00:00:00 This lecture is a series on valence and molecular structure, Pauling addresses ligancy, coordination numbers and complexes, metallic valence, oxidation numbers, hydrogen bonds, and weak forces.

00:00:30 This lecture is a series on valence and molecular structure, Pauling addresses ligancy, coordination numbers and complexes, metallic valence, oxidation numbers, and weak forces.

00:01:00 This lecture is a series on valence and molecular structure, Pauling addresses ligancy, coordination numbers and complexes, metallic valence, oxidation numbers, and weak forces.

00:01:30 This lecture is a series on valence and molecular structure, Pauling addresses ligancy, coordination numbers and complexes, metallic valence, and weak forces.

00:02:00 This lecture is a series on valence and molecular structure, Pauling addresses ligancy, coordination numbers and complexes, metallic valence, and weak forces.

00:02:30 as it appears in ordinary rhombic sulfur.

00:02:34 This fits in, this structure, a puckered ring of eight atoms, fits in very well with the general theory of valence that we have discussed.

00:02:46 I can't draw the whole ring, we have each sulfur atom forming two bonds and having two electron pairs.

00:02:55 These are the four orbitals that correspond to the argon shell.

00:03:02 Sulfur has completed its argon structure in forming a molecule of this sort.

00:03:11 Hydrogen chloride is a molecule that I mentioned, HCl, in which we have a covalent bond with about 20% partial ionic character.

00:03:23 I want to mention that we must not confuse partial ionic character in the HCl gas molecule with the ionization of HCl, HCl in aqueous solution.

00:03:39 These are two different matters.

00:03:41 In aqueous solution, HCl, hydrochloric acid, is a strong electrolyte, completely ionized.

00:03:48 It forms hydrogen ions, or perhaps we should say hydronium ions, in which a hydrogen is attached, an extra hydrogen ion is attached to a water molecule.

00:03:59 Oxygen has completed its octet, just as in water itself, but in this case it has a neon structure, just as in water itself.

00:04:09 In this case it has three shared pairs and one unshared pair in the neon valence shell.

00:04:19 A related question is the question of the use of orbitals that are not involved in the valence shell of the nearest noble gas, the noble gas with somewhat larger atomic number.

00:04:38 Let me use silicic acid and the related acids, phosphoric acid, sulfuric acid, perchloric acid, as an example.

00:04:47 Silicic acid is SiOH4, and we can draw a structure for it in this way, as G.N. Lewis first did, in which each of the oxygen atoms has achieved the helium, the neon structure.

00:05:07 In the same way for phosphoric acid, we can show POOH, OH, OH.

00:05:19 For sulfuric acid, SOOH, HO, and perchloric acid, ClOH, O, O.

00:05:34 In each of these structures, the central atom is shown as having achieved the argon configuration of electrons.

00:05:43 But the interatomic distances observed for these acids are such as to indicate that there is a considerable amount of double bond character in the silicon-oxygen bonds,

00:05:55 the phosphorous-oxygen bonds, the sulfur-oxygen bonds, the chlorine-oxygen bonds.

00:06:01 This double bond character could be achieved by making use of orbitals that are in the next shell beyond the argon shell.

00:06:12 I may make mention of the acid strengths of these acids.

00:06:16 There is a simple consideration that leads to an understanding of the observed acid strengths.

00:06:23 Phosphoric acid, H4SiO4, is a very weak acid, only a little stronger of an acid than water itself.

00:06:32 Now here we have an OH.

00:06:34 If the hydrogen ion ionizes away, this oxygen is left with a negative charge,

00:06:40 and it is the attraction of this oxygen for the hydrogen ion that makes the acid a very weak acid.

00:06:48 However, the hydrogen ion ionizes away from phosphoric acid.

00:06:53 We see that there are two oxygens left that are equivalent to one another,

00:06:58 so that we might say that there is a charge of minus one-half.

00:07:02 The total charge minus one of H2PO4 is divided between these two oxygens.

00:07:09 Neither one of them attracts the proton as it approaches,

00:07:13 so strongly as this one oxygen with charge minus one attracts the proton in silicic acid.

00:07:19 And in fact, phosphoric acid is much stronger than silicic acid.

00:07:23 It is still classed as a weak acid.

00:07:26 When sulfuric acid ionized, we can say that there is a charge of minus one-third

00:07:31 on each of these three oxygens of the HSO4 ion, HSO4 minus ion,

00:07:39 and so there is a still weaker attraction for the proton as it approaches.

