Major Concept Area: The Atomic/Molecular View of Matter
Specific Concepts in this Chapter:3-1 Lewis Structures of Molecules. Valence Electrons of Atoms. We have seen that an atom of an element has a characteristic number of electrons, equal to its atomic number Z. These electrons are arranged in shells about the nucleus, some being close to the nucleus, others far away. It is the electrons in the outermost shell, furthest from the nucleus, and therefore least tightly held, that are involved in chemical bonding. These are the valence electrons. The electrons close to the nucleus, called inner or core electrons, are much too tightly held to be lost to or shared with another atom. As we have seen, the number of valence electrons that an atom has is equal to the last digit of its group number. Thus Na, in group 1, has one valence electron; Al in group 13 has three valence electrons; Br in group 17 has seven valence electrons; and Fe in group 8 has eight valence electrons. The Lewis symbol for an element shows the valence electrons as dots arranged about the symbol for the element, as illustrated in Figure 3-1a for Na, Al, and Br. Dots are placed as if the symbol of the element were surrounded by an invisible square. (There is no physical significance to the square; it simply aids us in orderly thinking.) The first dot can be placed on any of the 4 sides, but the second, third, and fourth dots are then placed singly on the remaining 3 sides of the square; electrons are not placed in pairs (i.e., 2 dots on the same side of the square) until 4 have been placed singly. Dots that singly occupy the side of a square are referred to as unpaired electrons.
G.N. Lewis developed this approach to representing the valence electrons of an element before the quantum view of the atom discussed in Chapter 2 was complete. It is of interest from our perspective, though, to examine the correspondence between the Lewis symbol for an element and its valence electron configuration. In particular, we might expect the number of unpaired electrons in the Lewis symbol to correspond with the number of electrons that singly occupy valence orbitals of the atom. The Lewis symbols and valence orbital occupations of the atoms of period 2 are shown here. What we see is interesting and a bit puzzling. First, most of the atoms show the intuitively expected correspondence. Thus Li, N, O, F, and Ne exhibit the same number of unpaired electrons in the Lewis symbol and in the quantum orbital occupation diagram. Further, the numbers of unpaired electrons for these elements correspond with their usual valences; i.e., with the number of bonds that they form. However, for Be, B, and C in groups 2, 13, and 14, the numbers of unpaired electrons in the Lewis symbols do not correspond with the orbital occupation diagrams. Thus the Lewis symbol for carbon leads us to expect 4 unpaired electrons; the orbital occupation diagram predicts 2. The observed valence for carbon is (almost) invariably 4, in accord with the Lewis symbol. Similarly, the valences of Be and B are as expected from the Lewis symbols, but in conflict with the orbital occupation diagrams. Yet the success of the quantum theory of the atom has been so profound that we believe completely that the orbital occupation diagrams are correct. How are we to explain the bonding properties of elements in groups 2, 13, and 14 in terms of the orbital occupation diagrams? The orbital diagrams can be brought into correspondence with the observed valences by a simple expedient: the downspin electron of the pair in the s orbital is placed in an empty p orbital, with its spin parallel to those of the other electrons. When this is done for Be, B, and C, the numbers of unpaired electrons correspond with the predictions of the Lewis symbol, and with the observed valences. Thus the elements of groups 2, 13, and 14 behave as if their orbital occupation diagrams are as shown here.
The elements in group 18, called the Noble Gases, have 8 valence electrons, arranged in pairs on the 4 sides of the Lewis symbol square. The one exception is helium, He, which has 2 valence electrons. As their name indicates, these elements occur in nature as very unreactive gases; this implies that 8 valence electrons, called an octet, is in some sense a stable situation. As we saw in Chapter 2, 8 electrons is sufficient to fill the s and p orbitals of a shell. When the atoms of the elements undergo chemical reactions, the frequent result is a filled set of valence s and p orbitals for each atom involved -- i.e., each atom acquires the octet of valence electrons possessed by the noble gases. The sodium atom usually loses its single valence electron upon reaction, forming Na+. The sodium ion has the same number of electrons as the noble gas, Ne. The Al atom must lose 3 valence electrons to achieve a noble gas configuration, so it forms the Al3+ ion. In contrast, Br may much more readily gain a single electron to achieve the same number of electrons as Kr than lose 7 electrons. It therefore is found frequently in compounds as the Br- ion.
