00:00:00 This is the first in a series of three recorded lectures about valence and atomic structure given by Linus Pauling when he was a professor of chemistry at the California Institute of Technology.

00:00:31 This lecture is the first of three lectures on one part of chemistry, valence, and the structure of atoms, molecules, and crystals.

00:00:43 It was the British scientist Eddington who said that the study of the physical world, and I would say the biological world too, is a search for structure and not a search for substance.

00:00:59 If we want to understand the human body, we must know its structure in terms of the cells that make it up.

00:01:07 If we want to understand cells, we must know their structure in terms of molecules.

00:01:13 If we want to understand molecules, we must know their structure in terms of atoms.

00:01:19 And to understand atoms, we must know their structure in terms of electrons and nuclei, one nucleus down in the center of the atom with a number of electrons around.

00:01:31 To understand nuclei, as the physicists are trying to do now, we must know, we must learn their structure in terms of protons and neutrons, and perhaps mesons too.

00:01:44 And it may well be that at some time in the future, the fundamental particles, the electrons, protons, neutrons, mesons, will be found to have structure also in terms of still smaller particles that have not yet been discovered.

00:02:03 This subject, a branch of chemistry that correlates the multitude of facts of chemistry in an effective way and makes it easier for the student to learn and to remember the subject, this branch of chemistry is illustrated by the model that I hold here, a model showing the structure of ice.

00:02:27 Here we have the hydrogen atoms, the oxygen atoms, a water molecule, arranged together in space in a certain way. It is this arrangement, this structure, that accounts for the properties of ice.

00:02:42 I hope to be able to come back to a discussion of the structure and properties of ice later on.

00:02:50 Let us consider some substances and their properties that need to be explained in terms of structure.

00:02:57 You all know the example of diamond and carbon. Both of these substances are made up of carbon atoms only, diamond and graphite.

00:03:08 Here I have a diamond. It is the hardest substance known. Here we have a little octahedral crystal as they grow in nature. This came from South Africa.

00:03:23 This substance will scratch any substance that we know about. Then there is the other form of carbon, graphite. This is a chunk of natural graphite which is very soft, so soft that my fingernail will scratch it.

00:03:40 It is used, as you know, in lead pencils for writing. If I rub this piece of graphite across the paper, some of the pieces, some of the bits of graphite tear off and leave their impression there on the paper.

00:03:56 Later on we shall discuss the arrangement of the atoms in diamond and graphite and see how this arrangement explains their properties.

00:04:07 Then I have here two crystals, cleavages, cleavage specimens from naturally occurring crystals, salt, sodium chloride, which when it is hit a crack with a hammer breaks along planes at right angles to one another,

00:04:24 and Iceland spar, calcite, CaCO3, calcium carbonate, which breaks along planes that are not at right angles to one another. This property of cleavage is determined by the structure of the crystal.

00:04:41 Another interesting example of correlation between structure and properties that we now understand really essentially completely is provided by the silicate minerals.

00:04:54 Here I have a natural crystal of feldspar, orthoclase feldspar. The formula of this feldspar is K-A-L-S-I-3-O-8. It is a potassium aluminum silicate, aluminosilicate.

00:05:16 These other crystals, beryl, B-E-3-A-L-2-S-I-6-O-18, garnet, M-G-3-A-L-2-S-I-3-O-12, tourmaline. I can't remember the formula of tourmaline right at the moment.

00:05:34 Silica, quartz, S-I-O-2. These substances are hard and strong. They are the principal constituents of the heterogeneous material granite. The pink here is feldspar. The white grains, the white phase, are crystals, little crystals of quartz.

00:06:00 In this case, the atoms are held together by bonds that go in all directions so that the crystals are hard. Another example of a silicate, a silicate with different properties, is provided by asbestos.

00:06:14 This is a hard rock. It consists, it has nearly the same composition as the feldspar, M-G-3-S-I-2-O-5-O-H-4. If I take hold of this rock, I can pull it apart into little, minute, very thin fibers.