00:07:43 It is attracted toward all three, no one of them so strongly as in the H2PO4 minus ion.

00:07:50 Sulfuric acid is classed as a strong acid.

00:07:53 And of course, with the perchloric acid, when the proton ionizes away,

00:07:58 we have a charge of minus one-quarter on each of the oxygens.

00:08:02 Perchloric acid is a very strong acid.

00:08:09 This simple consideration applies also to acids of other sorts.

00:08:13 Boric acid, H3BO3, is a very weak acid because it has only OH groups attached to the central atom.

00:08:23 A standard example of a molecule that exceeds the octet is phosphorus pentachloride, PCl5.

00:08:32 The conventional formula, structural formula, for this molecule is the one shown here,

00:08:39 in which each chlorine atom has achieved the argon structure.

00:08:44 It is known that the molecule has the configuration of a trigonal bipyramid,

00:08:50 two chlorines above, three around the equator.

00:08:54 The structure as indicated here causes phosphorus to form five bonds.

00:09:01 And this would require that phosphorus make use of one orbital beyond the orbitals in the argon shell,

00:09:09 four orbitals in the argon shell.

00:09:12 This, however, is not the only structure that we may write for phosphorus pentachloride.

00:09:18 We may write a structure such as this one.

00:09:22 Three chlorines bonded around the equator.

00:09:25 The atoms, of course, must be in the same position for electronic resonance, resonance of the bonds.

00:09:31 And a chloride ion in this position, a positive charge on the phosphorus atom.

00:09:38 This P+, positively charged phosphorus, is now forming four covalent bonds using only the four orbitals of the argon shell.

00:09:47 And one ionic bond.

00:09:49 There are five structures of this sort in which the five chlorine atoms are successively given a negatively charge,

00:09:57 given a negative charge, and a resonance structure involving all of these

00:10:03 introduces just about the right amount of partial ionic character to the phosphorus-chlorine bonds.

00:10:09 That would be 16% of partial ionic character to the phosphorus-chlorine bonds,

00:10:15 corresponding pretty well to the difference in electronegativity of phosphorus and chlorine in the electronegativity scale.

00:10:30 There is another aspect of valence theory that I should like to discuss now.

00:10:36 This is ligancy, or coordination.

00:10:40 The coordination of several atoms, or groups of atoms, around the central atom.

00:10:47 For example, here in the sodium chloride crystal, we have sodium ion that, where is it?

00:10:56 Sodium ion surrounded by six chloride ions in an octahedral arrangement.

00:11:02 Chloride ion surrounded by six sodium ions.

00:11:06 It's customary to refer to the cation usually as the coordinating ion,

00:11:11 and to say that sodium has ligancy six in the sodium chloride crystal.

00:11:17 Its ionic valence is one.

00:11:20 We can say that it forms one-sixth ionic bonds with the six surrounding chloride ions.

00:11:27 In the hydrated beryllium ion, BEH2O4 times, there are four bonds formed between beryllium and the surrounding water molecules.

00:11:38 In the hydrated magnesium ion, MGH2O6 times, there are six water molecules around the magnesium ion, located at the corners of an octahedron.

00:11:50 In BEH2O4 times, they are at the corners of a tetrahedron.

00:11:55 Now, the bonds between the beryllium ion, or the magnesium ion, or aluminum ion, in ALH2O6 times, and the oxygen molecule,

00:12:09 involve the electron pairs, an unshared electron pair, of the water molecule.

00:12:15 These bonds are not, however, normal covalent bonds.

00:12:19 They are covalent bonds with partial ionic character.

00:12:22 Here we have beryllium, here magnesium and aluminum in the electronegativity scale, and oxygen over at 3.5, nitrogen at 3.0.

00:12:33 With a metal ion and oxygen or nitrogen in the water molecule, or the ammonia molecule,

00:12:44 the bonds have only one-third to one-half covalent character, two-thirds to one-half ionic character,

00:12:52 so that there is not a great amount of electric charge transferred from the oxygen atom of water or the nitrogen atom of ammonia to the central atom.

00:13:02 In fact, the amount of partial covalent character of these bonds is just about enough to neutralize the charge on the central atom,

00:13:12 to leave it electrically neutral.

00:13:14 We may say that there is a sort of electro-neutrality principle operating here,

00:13:20 that atoms strive to have zero charge rather than a charge of plus two for beryllium and magnesium, plus three for aluminum.

00:13:33 I should like to discuss one of the standard coordination complexes in this respect.