Elements with from 3 to 7 valence electrons often achieve an octet of electrons--a full set of valence s and p orbitals--by sharing, rather than gaining or losing, electrons. For example, the Br atom can achieve an octet if it can gain 1 electron by sharing. A second Br atom can supply this electron, and achieve the octet for itself in the process. Shared electrons contribute to the octets of both of the two sharing atoms. The electron sharing process is pictured in Figure 3-1b. The shared pair of electrons, located between the bromine atoms, is circled. Note that the single unpaired electron of one Br atom is paired with the single unpaired electron of the second Br atom. This pair is placed between them to indicate the sharing. The shared electron pair constitutes the bond between the two atoms, because it is attracted to both nuclei and therefore holds them together. The bond is called a covalent bond, because it involves cooperation between the 2 atoms so that each may achieve an octet. It is customary and convenient to represent electron pairs with lines rather than dots, as shown in Figure 3-1c. Keep in mind that each line represents 2 electrons -- an electron pair.
Frequently, the number of covalent bonds that an atom forms is the same as the number of unpaired electrons in its Lewis symbol (we will see subsequently that many atoms can be represented by more than one Lewis symbol, giving them some flexibility in the number of covalent bonds formed). Therefore Br, and the other halogens, commonly form one covalent bond. Oxygen has two unpaired electrons and can achieve an octet by sharing both of these with another oxygen atom. The two oxygen atoms then share a total of four electrons, each thereby achieving the octet. Two pairs of electrons shared between two atoms gives two bonds; the pair of bonds together is called a double bond, and is represented by a double line as in the structure for O2 in Figure 3-1d. You should satisfy yourself that two nitrogen atoms can achieve an octet by sharing three pairs of electrons to form a triple bond.
Carbon, with 4 unpaired electrons, forms 4 covalent bonds. Similarly, sulfur forms 2, phosphorus 3, silicon 4, hydrogen 1, and so on, based on the dot symbols in Figure 3-1e. Hydrogen is an exception to the octet rule, because it can accommodate only 2 valence electrons. In acquiring 2, it achieves the electron configuration of the noble gas, helium.
Lewis Structures for Molecules. The realization that when elements react to form compounds the atoms frequently achieve stable electron arrangements -- octets -- was first made by G.N. Lewis, a great American chemist. In tribute to the contributions made by Lewis to the theory of chemical bonding, molecular structures in which valence electrons are represented by dots or lines are called Lewis structures. The Lewis approach to structure, called Lewis theory, is our most-used theory of molecular structure. It is simple, yet sophisticated enough to provide an understanding of molecular properties such as shape, bond length, bond angle, and bond strength. Further, it allows explanation of chemical reactivity and mechanism in terms of structure for many chemical reactions, and suggests a general approach to acids and bases that is used widely. In due course, we will address all of these matters. In this section, we develop a systematic approach for obtaining the Lewis structures of molecules.
Some Lewis structures are easily obtained from the dot pictures of the constituent atoms. Dot pictures for carbon and fluorine are shown in Figure 3-2a. Clearly carbon is able to form four bonds, and each fluorine is able to form one. Therefore, one C atom bonds to four F atoms. The Lewis structure for CF4, tetrafluoromethane, is in Figure 3-2b. Similarly, the Lewis structures for ammonia and water are simply obtained, and are shown in Figure 3-2c. In these molecules, each atom forms a number of covalent bonds equal to the number of unpaired electrons in its dot picture, and each atom has an octet (a duet in the case of hydrogen, which gives it the configuration of He, with 2 valence electrons) in the final structure.
The Lewis structure is not always so readily obtained, however. For example, that for phosgene, COCl2, is shown in Figure 3-3a. Although inspection of this structure verifies that each atom has an octet and has formed the expected number of bonds, arriving at this structure from scratch requires some thought. Note the presence of a double bond between the carbon and oxygen atoms. How are we to know when double bonds and triple bonds, collectively called multiple bonds, are appropriate? To address this question, we now present a systematic and straightforward approach to the writing of Lewis structures.
For phosgene,
Situations will arise in which electrons remain to be added to the structure after the octets of all atoms are complete. In these situations, the remaining electrons are placed in pairs on the central atom. Example 3-3 below illustrates this situation.
