a bond with about one and a half bond character.

00:36:48 This is a model, a small model, showing the correct packing dimensions of the atoms of

00:36:56 sulfur dioxide, the two oxygen atoms attached to sulfur, the bond angle again about 120

00:37:03 degrees, and here again there's a double bond and a single bond with resonance between the

00:37:09 two structures, double bond-single bond and double bond-single bond.

00:37:16 The criticism has been made rather often of the theory of resonance that it is artificial.

00:37:23 It is said, for example, that nobody has ever found a benzene, nobody's ever synthesized

00:37:30 benzene that has one Kekulé structure, and that accordingly one should not talk about

00:37:37 the first Kekulé structure and the second Kekulé structure.

00:37:42 Now the fact is that the theory of resonance is no more artificial than ordinary structure

00:37:49 theory. It is true that nobody has ever succeeded in bringing into the laboratory a flask full,

00:37:56 a beaker full of benzene with the first Kekulé structure and another beaker full of benzene

00:38:01 with the second Kekulé structure. But in fact nobody has ever succeeded in bringing

00:38:07 into the laboratory a beaker full of carbon-carbon single bonds or carbon-carbon double bonds

00:38:13 or carbon-hydrogen bonds, and yet we are happy to talk about the carbon-hydrogen single

00:38:20 bond, the carbon-carbon double bond, as structural features of molecules, of the ethylene molecule,

00:38:28 the methane molecule, the ethane molecule. In fact, of course, every molecule is something

00:38:36 of its own. No two molecules are exactly alike. The carbon-carbon single bond, the carbon-carbon

00:38:43 distance in one molecule, the average carbon-carbon distance is a little bit different from the

00:38:49 average carbon-carbon distance in another molecule. In isobutane the carbon-carbon distance

00:38:56 may differ by a few thousandths of an angstrom from that in ethane. Yet the approximation

00:39:04 of the carbon-carbon distance to the standard value 1.54 is very good for many substances.

00:39:12 The carbon-hydrogen distance often has a standard value of about 1.08 angstroms. And we have

00:39:21 found it, chemists have found it very useful to talk about structures for molecules that

00:39:29 involve the idea of the carbon-carbon single bond, the carbon-carbon double bond, even

00:39:34 though these are constructs of the intellect rather than a part of nature that can be understood

00:39:42 completely isolated. Well, in the same way, it is found very useful to talk about the

00:39:48 resonance of the ozone molecule between this valence bond structure and this valence bond

00:39:54 structure, or to speak of ozone as a hybrid that has a structure that can be represented

00:40:00 by two different valence bond structures. There is another question that we can answer

00:40:08 with use of the theory of resonance, and in answering it we achieve a great simplification

00:40:15 of chemistry, coordination of a great number of facts of inorganic chemistry. I may use

00:40:21 hydrogen chloride as an example in discussing this question. What is the structure of hydrogen

00:40:28 chloride, HCl? Well, I can write its Lewis structure in this way. There's a bond, a covalent

00:40:36 bond between hydrogen and chlorine. Hydrogen has achieved the helium structure, chlorine

00:40:42 the argon structure. But of course, if I were giving the talk on ionic valence, I might

00:40:49 say I'll write H+, Cl-, and 30 years ago there was much argument as to which of these structures,

00:40:57 the ionic structure or the covalent structure, was the correct one. Well, we know the answer

00:41:07 now. The theory of resonance provides it. These two structures together can be written

00:41:12 for hydrogen chloride, a normal covalent structure similar to the structure in the hydrogen molecule

00:41:19 and the structure in the chlorine molecule, intermediate between these structures, and

00:41:24 an ionic structure with chlorine negative and hydrogen positive. Well, now we may ask

00:41:32 to what extent do these two structures contribute? And there are several ways of getting an answer

00:41:37 to this. In the hydrogen chloride molecule, the distance between the nuclei is 1.27 angstrom.

00:41:45 The electric dipole moment of HCl is known. It corresponds to a charge plus 0.2 on octane

00:41:54 hydrogen and minus 0.2 on chlorine. We can say then that there is about 20% ionic character

00:42:03 and 80% covalent character to the hydrogen chloride molecule. In fact, it is possible

00:42:11 to correlate the amounts of ionic character of molecules containing single bonds with

00:42:25 a scale, an electronegativity scale, starting with fluorine 4.0, oxygen 3.5, nitrogen 3.0,

00:42:33 carbon 2.5, hydrogen 2.1, boron 2.0, beryllium 1.5, lithium 1.0, chlorine 3.0, sulfur 2.5,

00:42:51 bromine 2.8, iodine 2.4. And the amount of partial ionic character depends upon how far

00:42:59 apart the elements are in this electronegativity scale. You see, this is a sort of skewed periodic

00:43:07 table. Instead, the halogens, instead of following line directly below the lighter one, are skewed

00:43:17 over in this way. The most electronegative element is fluorine, the next most electronegative

00:43:23 element oxygen, and so on across. If two elements differ in electronegativity by about

00:43:28 one unit, chlorine and hydrogen, 0.9, then there is about 20% partial ionic character.