00:13:43 Here we have a model representing the complex CONH3 six times, triple plus,

00:13:51 cobalt three hexamine, six ammonia molecules attached to a central cobaltic ion.

00:14:01 This group of atoms, this complex ion, has a total charge plus three,

00:14:08 but this charge is not to be considered as located on the cobalt atom.

00:14:14 If I draw the regular structure for the complex, represented as involving a cobalt ion,

00:14:24 I can say cobalt three plus NH3 out here, NH3.

00:14:33 I might draw this showing covalent bonds.

00:14:37 Then N, H, H, H, N, H, H, H, and then out in front here, N, H, H, H, and behind, N, H, H, H.

00:14:56 Now with the charge plus three, if these were normal covalent bonds,

00:15:02 a pair of electrons on the nitrogen would be shared with the cobalt,

00:15:06 six electrons would be transferred to cobalt, and the charge would become minus three.

00:15:11 But in fact, the position of cobalt in the electronegativity scale is such that we expect the cobalt-nitrogen bonds

00:15:20 to have about 50 percent covalent character, 50 percent ionic character.

00:15:25 That is just enough, then, six half-electrons transferred,

00:15:30 half of a covalent bond in each of the six directions,

00:15:36 to neutralize the three plus charges, leave the cobalt atom with zero charge,

00:15:41 and each nitrogen atom has then a charge of plus one-half.

00:15:47 But this isn't the end of the story.

00:15:49 The nitrogen-hydrogen bonds, as indicated by the difference in electronegativity of nitrogen and hydrogen,

00:15:58 hydrogen at 2.1, the nitrogen-hydrogen bonds have about one-sixth partial ionic character,

00:16:09 so that there is a charge of plus one-sixth of an electronic charge,

00:16:14 a magnitude of an electronic charge, on each hydrogen atom.

00:16:19 And this neutralizes the charge on the nitrogen, leaving it zero.

00:16:24 Consequently, the total charge of plus three on this complex ion

00:16:30 is divided up into 18 little charges of plus one-sixth each,

00:16:35 which are located on the 18 hydrogen atoms that are on the periphery of this complex.

00:16:41 This is, of course, a nice situation,

00:16:43 because a distribution of charge of this sort corresponds to electrostatic stability.

00:16:50 If we have a metallic sphere that is electrically charged,

00:16:55 all of the charge is on the surface of the sphere,

00:16:58 even though it is a solid metallic sphere.

00:17:02 The elements of charge repel one another until they reach the surface.

00:17:06 In fact, I think that we may say that in aqueous solution,

00:17:10 the hydrogen bonds that are formed by these hydrogen atoms with surrounding water molecules

00:17:15 neutralize these charges to some extent and put the charges in still smaller increments,

00:17:20 still farther away from the central part of this complex.

00:17:26 There's another aspect of the structure of this complex that I want also to mention.

00:17:32 That is the utilization of the orbitals.

00:17:37 Let me, let us consider the, let us consider the orbitals that are available for cobalt.

00:17:47 In the periodic table of the elements, cobalt is seen with atomic number 27.

00:17:55 Cobalt plus three, with three charges, well, I've erased the plus three.

00:18:00 Cobalt plus three, with three electrons removed from it, would have 24 electrons,

00:18:05 that is six more than the number for the argon structure.

00:18:12 If we consider the five 3D orbitals, we may place these six electrons in three of the orbitals.

00:18:21 Then we have 4S and the three 4P orbitals.

00:18:25 Here we have left, on the cobalt atom, six orbitals in the argon shell, or krypton shell.

00:18:34 Krypton shell is a shell of nine orbitals.

00:18:38 Three are used by the six unshared electrons of cobalt.

00:18:43 Six orbitals are left.

00:18:45 These orbitals are of such a nature that they are nicely suited to the formation of bonds,

00:18:53 six bonds pointing toward the corners of a regular octahedron.

00:18:58 These six orbitals are orbitals of this sort.

00:19:03 So that we have a, a nice story covering,

00:19:08 accounting in a satisfactory way for the existence and stability of the cobalt hexamine complex ion.

00:19:18 In fact, the electroneutrality principle,

00:19:22 which is the striving of every atom to achieve an electric charge that is close to zero,

00:19:29 sometimes partial ionic character of bonds keeps it from being exactly zero,

00:19:34 but by increasing the ligancy, one, it is often possible for the charge to be decreased closer to zero.