For phosgene, the trial structure is in Figure 3-3b.
The phosgene structure must clearly be amended because the carbon atom has only six electrons in the trial structure. A lone pair from the oxygen atom is moved in to form a second bond, preserving the octet on oxygen and at the same time establishing the octet for carbon. We emphasize that ONCE THE CORRECT NUMBER OF ELECTRONS IS PLACED IN THE STRUCTURE IN STEP 3, NO MORE MAY BE ADDED, AND NONE MAY BE REMOVED; electrons can, however, be MOVED. This process is shown in Figure 3-3c. (A lone pair of oxygen is preferred over one from chlorine for reasons that will be explained in a later section dealing with the concept of formal charge.) The result is an acceptable Lewis structure for phosgene. It is important to state at this point that an acceptable structure obtained by direct application of the procedure above is not necessarily the optimal (best) structure. In a later section, we will address the matter of optimizing the structure.
The procedure procedure for generating Lewis structures is illustrated with more examples below.
Example 3-1. Develop the Lewis structure for carbonic acid, H2CO3.
Solution. Refer
to Figure 3-4 throughout the following discussion.
Resonance. It frequently happens that more than one satisfactory Lewis structure can be drawn for a molecule. For example, the double bond in SO2 can be formed by using a lone pair from either oxygen -- there is no reason to prefer one oxygen over the other. Both of the structures in Figure 3-7a are then equally acceptable. These two equivalent structures for SO2 are called resonance forms. In discussing the bonding in SO2, it is best to draw both structures, connected by a double-headed arrow that is used to signify resonance, as in Figure 3-7b. Such a drawing acknowledges that the true structure of SO2 cannot be adequately represented by a single Lewis structure, but is instead more like an average of the resonance forms: a resonance hybrid. In writing two structures, chemists unintentionally create misunderstandings about the nature of resonance. To forestall these misunderstandings, we will take care here to state what resonance does NOT mean. It is NOT true that the actual molecular structure of SO2 oscillates, or changes, back and forth between the two Lewis structures in Figure 3-7. It is NOT true that some SO2 molecules have the left structure in Figure 3-7, while others have the right structure. Experimentally, only one type of SO2 molecule is found. IR spectroscopy (Chapter 4) indicates that the sulfur oxygen bonds in SO2 are intermediate between single and double bonds, and the two S-O bonds are identical. Neither S-O bond is single or double; both are somewhere in between. When red and yellow paint are mixed, the result, an average, is green paint. The green paint does not oscillate back and forth between red and yellow; it is not half red and half yellow; it is green at all times. Keep this analogy in mind when thinking about resonance.
It is important to be able to assess situations in which more than one Lewis structure may be drawn; i.e., in which resonance occurs. Generally, the following features in a structure are tipoffs that alternative (resonance) structures may be important:
You should realize that the necessity for writing resonance forms reflects a lack of completeness in the Lewis approach to bonding. Resonance is not real; it is an invention by which we bring the Lewis structure into harmony with the true molecular structure. However, the idea that we attempt to convey in drawing resonance forms--that certain electron pairs are not localized between a particular pair of atoms, but instead are delocalized over a number of bonded pairs of atoms--is very real. Delocalization of electrons substantially enhances the stability of a molecule.
We arrive at 3 resonance forms for thiocyanate. In contrast to the situation for carbonate, however, these 3 forms are not all equivalent. First, the form with 2 double bonds clearly differs from the triple-bonded forms. Second, the two end atoms are different. Having a singly bonded N and a triply bonded S is different from having a triply bonded N and singly bonded S. It is reasonable to ask whether the structures in Figure 3-9d are also legitimate resonance forms for thiocyanate. The answer is NO. These structures involve a different arrangement of atoms than do those in Figure 3-9c, and correspond to an entirely different species called the isothiocyanate ion. Once we set down the arrangement of nuclei, we cannot move the nuclei to generate resonance forms; we can move only electrons. Resonance forms reflect alternative arrangements of electrons within a fixed framework of atoms.
Resonance forms (1) and (2) are the major contributors to the structure of thiocyanate; form (3) makes little or no contribution. This conclusion is reached using the concept of formal charge, which we introduce now.