00:06:41 The reason for this, of course, is that the atoms are arranged along in long lines, are bonded together along just the one axis in the crystal. This is another form of asbestos. It is a form in which there are sheets that are rolled up into minute cylinders that run in this direction, and they are piled so loosely together that they fall apart.

00:07:08 Then there are minerals such as mica. Here I have a specimen of mica. It is pseudo-hexagonal. These are natural faces. It is the black phase present in granite.

00:07:22 In mica, the atoms are held together by strong bonds in layers, and these layers are only loosely attached to one another. I might be able, just by using my fingernail, to get hold of a few million of these layers and by pulling to separate them from the rest of the crystal and pull it apart in this way.

00:07:46 The layers are strong within the sheet, but they are very loosely superimposed on one another in this layer crystal.

00:07:55 Now, another example, metal. Metals have peculiar properties that are characteristic of them. They can be deformed in a special way. They are malleable, which means that they can be hammered out into sheets. They are ductile, which means that they can be drawn out into wires.

00:08:14 Here is a piece of copper, a sheet of copper. I can bend it and it distorts without breaking. It is tough in this respect, tough and strong. Other metals are still tougher and still stronger, the structural metals.

00:08:31 Here are some octahedral crystals, crystals with octahedral phase development of native copper, copper as it occurs in nature. We know the structure of the metal copper. It is illustrated by the model over here at the end of the table.

00:08:50 Here, each of these spheres represents a copper atom. We know that in a crystal of copper, in the little grains of copper that make up the sheet of the copper metal or a copper wire, the atoms are arranged in the way that is shown here, a way such that each atom has 12 neighbors.

00:09:12 If I look at this atom, I can see that there are six neighbors that surround it in the same plane. Then there are three in contact with it in the plane below and three in the plane above.

00:09:28 This way of arranging spheres in space is one of the closest packed ways. There is no way of getting a given number of spheres into a smaller volume than by arranging them in closest packing.

00:09:44 Each copper atom is 2.55 angstrom away from its neighbor. We may say that the effective diameter of the copper atom in copper metal is 2.55 angstrom. One angstrom is 100 millionth of a centimeter, 10 to the minus 8 centimeters.

00:10:04 This crystal of copper with this structure is a cubic crystal. The octahedron is closely related to the cube and the tetrahedron, you see here we have a tetrahedron, is also closely related to the cube.

00:10:20 This is the way in which cannonballs are sometimes piled in front of the courthouse on the lawn in the tetrahedron. If you are skeptical about the tetrahedron in relation to the cube, I may make a drawing.

00:10:36 Here we have a representation of a cube. If I now connect the corners that are not adjacent to one another, I can connect these corners with one another and in this way get a drawing of a tetrahedron in a different orientation from this one.

00:11:06 Well, I think that I can prove that this has cubic symmetry in a different way. If I start removing copper atoms from this model, I obtain, after a while, I reach a state where I can lift out a group that have been fastened together.

00:11:28 And you see that here we have 14 atoms, obviously, in a cubic arrangement. There are eight at the corners of the cube, indicated here, and then six others that occupy the centers of the six faces of the cube.

00:11:47 The copper crystal has cubic symmetry. Each atom is bonded to the 12 surrounding atoms.

00:12:08 Perhaps the most important way goes back about 100 years now. It was just 100 years ago that Franklin, Kekulé, and Cowper, and other people making their contributions, originated the idea of the chemical bond and valence.

00:12:28 It was known at that time, 100 years ago, that substances such as salt have formulas such as NaCl, hydrogen fluoride is HF, water, H2O, ammonia, NH3, methane, CH4.

00:12:54 It was suggested that there are bonds that hold the atoms together, Na to Cl, H to F, water, H to O, and another HO bond, with ammonia, NH, NH, NH, and with methane, CH, CH, H, H.