00:19:42 This electrostatic, this electroneutrality principle explains in a pretty satisfactory way

00:19:49 why it is that so many elements in the periodic table,

00:19:53 especially in the transition region,

00:19:57 form ions in aqueous solution with charge plus two or plus three.

00:20:04 Iron, cobalt, nickel, copper, zinc, manganese, chromium,

00:20:10 the principal ions, cations of these metals,

00:20:14 are those in which the charge on the ion is plus two or plus three.

00:20:19 These metals all have electronegativity around in this region.

00:20:24 The amount of partial covalent character of the bonds is somewhere around one-third to one-half,

00:20:31 which is just enough with octahedral coordination

00:20:35 to neutralize the charge of plus two or plus three on the central ion

00:20:41 and move the charge out toward the periphery of the hydrated ion,

00:20:46 in the case of an ion in aqueous solution.

00:20:50 There is another aspect of the theory of valence that I should mention now,

00:20:54 and this is one that has been understood,

00:20:58 at any rate understood to the extent that we shall discuss now,

00:21:01 only during the last few years.

00:21:04 This is the matter of metallic valence.

00:21:07 What is it?

00:21:08 What is the nature of the forces that hold the copper atoms together in the metal copper,

00:21:14 in the crystal of copper?

00:21:17 Well, let us consider copper.

00:21:20 I think that I would prefer to consider aluminum.

00:21:23 Let us consider the metal aluminum.

00:21:26 It has the same structure as copper, cubic closest packing, as shown here.

00:21:31 Each atom of aluminum here is surrounded by twelve neighbors that are equally distant from it.

00:21:42 Six in this layer, three in the layer behind, three in the layer in front.

00:21:47 Now, aluminum has atomic number 13.

00:21:52 It has three electrons outside of the neon shell,

00:21:56 plenty of orbitals, four orbitals in the argon shell,

00:21:59 so that we would expect it to form three covalent bonds using its three electrons.

00:22:06 In order that it be bonded equally to twelve neighbors,

00:22:11 we may describe the three bonds as resonating among the twelve structures

00:22:18 and holding the aluminum atoms together.

00:22:21 The same sort of resonance of covalent bonds among a large number of alternative positions

00:22:27 occurs in other elements.

00:22:29 For example, in the metals potassium, calcium, scandium, titanium, vanadium, chromium,

00:22:36 the properties of these metals correspond nicely to the idea

00:22:41 that we have one, two, three, four, five, six electrons,

00:22:48 six bonds formed by each atom and resonating around the positions

00:22:53 connecting the atom with the neighboring atoms.

00:22:57 The malleability and ductility can be understood in terms of this resonance.

00:23:02 Also, the property of electric conduction, the ability of the metal to conduct the electric current.

00:23:10 I may mention that there are two kinds, or two common kinds,

00:23:14 of closest packing of spheres that are represented by the metals.

00:23:20 This is cubic closest packing, analogous to this structure.

00:23:24 Along the threefold axis of the structure, there is repetition after three layers.

00:23:30 There are two alternative ways of placing any layer above the layer beneath it,

00:23:37 this way or this way.

00:23:39 In cubic closest packing, these layers, these ways repeat

00:23:45 so as to give repetition after three layers.

00:23:48 In hexagonal closest packing, there is repetition after two layers.

00:23:52 This gives a hexagonal crystal.

00:23:54 Magnesium and many other metals have this structure.

00:23:57 Aluminum, copper, silver, gold, many other metals have this structure, cubic closest packing.

00:24:05 I think that it is interesting that in 1890, many years before x-ray diffraction was discovered,

00:24:14 the English amateur scientist William Barlow had assigned this hexagonal closest packed structure to magnesium

00:24:23 on the basis of the knowledge that magnesium crystallizes as hexagonal crystals

00:24:29 with a certain ratio of this distance to this in the crystal,

00:24:35 and had assigned cubic closest packing to aluminum, copper, silver, gold, and other metals.

00:24:42 In fact, he had assigned the sodium chloride structure to sodium chloride and other alkali halogenides,

00:24:51 the cesium chloride structure to cesium chloride,

00:24:55 the sphalerite structure to the cubic form of zinc sulfide,

00:24:59 the wurtzite structure to the hexagonal form of zinc sulfide,

00:25:03 the fluorite structure to fluorite, CaF2,

00:25:08 and he was right on all of these assignments.

00:25:14 He wasn't sure, of course, that he was right, but it has turned out that his ideas about closest packing of spheres and so on

00:25:23 were right and permitted him to find the correct structures.