Formal Charge. The formal charge of an atom in a covalent structure is obtained by assigning electrons to it according to certain rules, and comparing this assigned number of electrons with the number that the atom normally has, based on the last digit of its group number. The formal charge is the difference between the normal number and the assigned number. The rules for assigning electrons follow:
Example 3-6. Calculate formal charges for the atoms in the sulfur dioxide molecule, shown in Figure 3-5c.
Solution. Assign electrons to each atom based on the 2 rules and compare with the normal number of electrons for the
atom. The difference between normal and assigned numbers is the formal charge:
| Atom | Assigned # e | Normal # e | Formal Charge |
|---|---|---|---|
| O on left | 2(2) + 1/2 2(2) = 6 | 6 | 0 |
| O on right | 3(2) + 1/2 (2) = 7 | 6 | 6-7 = 1- |
| S | 2 + 1/2 (6) = 5 | 6 | 6-5 = 1+ |
Note that the sum of the formal charges of all atoms gives the overall charge on the molecule (or ion), in this case zero. The central atom has a positive formal charge; this will frequently (though not always) be true. Oxygen atoms have 0 or -1 formal charge, depending on whether they form 2 bonds or 1 to other atom(s).
| Structure | C | N | S |
|---|---|---|---|
| N=C=S | 4-4 = 0 | 5-6 = -1 | 6-6 = 0 |
| N(3)C-S | 4-4 = 0 | 5-5 = 0 | 6-7 = -1 |
| N-C(3)S | 4-4 = 0 | 5-7 = -2 | 6-5 = +1 |
We can now use several guidelines about formal charge in molecules to assess the relative stabilities and therefore contributions of the three resonance forms to the true structure of the thiocyanate anion. The guidelines, based upon the structures of a large number of species, are presented below.
Guidelines 1-3 are quite sensible. The first indicates that atoms do not stray too far from their "normal" numbers of electrons. The second states the obvious result that charges of the same sign on neighboring atoms generates electrical repulsion and causes weakening of the bond between them. Finally, separation of charges of opposite sign requires an expenditure of energy and is therefore to be avoided, according to Guideline 3.
Guideline 4 introduces the term electronegativity, a concept that is widely used in chemistry. We will delay until later a detailed discussion of this concept. For now, we simply state that electronegativity is a measure of the ability of an atom to attract the electrons in its bonds, and that it tends to increase from left to right and from bottom to top in the periodic table. The most electronegative atoms are located in the upper right corner of the table; the least electronegative, in the lower left. Fluorine is the element of highest electronegativity, followed by oxygen. The least electronegative element is francium, at the bottom of group 1. Since electronegativity indicates the tendency of an atom to attract electrons, the more electronegative of two bonded atoms tends to have negative formal charge, while the less electronegative atom tends to positive formal charge. This is the basis for Guideline 4. We now apply these rules to the assessment of the resonance forms of thiocyanate.
Structure (1) obeys all the guidelines. The single formal charge is on the N atom, and is consistent with its relatively high electronegativity. Structure (2) is consistent with Rules 1-3. Although S is more electronegative than carbon, it is less so than N, so placing the single negative formal charge on the S atom is less favorable than placing it on N as in structure (1). Structure (2) is acceptable, but somewhat less so than structure (1). Finally, structure (3) is the least favorable because it violates both Guidelines (1) and (3). It makes at most a minor contribution to the structure of thiocyanate. In conclusion, the thiocyanate ion is best described in terms of the first two resonance forms in Figure 3-9c.
Finally, we return to the structure of phosgene in Figure 3-3. In amending the trial structure for phosgene, we chose to use a lone pair from the oxygen atom for double bond formation with carbon, rather than a lone pair from a chlorine atom. Why? You should verify that use of a chlorine lone pair would generate a structure with a formal charge of 1+ on the chosen chlorine and 1- on oxygen. According to the formal charge guidelines, this is a less favorable arrangement than that in Figure 3-3, which has formal charge zero on every atom.