00:13:21 Hydrogen and fluorine, sodium and chlorine are said to be univalent, to have valence one. Water, oxygen, is bivalent. It can form two chemical bonds. Nitrogen is turvalent. Carbon is quadrivalent.

00:13:36 I have here some models illustrating this, standard ball and stick models, H2O, NH3, CH4.

00:13:48 Many, much of the development of chemistry during the last 100 years has been the result of the development of chemical structure theory. Chemists have learned how to arrange the valence bonds in drawing a structural formula of a substance.

00:14:09 But it has been found that the problem is really not a completely simple one. The idea of valence in the old-fashioned, rather vague form has been found to be unsatisfactory.

00:14:24 And during recent decades, especially in the period beginning about 1916, this concept of valence has been replaced by several more precise concepts. The concept of ionic valence, the concept of covalence, of metallic valence, and some others, too, that have less general significance.

00:14:49 In order to understand these more precise concepts of valence, we have to know something about the electronic structure of atoms.

00:15:02 Let us start out with the discussion of ionic valence. Here we have the periodic system of the elements. The elements are arranged in order of their atomic numbers.

00:15:15 Hydrogen, the simplest atom, consists of a nucleus with electric charge plus one in electronic units and a single electron outside of the nucleus.

00:15:27 Helium has two electrons outside of a nucleus with charge plus two. Lithium has three electrons outside of a nucleus with charge plus three, and so on.

00:15:38 Neon, here, has ten electrons surrounding a nucleus with charge plus ten.

00:15:45 Now, the electronic structures characteristic of two electrons, as in helium, ten electrons, as in neon, are especially stable.

00:15:56 This is the reason that helium and neon do not form chemical compounds of the ordinary sort in the way that hydrogen, lithium, and other elements form chemical compounds.

00:16:09 The third electron on lithium is held only loosely by the atom. It is easy to pull that electron away from the lithium atom.

00:16:22 Moreover, fluorine with nine electrons has a considerable affinity for an additional electron. It can pick up an electron.

00:16:34 The result of this is that if lithium metal and fluorine gas come together, there is a vigorous chemical reaction that leads to the formation of the salt, lithium fluoride.

00:16:48 The structure of lithium fluoride is the following one. Lithium has lost one electron and become the lithium ion with the same number of electrons as helium.

00:17:01 Fluorine has gained one electron and become the fluoride ion with the same number of electrons as neon.

00:17:10 Then there is the electrostatic attraction between these ions of opposite electric charge, the same sort of attraction that operates between two pitfalls,

00:17:21 one of which has a positive charge and one a negative charge, between any two objects that have electric charges of opposite sign.

00:17:29 It is this strong electric attraction between the ions, the lithium ion and the fluoride ion, that holds these ions together in the lithium fluoride gas molecule,

00:17:42 which you obtain at high temperatures when lithium fluoride is strongly heated, or in the lithium fluoride crystal.

00:17:50 We shall start the discussion of the electronic structure of molecules, the electronic interpretation of valence, by discussing the electronic structure of atoms.

00:18:03 We know a great deal about the electronic structure of atoms nowadays, and it is the physicists who have determined the information for us.

00:18:13 The sort of experimental material that they have used in finding out about electronic structure of atoms is mainly the spectra, the light emitted by atoms,

00:18:26 by substances when they are strongly heated or subjected to the action of an electric spark or an electric arc.

00:18:35 The first precise description of an atom, not exactly right, was given by Niels Bohr, over 40 years ago now.

00:18:47 Bohr described the hydrogen atom in its normal state in the following way.

00:18:53 He said that there is a small heavy nucleus, the proton, and an electron which moves about it in a circular orbit.

00:19:04 The radius of the circular orbit was given by his calculations as 0.530 angstrom, and the speed with which it moves in its orbit as 2.18 times 10 to the 8th centimeters,

00:19:25 that is a little less than two-thirds of one percent of the speed of light.

00:19:31 Now, the modern picture of the hydrogen atom in its normal state is somewhat different.