00:25:29 A very important use of valence, old-fashioned valence,

00:25:34 was in balancing equations for oxidation-reduction reactions.

00:25:39 Now that valence, the old idea of valence, has been replaced by a number of new and more precise concepts,

00:25:49 we have still a problem of doing something about oxidation-reduction reactions,

00:25:55 and this problem has been solved by introducing another concept, the concept of oxidation numbers.

00:26:04 Oxidation numbers assigned to atoms permit us to keep track of the electrons in an easy way,

00:26:13 whereas the other aspects of valence that we have been discussing are less artificial,

00:26:25 are really an effort to understand what nature is like,

00:26:30 just what the electrons are doing in a complex such as the cobalt hexamine ion.

00:26:37 Oxidation number is, by nature, artificial.

00:26:42 It is something that we introduce with the use of certain rules.

00:26:47 One of the rules about oxidation number is that in an element, the oxidation numbers of the atoms are zero.

00:27:01 For example, in the chlorine molecule, Cl2, each chlorine atom started out with 17 electrons.

00:27:09 Two of the electrons are shared, but we split those two electrons between the two atoms,

00:27:15 so that each atom still has 17, no resultant charge,

00:27:19 and we say that for Cl2, in Cl, the oxidation number of each atom is zero.

00:27:25 Similarly for hydrogen, similarly for copper, or aluminum, or any other metal,

00:27:31 the electrons are divided up equally among the atoms,

00:27:34 and inasmuch as each atom is, inasmuch as the whole metal is electrically neutral,

00:27:41 the individual atoms must be electrically neutral too.

00:27:46 In the case of a molecule such as H2O, O-H-H,

00:27:53 the electrons that are shared between two atoms of different elements, oxygen and hydrogen,

00:28:01 are assigned to the more electronegative of the elements.

00:28:06 Now oxygen, we remember the electronegativity scale.

00:28:12 Oxygen is more electronegative than hydrogen.

00:28:15 We assign these electrons to oxygen so that oxygen becomes an O-2.

00:28:22 Hydrogen is H-plus-1.

00:28:25 The sum of the oxidation numbers in the molecule must add up to zero,

00:28:30 because the molecule is electrically neutral.

00:28:33 If we consider the hydronium ion, H-H-H, here,

00:28:41 the hydronium ion that has a plus charge,

00:28:44 again we assign the electron pairs that are shared with hydrogen to the oxygen atom.

00:28:49 Oxygen has oxidation number minus two, hydrogen plus one, hydrogen plus one, hydrogen plus one,

00:28:58 and the sum of the oxidation numbers for all the atoms adds up to plus one,

00:29:03 which is the charge on the complex ion.

00:29:08 With the, now, hydrogen peroxide, H-2O-2,

00:29:15 the oxidation numbers can be assigned in either one of two ways.

00:29:21 We may say that hydrogen has oxidation number plus one.

00:29:25 The two oxygen atoms are equivalent.

00:29:28 Therefore, in order that the molecule be electrically neutral,

00:29:32 oxygen must have oxidation number minus one.

00:29:35 Or, knowing the structure of the molecule, it has this structure.

00:29:39 In fact, it is known that there is a dihedral angle between the H-O-O plane

00:29:44 and the other H-O-O plane, about as shown here.

00:29:48 O-O distance, well, 1.47 angstrom, O-H distance, 0.96 angstrom, and so on.

00:29:57 And the electronic structure that we can assign to it is this one.

00:30:07 This pair of electrons is to be assigned to this oxygen atom.

00:30:11 The shared pair split so that this oxygen atom has a total of seven,

00:30:16 one, two, three, four, five, six, six, seven electrons surrounding the nucleus

00:30:21 and, of course, the two electrons of the helium shell also.

00:30:24 This means that the oxygen atom ends up with a charge of minus one.

00:30:29 The oxidation number of oxygen is minus two in almost all oxides,

00:30:36 minus one in the peroxides, where there is an O-O single bond,

00:30:41 and zero in the elementary substance.

00:30:44 We can discuss oxidation numbers of other elements

00:30:49 in certain compounds without discussing the distribution of the electrons.

00:30:58 For example, consider the permanganate ion, MnO4 with a charge of minus one.

00:31:05 Oxygen, this is not a peroxide.

00:31:08 The properties are not those of a substance containing an oxygen-oxygen single bond,

00:31:13 and so we assign to oxygen the oxidation number minus two.