Exceeding the Octet. Although we have used the octet rule as the basis for development of a systematic approach to Lewis structures, only the atoms of period 2 of the periodic table obey it (almost) without exception. Any atom having valence shell principal quantum number > 3 may exceed the octet (violate the octet rule). We have already seen this for SeF4 in Example 3-3. We will see many other examples later. When the octet of electrons is exceeded, it is usually at the central atom. An atom can exceed the octet only if it has atomic orbitals available for housing the additional electrons. As we have stated, eight electrons is sufficient to fill the s and p subshells of the valence shell (outermost main shell) of the atom. To accommodate more than eight electrons in the valence shell, an atom must have available orbitals in addition to the s and p. Atoms for which the valence shell has n > 3 have a valence d subshell comprised of five d-type atomic orbitals. When an atom exceeds the octet, it makes use of d orbitals to house the additional electrons. The Se atom in SeF4 uses a total of 5 valence orbitals (one s, three p, and one d) to accommodate the four bonding pairs and one lone pair of electrons that surround it. The sulfur atom in SF6 uses 6 valence orbitals (one s, three p, and two d) to accommodate the six bond pairs. And the Te atom in TeF82- uses 8 valence orbitals (one s, three p, and four of the five d) to house eight electron pairs! Note that we would not expect an atom with valence shell n > 3 to be able to accommodate more than 9 electron pairs in its valence shell because it has only this number of orbitals available in the s, p, and d subshells. Similarly, elements from period 2 can not house more than 4 electron pairs, because the n= 2 shell has no d subshell. The atoms in period 2 are strictly limited by the octet rule.
Earlier, we mentioned parenthetically that many atoms can be represented by more than one Lewis symbol. This is very closely connected with the availability of d orbitals in the valence shell, and we will now examine this matter before moving on. The sulfur atom is a good vehicle for illustration, because it shows a substantial amount of flexibility in the number of covalent bonds that it is able to form. The usual Lewis symbol for S, and the orbital occupation diagram with which it corresponds, is shown here. This Lewis symbol allows us to rationalize the many 2-valent compounds that are known for sulfur, among them H2S, SCl2, and (CH3)2S. Formation of two covalent bonds is readily rationalized in terms of the two unpaired electrons in the Lewis symbol (and orbital occupation diagram). Thus in H2S, each H atom pairs its single unpaired electron with one of the unpaired electrons of S, resulting in completed s and p subshells for S, and completed s subshells for H. The other two-valent molecules are understood in similar ways. However, sulfur also forms a number of four-valent compounds (for example, SF4); and six-valent compounds (for example, SF6), which cannot be readily accounted for in terms of the simple Lewis symbol above. However, useful Lewis symbols for S can be obtained by unpairing electrons, one pair at a time. The resulting Lewis symbols then show four and six unpaired electrons, as shown here. Corresponding orbital occupation diagrams can be developed by bringing the d subshell into the picture.
Using these expanded Lewis symbols, we readily account for the flexivalent nature of the sulfur atom, and in fact for similar flexibility for most atoms with valence shell n > 3. The following generalization will prove useful to us in rationalizing many molecular structures:
A p-block atom usually forms compounds with a number of covalent bonds lying in the range between the number of unpaired electrons in its simplest Lewis symbol, and the total number of valence electrons that it has. Further, other common numbers of covalent bonds lie between these extremes, separated by increments of 2.
Applying this to S, we would predict that it should exhibit a minimum of 2 covalent bonds and a maximum of 6, with compounds containing 4 covalent bonds being common. Applying the guideline to chlorine enables us to predict a minimum of 1, a maximum of 7, with 3 and 5 covalent bonds being common. In fact, the compounds HCl (minimum), ClF7 (maximum), ClF3, and ClF5 are well known.
A Formal Charge Refinement--Optimizing the Lewis Structure. We can combine our formal charge criteria for acceptable Lewis structures with the ability of many (central) atoms to exceed the octet to obtain improved structures for molecules in which the central atom is from period n > 3. By way of illustration, consider the structure of sulfuric acid, in Figure 3-10a. This structure results from application of the systematic approach to development of Lewis structures presented earlier. Although the sulfur and oxygen atoms obey the octet rule, the formal charges are a bit extreme. Specifically, S has 2+ formal charge, and the two terminal oxygen atoms not bonded to hydrogen have formal charges of 1-. By using lone pairs on these two oxygens to form double bonds to S, the formal charges of all three atoms can be reduced to zero. This causes the sulfur atom to exceed the octet, but this is acceptable for an atom from period 3. The resonance form in Figure 3-10b, called the minimum formal charge structure, results. It is this structure that is usually drawn for sulfuric acid.