00:19:38 We describe the hydrogen atom now as consisting of the same central nucleus, the proton, and the electron, which instead of moving circularly, moves in and out.

00:19:51 It is known that the electron does not have angular momentum in its orbit.

00:19:57 It is not moving sideways, but only in and out.

00:20:00 The average speed, the root mean square speed with which the electron moves, is just the speed that was assigned to the electron by Bohr.

00:20:11 And the average distance of the electron from the nucleus is the same as the radius assigned 40 years ago by Bohr to the circular orbit of the Bohr atom.

00:20:26 In addition to this orbit for the normal state of the hydrogen atom, there can be excited states.

00:20:33 Bohr talked about a larger circular orbit as representing the first excited state, or an elliptical orbit.

00:20:43 According to quantum mechanics, the next most stable orbit for an electron in a hydrogen atom is another one in which the electron moves in and out about the nucleus.

00:20:56 The third most stable one is one in which the electron moves in essentially an elliptical orbit such that there is some sideways motion, too, some angular momentum.

00:21:08 The normal state is represented by the symbol 1s. We talk about the 1s orbital.

00:21:15 Then the next state by the symbol 2s, and then the symbol 2p.

00:21:22 And there are three kinds of orbits with the symbol 2p.

00:21:26 We may speak of them, think of them as having the motion in the plane of the blackboard, or in a plane at right angles to the plane of the blackboard this way, or in the third plane at right angles to both of the other two planes.

00:21:41 There is the most stable orbital, the 1s orbital, the next most stable 2s, and then three 2p orbitals.

00:21:52 The electron has a spin, as discovered in 1925 by Elon Beck and Scott Smith.

00:21:59 And this spin of the electron can orient itself in two ways, either, let's say, with the Earth's magnetic field or opposed to the Earth's magnetic field, either parallel or anti-parallel.

00:22:15 The Pauli exclusion principle, discovered by Pauli in, I think, 1925 or 1926, Pauli exclusion principle states that no two electrons in the universe can be in exactly the same state.

00:22:40 If the two electrons are moving around the same nucleus, for example, if we consider a helium atom with a nuclear charge of plus two, there can be one electron in a 1s orbital, and then a second in a 1s orbital, the same orbital, provided that its spin is opposed, so that one of them has positive spin and one has negative spin.

00:23:05 There is a permanent magnetic moment associated with the spin of the electron. We can think of this as corresponding to a small magnet.

00:23:14 The spin must be oriented with the north pole up, in the one case, for the one electron, and the north pole down for the other, so that the two little magnets neutralize each other's magnetic fields, and helium turns out not to have a magnetic moment.

00:23:32 The third electron in an atom such as lithium will have to occupy another orbital. The 1s orbital is completely occupied when it has two electrons in it as a helium.

00:23:45 This is indicated by putting a superscript 2 on 1s. 1s squared is the symbol for the electron configuration of the helium atom.

00:23:57 Now we may discuss the structure of all of the elements that make up the world as we know it in relation to the periodic system of the elements.

00:24:14 Let us represent the various elements by showing how their electrons occupy orbitals, and we can plot energy vertically.

00:24:28 We start out with the 1s orbital. Hydrogen can have one electron in the 1s orbital. I represent it by putting in an arrow pointing upward.

00:24:39 Helium can have a second electron, two electrons in the 1s orbital. I show then the arrow pointing down.

00:24:49 By power's principle, that is all the orbitals, the electrons that can be placed in the 1s orbital.

00:24:56 The next orbital is 2s. When we come to lithium, the lithium atom with three electrons can have two in the 1s orbital, giving a completed helium shell, and then one in 2s.

00:25:15 Beryllium, with atomic number four and four electrons, can be represented by having two electrons in the 2s orbital. Its electron configuration is 1s squared, 2s squared.