00:31:17 There are four of these oxygen atoms.

00:31:19 This gives a total of eight negative charges.

00:31:22 One of them still remains in the ion itself.

00:31:26 Hence, manganese must be plus seven.

00:31:30 Well, of course, with the electronic structure,

00:31:34 whatever the electronic structure is,

00:31:36 each oxygen atom must have four electron pairs in its valence shell,

00:31:41 either shared or unshared.

00:31:43 Some of them probably shared with manganese,

00:31:46 but oxygen is much more electronegative than manganese.

00:31:50 Manganese is somewhere in this region,

00:31:52 so that we would assign these electron pairs to oxygen and not to manganese.

00:31:58 All seven valence electrons of manganese have been taken away from it.

00:32:03 It is manganese with oxidation number plus seven.

00:32:07 Now, the assignment of oxidation numbers to the atoms

00:32:12 in a molecule or complex ion,

00:32:17 having been made,

00:32:26 we may go ahead with the job of balancing the equation for a reaction.

00:32:32 Let us take, well, I've been talking about hydrogen peroxide.

00:32:36 I remember a nice oxidation-reduction reaction that involves hydrogen peroxide.

00:32:42 If one has hydrogen peroxide in a beaker with some sulfuric acid

00:32:48 and then adds potassium permanganate,

00:32:52 that is, adds the permanganate ion,

00:32:55 a beautiful magenta color,

00:32:57 the permanganate ion is destroyed,

00:33:02 as shown by the loss of color.

00:33:04 And oxygen is evolved.

00:33:09 Hydrogen peroxide is oxidized by the permanganate ion in acid solution.

00:33:16 Of course, to write the equation for this reaction,

00:33:20 we need to know what it is that is reacting

00:33:24 and what the products of the reaction are.

00:33:27 The way to find out is by experiment.

00:33:30 Or if somebody else has carried out the experiment already,

00:33:34 by reading a textbook or a paper in the journal.

00:33:39 And if the statements made in the textbook and in the paper are reasonable,

00:33:45 they can be accepted.

00:33:47 Now, in this case, permanganate ion is reduced by the hydrogen peroxide

00:33:53 to manganese ion, Mn++.

00:33:56 And hydrogen peroxide is oxidized to oxygen.

00:34:00 You can see bubbles of gas coming out of the reaction mixture,

00:34:04 and you can identify the gas easily as oxygen.

00:34:08 I like to balance oxidation-reduction reactions.

00:34:13 I like to balance the equations for oxidation-reduction reactions

00:34:17 by writing electrode reactions.

00:34:21 For example, let us take H2O2.

00:34:25 And say that it forms hydrogen ions plus oxygen,

00:34:34 which escapes.

00:34:37 Now, let us assume that this reaction is taking place by itself,

00:34:42 perhaps in an electrolytic cell,

00:34:45 where there are electrodes present that can provide electrons or take up electrons.

00:34:52 Here, I have started to write the electrode reaction,

00:34:57 but there is not conservation of electric charge.

00:35:01 Hydrogen ions are formed so that I can write plus two electrons to conserve charge,

00:35:08 and now everything is conserved.

00:35:10 Hydrogen atoms are conserved because I wrote two in front of the H+.

00:35:15 Oxygen atoms are conserved, and the electric charge is conserved,

00:35:20 which means that electrons are conserved.

00:35:23 The oxidation number of hydrogen is plus one out of oxygen minus two.

00:35:28 Hydrogen, again, is plus one here

00:35:30 so that there has been no change in valence in oxidation number of hydrogen.

00:35:35 But here, oxygen is minus one.

00:35:39 This is a peroxide.

00:35:41 Oxygen has changed from minus one to zero,

00:35:45 and if I look at the atoms that have changed their oxidation number,

00:35:49 I see that two oxygen atoms have gone up from minus one to zero,

00:35:56 which means that two electrons have been given off,

00:36:00 and they are indicated here, so everything is rosy.

00:36:06 Now, the other reaction with the permanganate ion,

00:36:13 we can write as an electrode reaction, too.

00:36:16 It's so simple that you don't need to have any rules.

00:36:19 This one is a little more complicated.

00:36:22 Here, permanganate is reduced in acid solution to the manganese ion,

00:36:29 by positive manganese.

00:36:31 In the permanganate ion, oxygen has oxidation number minus two,

00:36:37 manganese plus seven, so that manganese has changed by five.