The minimum formal charge structure for any molecule can be obtained in a straightforward manner. Starting with the structure generated using the systematic procedure, assign formal charges to all atoms. If the central atom is not from period 2, introduce double bonds between terminal atoms of negative formal charge and the central atom until the central atom formal charge is zero. One double bond removes one unit of positive formal charge from the central atom, so to achieve zero formal charge requires a number of double bonds equal to the positive formal charge in the initial structure. Initial and minimum formal charge structures for H4SiO4, H3PO4, and HClO4 are shown in Figure 3-11.
3-2 The Three-Dimensional Structures of Molecules: VSEPR. Although Lewis structures give us a feel for the manner in which electrons are distributed and shared in molecules, they fail to convey a sense of molecular shape -- the 3-dimensionality of molecules. Thus the Lewis structure for water makes it appear as though the molecule is linear; in fact, it is bent, like a V, as shown in Figure 3-12a. Similarly, methane is not a square and planar molecule, as the Lewis structure implies; as Figure 3-12b indicates, it is instead tetrahedral. The experimental determination of the 3-dimensional shape of a molecule, whether it be a relatively simple molecule like water or a complex and large molecule like hemoglobin, the oxygen carrying protein of blood, involves a combination of spectroscopic methods and the methods of x-ray diffraction. Based on the experimentally-determined structures of large numbers of molecules, it has been possible to develop an extremely simple theory that allows the prediction of 3-dimensional structure with a high degree of success. This theory is called the Valence Shell Electron Pair Repulsion (VSEPR) Theory. It is based upon a single very simple tenet: electron groups surrounding an atom in a molecule distribute themselves to minimize the repulsions between them. In other words, they get as far apart as is geometrically possible. We must establish three things in order to apply this idea. First, what constitutes an electron group? Second, what geometrical arrangement minimizes repulsions between a particular number of such groups? Third, once the groups are distributed, what is the molecular shape?
An electron group is any of the following: a lone (nonbonding) pair of electrons; a single bond; a double bond; a triple bond; a single electron. Counting the number of groups around an atom in a molecule is therefore quite easy.
| H2O | 4 |
| CH4 | 4 |
| PF5 | 5 |
| COCl2 | 3 (the double bond counts as a single group!) |
| NO2 | 3 (the double bond and single electron count as single groups!) |
The geometrical arrangements that minimize repulsions among up to 6 groups are given in Table 3-1, with structural representations shown in Figure 3-14.
| Number of groups | Distribution | Example |
|---|---|---|
| 2 | linear | BeH2 |
| 3 | trigonal planar | COCl2 |
| 4 | tetrahedral | CH4 |
| 5 | trigonal bipyramidal | PF5 |
| 6 | octahedral | SF6 |
Trigonal planar means that the central atom and the 3 groups around it all lie in the same plane, and that the 3 groups are arrayed in triangular shape about the central atom. Trigonal bipyramidal means what it says: 2 pyramids, each with a triangular base, placed base-to-base. An octahedral distribution means that the 6 groups form an octahedron about the central atom. An octahedron is a regular figure with 6 vertices and 8 equilateral-triangular faces. You can think of it as a base-to-base joining of 2 square-based pyramids. In this view, it is somewhat similar in origin to the trigonal bipyramid. Please take some time to learn the shape-descriptive terminology in Table 3-1, and to develop a mental image of each of the common group distributions in Figure 3-14.