00:25:30 Then we have the three 2p orbitals. They can be occupied successively by electrons in boron, carbon, nitrogen, oxygen, fluorine, neon. At neon, this shell, too, is completed, the neon shell.

00:25:54 Now we come to the third shell in the periodic table, a 3s orbital, two 3p orbitals, and that's all that I want now, two 3p orbitals.

00:26:12 The succession of elements here, sodium, magnesium, scandium, let me see, silicon, phosphorus, sulfur, chlorine, argon, this succession of eight elements brings us up to the noble gas argon, and we can say that this third shell is the argon shell.

00:26:42 Next we come to the fourth shell, with atomic number 19, potassium. Here we have two electrons, ten electrons, eighteen electrons. These numbers, two ten and eighteen, are characteristic of the first three noble gases.

00:26:58 With potassium, we have the 4s electron. With calcium, then, a pair of 4s electrons. Then the 4p orbitals and the 4d orbitals. One, two, three, four, five of the 3d orbitals.

00:27:23 This shell is called the krypton shell, a shell of eighteen electrons occupying nine orbitals.

00:27:32 These can be occupied by eighteen elements, potassium, calcium, scandium. I think that I said scandium down here. Of course, here I should have said sodium, magnesium, aluminum, silicon, and so on.

00:27:52 Here we have the first long period of eighteen elements. Potassium, calcium, scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, zinc, gallium, germanium, arsenic, selenium, bromine, and krypton.

00:28:07 This ends up with krypton, and we call it the krypton shell of eighteen elements.

00:28:17 Here I should mention that the usage of this term shell varies somewhat. It has been customary to refer to the k shell, the l shell, and the m shell, and so on.

00:28:30 Well, the m shell in the old designation is the shell that contains all of the orbitals with the same total quantum number, 3s, 3p, and 3d. But so far as we are concerned in chemistry, it is more important to lump together the orbitals with roughly the same energy.

00:28:50 And here, these are the 4s orbitals, the 3, 4p orbitals, and the 5, 3d orbitals.

00:28:59 The next shell involves the second long period, again, of nine orbitals, 5s, 5p, 4d, and eighteen elements ending up with xenon.

00:29:27 Xenon, Xe, and this shell of eighteen electrons, nine orbitals, we can call the xenon shell.

00:29:37 The next shell, 6s, then the 6p orbitals, 5, 5d orbitals, and 7, 4f orbitals comprises the radon shell.

00:30:02 This is a very long shell, sixteen orbitals all together, thirty-two elements.

00:30:09 It brings us up to atomic number, well, let's see, helium has atomic number two, neon ten, argon eighteen, krypton thirty-six, radon fifty-four, xenon fifty-four, radon eighty-six.

00:30:31 Following this comes the second very long shell, 7s, 7p, 6d, 5f, another thirty-two elements that would bring us up to element 118 that we may call echoradon.

00:30:50 We have then a complete explanation of the periodic system of the elements.

00:30:57 The helium shell, one orbital, two elements.

00:31:00 Outside of that is the neon shell, a 2s orbital and three 2p orbitals, eight more electrons bringing us up to atomic number ten.

00:31:11 Then the argon shell of eight electrons, the krypton shell of eighteen electrons, the xenon shell of eighteen, the radon shell of thirty-two, and going on to the next shell with thirty-two elements it would end up with 118.

00:31:31 The elements from titanium, from scandium on through zinc we may call the transition elements of the iron group.

00:31:43 They correspond to putting ten electrons into the five 3d orbitals.

00:31:49 Similarly, the elements from yttrium on to cadmium we can call the transition elements of this group.

00:31:56 Following lanthanum there come fourteen elements, the lanthanons, from cerium to lutetium that correspond to the introduction of fourteen electrons one at a time into the seven 4f orbitals.

00:32:17 A great deal is known about the distribution of electrons in the various atoms and ions.

00:32:25 This information has been obtained in part by experimental methods and in part by theory, by quantum mechanical theory.