00:36:42 This means that we need five electrons in order to carry out the reduction of manganese,

00:36:50 the de-electronation, the electronation of manganese from plus seven to plus two.

00:36:58 Two charges over on this side, plus seven, minus five gives us...

00:37:07 Oh, this is minus one.

00:37:09 Minus five and minus one is six over here.

00:37:12 We need a total of eight plus charges.

00:37:15 This is in acid solution, so I write plus eight plus with hydrogen ion,

00:37:21 and now, to balance the atoms, I have plus four H2O.

00:37:27 These two electrode reactions can be combined with one another

00:37:33 if we make the same number of electrons used up in this reaction as formed in this reaction.

00:37:40 I think that I can multiply this reaction by five and this one by two without making any mistakes

00:37:48 and write two MnO4 minus plus five H2O2,

00:37:57 and here, there would be five, ten electrons that balance the two electrons.

00:38:03 Sixteen H pluses and ten H pluses leaves plus six H plus to form two Mn double plus plus five O2

00:38:14 that comes off plus eight H2O.

00:38:18 This should complete the reaction.

00:38:21 There should be conservation of charge.

00:38:24 Two minuses and six pluses is four pluses, and there are the four pluses.

00:38:29 Conservation of manganese atoms, conservation of oxygen atoms.

00:38:33 Here, altogether, eight and ten is eighteen.

00:38:37 There are eight and ten is eighteen.

00:38:39 And conservation of hydrogens, ten and six, sixteen, and a total of sixteen over there,

00:38:44 so that we have succeeded in balancing this equation.

00:38:51 The next topic that I want to talk about deals with rather weak forces,

00:38:59 the forces that operate between molecules holding them together,

00:39:05 but that are not considered to involve valence bonds of the ordinary sort.

00:39:11 Water is a very good example of a substance for discussion

00:39:17 because the properties of water are determined by a rather weak force of a special sort,

00:39:24 the force that is involved in the hydrogen bond.

00:39:28 The hydrogen bond was, I think it is proper to say,

00:39:32 that it was discovered by Latimer and Rodebusch,

00:39:36 two professors in the University of California in 1922,

00:39:40 and it is a very important part of structural chemistry.

00:39:45 Let us consider water and ice, the ordinary form of crystalline, solidified water.

00:39:52 I should have brought along a bucket of water and a cake of ice to illustrate this part of the talk,

00:39:57 but you know what water and ice are like.

00:40:01 In particular, you know one of the peculiar properties,

00:40:05 almost unique properties, that water and ice have.

00:40:10 Ice, the crystalline form, is less dense than water, the liquid form.

00:40:16 So that water, it is 8% less dense.

00:40:21 So that a cake of ice floating in water, an iceberg floating in water,

00:40:25 has 8% of its volume projecting above.

00:40:29 Well, of course, icebergs usually float in salt water.

00:40:32 That means the density of salt water is greater.

00:40:35 About 12% of the iceberg projects above the surface of the ocean.

00:40:40 This is a very valuable property that water has.

00:40:45 It means that when ice forms on a lake or on the ocean,

00:40:49 it forms on top rather than on the bottom,

00:40:52 so that in the summertime the ice can melt.

00:40:55 We do not have the situation that our oceans and our ponds are solid ice from the bottom up

00:41:01 and only a little bit of the surface melts into liquid water in the summer.

00:41:06 This fact was mentioned by John Tyndall,

00:41:11 an English scientist in the Royal Institution about 75 years ago,

00:41:16 when he said that this unique property of water, of expanding on freezing,

00:41:22 illustrates the beneficence of the creator.

00:41:28 He, of course, was not quite right in calling it a unique property

00:41:33 because a few other substances have been found that have the property of expanding on freezing.

00:41:40 One of them is antimony.

00:41:43 Well, in a sense, the fact that antimony expands on freezing

00:41:48 also illustrates the beneficence of the creator.

00:41:52 After the invention of printing,

00:41:55 type is made not from lead but from a lead-antimony alloy.

00:42:00 Lead contracts on freezing,

00:42:02 and if molten lead were poured into the matrix, the mold, to make the typeface,

00:42:07 as it shrunk away from the typeface, it would shrink in different ways,

00:42:11 so if one had a poor impression of the matrix and of the printed page,

00:42:18 it would not be very clear.

00:42:19 By adding antimony to the lead to make an alloy that does not shrink,

00:42:24 the antimony counteracts the effect of the lead.

00:42:27 The alloy does not shrink.