We see from these examples that two situations arise. In the first, all electron groups on the central atom are used in bonding other atoms. This is the case for CH4, PF5, and COCl2. In the second, only some electron groups are shared with other atoms; the remainder are unshared. This is the case for H2O and NO2. In all cases, the distribution of electron groups is as indicated in Table 3-1. However, the molecular shape is a description of relative atom positions. When the number of attached atoms is less than the number of electron groups, descriptions of electron distribution and shape are different. First, consider the situation in which all groups are shared with other atoms. In these cases, the descriptors for group distribution are also used for shape. Thus, methane has a tetrahedral shape (as well as a tetrahedral group distribution), phosphorus pentafluoride has a trigonal bipyramidal shape, and sulfur hexafluoride has an octahedral shape. When there are nonbonding electrons on the central atom, the number of attached atoms is less than the number of electron groups. We have previously seen numerous examples: ammonia, water, sulfur dioxide, and selenium tetrafluoride. The shapes of such molecules are described using words that are indicative of where the atoms are. Nonbonding electrons, although important in determining group distribution and therefore shape, are ignored in the geometrical description of shape. Thus for example, the group distribution about the nitrogen atom in ammonia is tetrahedral, just as in methane; but the molecule is said to have a trigonal pyramidal shape. This descriptor tells us where the atoms -- one N and three H -- are relative to one another. Similarly, the group distribution in water is tetrahedral, just as in methane and ammonia; but since there are only 3 atoms, which describe a "V" in space, the water molecule is said to be bent. Further examples for electron groups numbering from two to six are in Table 3-2.
| # groups | # atoms | distribution | shape | Example |
|---|---|---|---|---|
| 2 | 2 | linear | linear | CO2 |
| 2 | 1 | linear | linear by necessity | CO |
| 3 | 3 | trigonal planar | trigonal planar | BF3 |
| 3 | 2 | trigonal planar | Bent | SnCl2 |
| 4 | 4 | tetrahedral | tetrahedral | CH4 |
| 4 | 3 | tetrahedral | trigonal pyramidal | NH3 |
| 4 | 2 | tetrahedral | bent | H2O |
| 5 | 5 | trigonal bipyramid | trigonal bipyramid | PF5 |
| 5 | 4 | trigonal bipyramid | teeter-totter | SF4 |
| 5 | 3 | trigonal bipyramid | T-shaped | BrF3 |
| 6 | 6 | octahedral | octahedral | SF6 |
| 6 | 5 | octahedral | square pyramidal | BrF5 |
| 6 | 4 | octahedral | square planar | XeF4 |
Figure 3-15 shows the three-dimensional structures of ammonia, sulfur tetrafluoride, bromine trifluoride, bromine pentafluoride, and xenon tetrafluoride. The molecular structures are drawn using the so-called wedge-hash system. In this system, as many as possible of the bonds between central and terminal atoms are placed in the plane of the paper, and are represented as solid lines. Bonds that must by restraints of geometry protrude out of this plane are represented using wedges. The wedge shape represents the bond as getting thicker, or fatter, as it approaches us. Finally, bonds that retreat behind the plane of the paper are represented using dashed or dotted lines. You should become skilled at using this notation to represent the three-dimensional structures of molecules.
The shape of a molecule is referred to as its stereochemistry. Thus methane, CH4, is said to have tetrahedral stereochemistry about the carbon atom. Similarly, NH3 has trigonal pyramidal stereochemistry, and SF6 has octahedral stereochemistry.
| Molecule | Group Distribution | Shape |
|---|---|---|
| H2O | tetrahedral | bent |
| CH4 | tetrahedral | tetrahedral |
| PF5 | trigonal bipyramidal | trigonal bipyramidal |
| COCl2 | trigonal planar | trigonal planar |
| NO2 | trigonal planar | bent |
Bond Lengths and Bond Angles in Molecules. In this section, we continue our discussion of the structures of molecules by saying something about the lengths of chemical bonds, and the angles that bonds make with each other about a central atom. Lengths are relatively easy to understand, so we discuss these first, in terms of a couple of simple ideas.
Bond angles are also extremely important in three-dimensional structure, and it is important to be able to make a simple qualitative prediction of their magnitudes. Regularly-shaped molecules have the bond angles expected on the basis of the associated geometrical figure. Thus BF3, a perfect equilateral triangle (trigonal planar), has angles of exactly 120o between adjacent B-F bonds. Methane, CH4, is a perfect tetrahedron, with angles of 109.5o between the C-H bonds. Phosphorus pentafluoride is regularly-shaped, but differs from BF3 and CH4 in that the P-F bonds are of two different types. The three fluorines that define the equilateral triangle where the two pyramids are joined are separated from one another by angles of 120o, just as are the bonds in BF3. These are said to occupy equatorial positions. The remaining two fluorines, one above and one below the equilateral triangle, lie along a straight line that also passes through the phosphorus atom. These fluorines are said to be axial. The angle between an axial and an equatorial fluorine is 90o, and that between the two axial fluorines, 180o.