00:32:34 The results of x-ray experiments and electron diffraction experiments have shown that the electron distributions agree well with those that have been calculated by theoretical physicists using the Schrodinger wave equation, the fundamental equation in quantum mechanics.

00:32:53 I have some drawings that I made, in fact, twenty-four years ago when I was going to give a lecture in Santa Barbara.

00:33:04 Some drawings that show how the electrons are distributed in the various ions.

00:33:11 I don't remember just why I was so interested in ions at that time, but I made the drawings for, for example, the bromide ion, a bromine atom that has picked up an extra electron.

00:33:23 And for the rubidium ion, a rubidium atom that has lost one electron.

00:33:30 These drawings are good representations, I believe pretty, pretty accurate rough representations of the electron distributions in the various ions.

00:33:46 Here I have the drawing of the lithium, the nucleus at the center, the lithium ion, Li+, the nucleus at the center, and then two electrons constituting a completed helium shell that move in and out and have a distribution in space that is indicated by this drawing.

00:34:12 As we go on across the periodic table from lithium, toward the end of the first short group, we come to the fluorine atom, which, being just short of neon, can pick up one additional electron.

00:34:31 The electron, electronic structure of the fluoride ion is shown here. The nucleus, two electrons close in to the nucleus that constitute the helium shell, shrunk in because the nuclear charge is large, much larger than for lithium.

00:34:49 And then eight electrons in this fluoride ion, two of which are moving in and out radially, the other six in somewhat elliptical orbits, with the electron distribution shown here.

00:35:02 You see that the fluoride ion is several times larger, roughly three times the diameter of the lithium ion.

00:35:16 And here is the sodium ion. Sodium ion, sodium has 11 electrons. One of them has been lost to form the sodium ion, Na+, leaving 10 electrons just as in the fluoride ion.

00:35:32 These 10 electrons are arranged, are distributed as shown here. The two in the helium shell are close in. The eight that constitute the neon shell are also shrunk in somewhat from the dimensions in the fluoride ion.

00:35:48 This is the effect of the increase by about 20% in effective nuclear charge on going from fluorine to sodium. The scale is shown here, one angstrom. The sodium ion is about one angstrom in radius. The conventional crystal radius for sodium ion is 0.95 angstrom.

00:36:10 From sodium we continue across the first short period of the periodic table to chlorine, which is just one short of argon. The chlorine atom picks up an electron easily to form the chloride ion, and the structure of the chloride ion is as indicated here.

00:36:29 Two electrons in the K shell, the helium shell, then eight in the neon shell, and eight more in the argon shell, giving the ion with one negative charge.

00:36:51 Here I have the next alkali metal ion, the cation potassium, a charge of 19. One electron missing from it, the outermost electron beyond the argon shell is easily removed, leaves it with 18 electrons and a positive charge.

00:37:12 The electronic structure is almost identical with that of the chloride ion. The two innermost electrons have shrunk in a bit. The eight electrons of the neon shell have shrunk a bit, and the eight electrons of the argon shell have shrunk in a bit.

00:37:31 It is evident that we would expect the radius, the effective radius, the effective size of potassium ion to be somewhat less than that of the chloride ion. Their dimensions are potassium, I think, 1.33 angstrom, chlorine, 1.81 angstrom.

00:37:54 Now we move on to bromide ion, atomic number 35, 36 electrons. Two in the helium shell, eight in the neon shell, eight in the argon shell, and 18 in the krypton shell.

00:38:14 Rubidium is the isoelectronic ion. 37 is its atomic number. It has lost one electron. The 36 electrons are arranged in the same shell. Two in helium, eight in neon, eight in argon, 18 in the krypton shell, and the ion has shrunk in size compared with the bromide ion.

00:38:40 The element iodine, with atomic number 53, is just one short of xenon. It can pick up one electron, getting 54 electrons, and its electronic structure is as shown here.

00:38:58 Two K electrons, very close in to the nucleus, then eight electrons in the neon shell, eight in the argon shell, 18 in the krypton shell, and 18 in the xenon shell.