00:42:29 As it solidifies, it gives a good, sharp impression to the type from the matrix

00:42:36 and of the printed pages correspondingly beautiful and clean.

00:42:41 Now, why is it that ice has lower density than water, that ice floats?

00:42:48 We may say, why is it that ice forms in the world as it is now,

00:42:53 with the Earth the proper distance that it is from the sun?

00:42:58 This is another peculiarity of water.

00:43:01 If we compare water, hydrogen sulfide, hydrogen selenide, hydrogen telluride,

00:43:08 the hydrogen compounds of the elements in this group six of the periodic table,

00:43:14 we see that hydrogen selenide, hydrogen telluride, hydrogen selenide,

00:43:20 hydrogen sulfide are gases at room temperature,

00:43:23 and the boiling points are decreasing in such a way that by extrapolation,

00:43:29 we would predict for water a boiling point of about minus 100 degrees centigrade

00:43:34 instead of plus 100 degrees centigrade.

00:43:37 It is the fact that hydrogen bonds are formed between the water molecules

00:43:41 that causes water to have such a high boiling point and melting point

00:43:49 relative to other substances with the same molecular weight.

00:43:53 The hydrogen bond in water is an interaction,

00:44:03 an interaction of the proton of a water molecule,

00:44:08 a hydrogen atom of a water molecule,

00:44:11 with an unshared electron pair of another water molecule.

00:44:17 And each water molecule can form four such hydrogen bonds.

00:44:23 Here, a hydrogen bond can be formed using the proton of another oxygen atom,

00:44:28 another water molecule here too,

00:44:31 and here a hydrogen bond using the proton of this oxygen atom.

00:44:36 In order that a hydrogen bond be formed, there must be available an electron pair,

00:44:42 an unshared electron pair of one atom,

00:44:45 and a hydrogen attached to another atom that is sufficiently electronegative

00:44:50 so that there is some positive charge on the hydrogen atom.

00:44:55 The structure of the hydrogen bond can be thought of as involving in part

00:45:00 electrostatic attraction of the proton when we have considered the bond to be ionic,

00:45:08 it is about 30 percent ionic,

00:45:11 and the electron pair in part the formation of a weak covalent bond

00:45:18 involving this pair of electrons and the proton

00:45:21 when this pair of electrons is not involved in bonding.

00:45:26 The structure of ice as determined by x-ray diffraction is shown by this model.

00:45:32 Here, the oxygen atoms are arranged in a way resembling the arrangement,

00:45:38 not identical with, but resembling the arrangement of carbon atoms in diamond.

00:45:43 This oxygen atom is surrounded by four other oxygen atoms at tetrahedron corners.

00:45:49 It forms four hydrogen bonds,

00:45:51 two using its own hydrogens, two using the hydrogen atoms of adjacent water molecules.

00:45:58 Closest packing of water molecules would involve ligand C of 12 for each oxygen.

00:46:06 Here we have only ligand C4,

00:46:08 and it is because of the low value of the ligand C4 that this structure,

00:46:14 the structure of ice, corresponds to a low density.

00:46:20 The energy of the hydrogen bond, OHO, in ice and water,

00:46:26 there are still hydrogen bonds in liquid water, about three quarters as many as in ice.

00:46:31 The energy is about five kilocalories per mole of hydrogen bonds,

00:46:36 that is about 10 per mole of water molecules.

00:46:39 It is this extra stabilization of liquid water and crystalline water

00:46:45 that gives rise to the high melting point and boiling point of the substance.

00:46:51 And, of course, the hydrogen bond is responsible also for many other properties,

00:46:55 characteristic properties such as the very high dielectric constant of water.

00:47:01 Only the most electronegative atoms form hydrogen bonds,

00:47:06 fluorine, oxygen, and nitrogen.

00:47:10 The human body is made up largely of compounds of fluorine,

00:47:18 not fluorine, of nitrogen and oxygen and carbon and hydrogen.

00:47:24 And many of these molecules interact with one another through the formation of hydrogen bonds.

00:47:32 I believe that as our understanding of the structure of molecules,

00:47:40 of chemical valence, including such weak interactions of the hydrogen bond,

00:47:46 becomes more and more extensive and more and more precise,

00:47:51 as we obtain a knowledge about the molecular structure of the human body,

00:47:58 we shall be able to make more and more progress in the fields of biology and medicine,

00:48:06 and that this aspect of chemistry, structural chemistry,

00:48:11 will be found to provide the basis for a significant contribution to the welfare of man,

00:48:22 to human happiness.

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