00:43:35 If they differ in electronegativity by about two units, the partial ionic character is

00:43:41 more than 50%, some 60 or 70%. This electronegativity scale was set up from the consideration that

00:43:49 whenever there is resonance between two structures, the substance is stabilized. Benzene is much

00:43:57 more stable than an ordinary unsaturated compound involving a double bond. It is the resonance

00:44:04 energy between the two tachylate structures that provides the extra stabilization. Hydrogen

00:44:11 chloride is more stable than it would be if it had a normal covalent structure. H2 plus

00:44:18 Cl2 forms 2HCl with deliberation of 2 times 22 kilocalories per mole of energy. The bond

00:44:29 HCl bond is 22 kilocalories per mole more stable than the average of the HH bond and

00:44:38 the ClCl bond. Hydrogen and fluorine, H2 plus F2, form 2HF with 2 times 64 kilocalories

00:44:48 per mole. Hydrogen and bromine form 2HBr with 2 times 12. Hydrogen and iodine form 2Hi with

00:44:58 2 times 2 kilocalories per mole, very nearly zero. Now iodine, 2.4, and hydrogen, 2.1,

00:45:07 have nearly the same electronegativity. Consequently, the Hi bond is almost a normal covalent bond,

00:45:15 very little partial ionic character, and correspondingly, the bond is hardly any more stable than the

00:45:22 average of the bond for a hydrogen molecule and an iodine molecule. Bromine is somewhat

00:45:30 more electronegative than hydrogen, 2.8 against 2.1, and the bond is 12 kilocalories per mole

00:45:38 more stable. Chlorine is still more electronegative, difference of 0.9, the bond is 22 kilocalories

00:45:45 per mole more stable. For fluorine, 64 kilocalories per mole more stable. As a rough approximation,

00:45:53 we can say that the partial ionic character of a bond is equal to the amount of extra

00:46:00 stability of the bond as given by the heat of formation of the substance in kilocalories

00:46:05 per mole, about 2% partial ionic character in Hi, 12% in HBr, 22% in HCl, 64% in HF.

00:46:15 Now knowing the electronegativities of elements, we can make predictions about the heats of

00:46:21 formation of all substances that involve single bonds. I can take, for example, graphite and

00:46:29 hydrogen to form methane. What would be the heat of the reaction? Graphite plus hydrogen

00:46:35 to form methane. Carbon, 2.5, hydrogen 2.1, the bond corresponds to about 4 tenths difference.

00:46:44 I know by comparison with Hi and HBr, there will be somewhere around 5 kilocalories per

00:46:52 mole extra stability of the hydrogen-carbon bond. And for a methane molecule with 4 of

00:47:02 these bonds then, about 20 kilocalories per mole as the heat of formation of the molecule.

00:47:09 There are many other properties of substances that can be discussed in a straightforward

00:47:14 way on the basis of the electronegativities of the atoms and the partial ionic character

00:47:23 of the bonds.

00:47:28 The relation between the energy that is liberated and the difference, or when a bond between

00:47:36 two atoms is formed, and the difference in electronegativity of the atoms is the following.

00:47:43 The extra energy, resonance energy, due to partial ionic character of a covalent bond

00:47:50 is approximately equal to 25 kilocalories per mole, 25 kilocalories per mole, times

00:48:02 the square of the difference in electronegativity of the two atoms. I can write xA minus xB

00:48:14 where x represents the electronegativity. xA is the electronegativity of atom A, xB

00:48:20 the electronegativity of atom B. The difference squared multiplied by 25 kilocalories per

00:48:27 mole gives the heat of formation of the bond and multiplied by 25 percent gives the partial

00:48:34 ionic character of the bond.

00:48:39 This explanation of the heat of reactions, all sorts of reactions, applies to substances

00:48:50 containing single bonds. One must be careful not to try to apply it to substances involving

00:48:58 double bonds or triple bonds because the double bond and the triple bond have characteristic

00:49:06 bond energies associated with them.

00:49:11 We have talked about ionic bonds and about covalent bonds and about bonds that represent

00:49:17 resonance between ionic bonds and covalent bonds, bonds with partial ionic character.

00:49:22 This doesn't exhaust modern valence theory. There are still such questions as what is

00:49:30 the nature of the bonds that hold together the copper atoms in a copper crystal where

00:49:35 each atom is similarly situated with respect to its twelve neighbors. What about the hydrogen

00:49:43 bonds? What about oxidation numbers of atoms? Well, it is questions of this sort that we

00:49:50 shall come back to in our next lecture.

00:49:59 Thank you.