00:39:12 Iodine, the iodide ion is somewhat larger than the bromide ion, which is somewhat larger than the chloride ion, and so on.

00:39:21 Cesium loses one of its 55 electrons easily, to assume the electronic structure of xenon. It has two K electrons, eight in the neon shell, eight in the argon shell, eight in the krypton shell, and eight in the xenon shell.

00:39:42 The sizes of ions, the sizes of these alkali ions and halogenide ions, and also the sizes of the other ions, beryllium double plus, magnesium double plus, calcium double plus, strontium double plus, barium double plus, and so on, are of much value in the discussion of the properties of substances.

00:40:09 Sodium chloride, when heated very strongly, forms diatomic gas molecules, NaCl. It also forms some more complicated molecules, Na2Cl2, and so on.

00:40:23 These easily condense to form sodium chloride crystal. The structure of the sodium chloride crystal is indicated by this model.

00:40:33 This model is about on the scale of one inch to one angstrom, linear magnification 250 million fold, so that it isn't a very good representation of the big crystal of sodium chloride that we have, that we saw earlier in this lecture.

00:40:52 If we wanted to make this model represent the structure of the crystal of sodium chloride, this one, we would have to continue it on until it was about three times the diameter of the Earth.

00:41:09 That is, its volume would be about 27 times that of the Earth if the atoms were this big.

00:41:16 Well, here we have the chloride ion and the sodium ion on the scale corresponding to their relative electron distributions.

00:41:27 1.81 angstrom for the radius of chlorine, 0.95 angstrom for the radius of sodium.

00:41:35 They are arranged in this way in the sodium chloride crystal. Each sodium ion is surrounded by an octahedron of six chloride ions, and each chloride ion is surrounded by an octahedron, four here, one behind and one in front, of six sodium ions.

00:41:54 The ligancy, or coordination number, of the sodium ion is six in this structure.

00:42:01 It is easy to understand why sodium chloride has cubic cleavage.

00:42:06 You see, here in this front face, there are nine to thirteen of these chloride ions and twelve sodium ions.

00:42:16 But if it were a bigger face, there would be exactly the same number of sodium ions and chloride ions, so that this layer of the crystal would be electrically neutral.

00:42:27 We could expect, then, that it might be possible to split off the electrically neutral layer, and in this way achieve the cubic cleavage of the crystal.

00:42:37 On the other hand, if we cut along this diagonal, perpendicular to the body diagonal of the cube, we have first a layer of chloride ions with negative charge, then a layer of sodium ions with positive charge, then a layer of negative ions with chloride, of chloride ions with negative charge.

00:42:56 It would be hard to separate these successive charged layers from one another.

00:43:04 Many properties of substances can be discussed in terms of the sizes of the ions.

00:43:13 One example is the formula of hydrates.

00:43:17 Sodium chloride doesn't form hydrates ordinarily.

00:43:21 Out of aqueous solution, salt crystallizes as anhydrous NaCl.

00:43:27 The attraction of the sodium ion and the chloride ion for water molecules is not very great.

00:43:32 But the ions with larger electric charge, the bivalent ions, beryllium, magnesium, calcium, usually crystallize out of aqueous.

00:43:43 Their salts crystallize with water of crystallization.

00:43:47 And the water of crystallization is, to some extent, predictable.

00:43:54 For example, beryllium is a small ion.

00:43:57 Magnesium is a larger ion.

00:44:00 The size of magnesium relative to the size of a water molecule is about the same as sodium relative to chlorine.

00:44:08 We would expect, then, that magnesium ion would coordinate six water molecules about itself at the corners of an octahedron.

00:44:17 And, in fact, magnesium chloride crystallizes with the formula MgCl2 6H2O.

00:44:24 Many of the salts of magnesium appear as crystallized from aqueous solution with six molecules of water,

00:44:33 which, without doubt, in fact, we know from x-ray diffraction experiments, are arranged octahedrally about the magnesium ion.

00:44:42 The beryllium ion is smaller, so small that it can fit inside of a tetrahedron of four water molecules arranged in this way.

00:44:53 And beryllium sulfate crystallizes as BESO4 4H2O,

00:45:00 the four water molecules being arranged in this tetrahedral manner around the beryllium ion.

00:45:10 In addition to the metals that are close to the noble gases in the periodic table,

00:45:18 lithium and beryllium close to helium, sodium and magnesium close to neon, and so on,

00:45:25 and that easily lose one or two or three electrons to become positive ions,

00:45:32 there are also a number of other metals, those in the transition groups, that easily lose electrons to become cations.

00:45:42 For example, chromium, manganese, iron, cobalt, nickel, copper, zinc appear in most of their compounds as cations with charge plus two or plus three.

00:45:55 Zinc, in the period 2B of the periodic table, zinc forms the ion Zn++, Zn double plus,

00:46:06 with atomic number 30, it loses two electrons easily to form the zinc ion, which has 28 electrons.

00:46:18 Now 18 of these 28 electrons are in the shells up to argon, completed argon structure.

00:46:26 Ten more occupy, ten more are present in the krypton shell.

00:46:33 They are just enough to occupy the five orbitals of the 3D subshell.

00:46:39 Copper, when it loses one electron to form the cuprous ion, has also achieved the structure in which there are ten electrons in the five 3D orbitals.

00:46:54 But of course, this state, this state with valency one, charge plus one, is not the most stable one for copper.

00:47:02 Most copper salts, such as copper sulfate, blue vitriol, CuSO4 5H2O, most copper salts involve copper that has lost two electrons.

00:47:13 And there is no simple explanation of the tendency of copper to lose two electrons.

00:47:21 The most that we can say for these metals in the transition series is that they lose one electron easily.

00:47:30 The second electron is pulled off with greater difficulty because one is removing the electron from an ion that already has a positive charge that is pulling the electron back.

00:47:42 And sometimes it is possible to remove also a third electron.

00:47:47 These elements in the transition period usually turn up with ions that have charge plus two or plus three.

00:47:59 And although it is possible to get some sort of understanding of why one, understanding of why one charge, plus two or plus three, is the more stable for nickel, say, and another the more stable for cobalt, this is not a simple branch of chemical theory.

00:48:27 This sort of valence, we can say that there is a chemical bond connecting the sodium ion with the six chloride ions that surround it in this crystal.

00:48:39 This sort of valence is, I think, very well understood.

00:48:44 The sodium ion here has a single positive charge.

00:48:49 It is not attached to a chloride ion to form a sodium chloride molecule in the crystal.

00:48:56 It is similarly related to all six of the chloride ions that surround it.

00:49:02 I think that it is sensible to say that there is a one-sixth bond, one-sixth of an ionic bond between each sodium ion and each of the six chloride ions around it.

00:49:14 And that the chloride ion itself, with charge minus one, has its charge satisfied by the six one-sixth bonds that come to it from the six sodium ions that surround it.

00:49:28 Many substances can be discussed satisfactorily in terms of the ionic bond with transfer of electrons from one atom to another.

00:49:40 On the other hand, there are many substances that can't be discussed in this way.

00:49:45 For example, the hydrogen molecule, H2.

00:49:48 Neither hydrogen atom picks up an electron from the other.

00:49:52 Instead, the molecule has the structure shown here.

00:49:56 The two electrons are held jointly by the two atoms.

00:50:00 They constitute the bond between the two atoms.

00:50:03 To form this sort of a bond, the covalent bond, the bond that Professor G.M. Lewis of Berkeley called the chemical bond,

00:50:12 we need to have an orbital for each of the two atoms and a pair of electrons.

00:50:18 During the next hour, we shall talk about the covalent bond and the structure of molecules containing bonds of this sort.

00:50:33 Music.