Bond Angle Refinements. The VSEPR Theory allows us to easily predict the overall shape of a simple molecule based on the Lewis structure, and bond angles for those highly symmetrical molecules in which all central atom electron groups are shared with terminal atoms, and in which all terminal atoms are the same. With the addition of just a few more simple ideas, the theory can be extended to allow us to say something about bond angles in less symmetrical situations as well. We begin with some experimental facts. The electron group distributions in methane, ammonia, and water are tetrahedral. However, whereas the bond angle in methane is the expected 109.5o, that in ammonia is 107o, and that in water is still smaller at 104o. Why? The nonbonding electron pair that occupies one of the four positions around the nitrogen atom in ammonia belongs entirely to the nitrogen atom; it is not shared with any other atom. It is therefore closer to nitrogen than are the 3 single bond pairs, and requires more room. The result is that the three bond electron pairs are repelled more by the lone pair than by each other, and are squeezed closer togther than in methane; the bond angle is reduced. The effect is even greater in water, where two of the four groups are nonbonding pairs. Similarly, it is found experimentally that the angle between the two C-F bonds in COF2 (similar to phosgene, COCl2) is 108o, noticeably less than the ideal value of 120o. This is attributed to the double bond between C and O, which involves four electrons rather than two, and therefore takes up more space. Finally, the O-N-O angle in NO2 is 132o, somewhat larger than the ideal value of 120o. As might be expected, the single electron group on the central N atom exerts less repulsion than would a nonbonding pair, and less even than a bond pair of electrons. As a consequence, the angle between bond pairs opens up.
Based on these observations, the following generalizations may be made:
With these ideas in hand, we now address the strange structures for SF4 and BrF3 in Table 3-2 and Figure 3-15. There are 5 electron groups around the central atom in both species, so the group distribution is trigonal bipyramidal. In both cases, lone pairs, which exert the largest repulsions on other electron pairs, occupy equatorial rather than axial sites because by so doing they minimize 90o interactions with other electron pairs. A lone pair in an axial position would have three such interactions (with the equatorial pairs); in an equatorial position, it has only two 90o interactions (with the axial pairs). Lone electron pairs occupy equatorial sites in the trigonal bipyramid. Similar arguments apply for square planar XeF4, in which the two lone pairs are as far apart as possible at 180o.
Lewis structures are shown in Figure 3-17. Based on these structures, the bond angles are developed as follows:
| Molecule: | N2O | SO42- | SO32- | O3 | ClO2 |
| # electron groups: | 2 | 4 | 4 | 3 | 4 |
| group distribution | linear | tetrahedral | tetrahedral | trigonal planar | tetrahedral |
| stereochemistry | linear | tetrahedral | trigonal pyramid | bent | bent |
| bond angles | 180 | 109 | < 109 | <120 | >109 |
It is possible to make a number of statements about bond lengths. The NN bond in N2O is somewhere between double and triple, based on an average over the two acceptable resonance forms. It should have length intermediate between these extremes. Similarly, the NO bond length should be intermediate between that for the N-O and N=O bonds.
For SO42-, bond lengths should all be the same, and should be somewhat shorter than the S-O single bond length. Since S is a larger atom then O, the SO bond length should be longer than the O-O single bond.
For SO32-, bond lengths should again be all the same, and should be slightly shorter than single bond lengths. They should be similar to the bond lengths in SO42-.
For O3 there are two equivalent (identical) resonance forms. Averaging over them, we conclude that each OO bond should be intermediate in length between the OO single bond (as in hydrogen peroxide) and double bond (as in O2).
Finally, for ClO2, the two ClO bonds should have the same length, appropriate to that of a double bond.
It may have occurred to you that there is a discrepancy between the experimentally observed bond angles in molecules (109, 120, and 180o) and the spatial distribution of the valence s and p orbitals discussed in Chapter 2. It is reasonable to assume that the valence orbitals of an atom play a role in the formation of bonds to other atoms; however, at this point we are unable to explain why orbitals directed at 90o to one another form bonds that are separated by 109, 120, or 180 degrees. In Chapter 6, we will present a reasonably simple approach to rationalizing the discrepancy.
We will rely heavily on the principles of molecular stereochemistry in work to come. Please study and practice using these principles until you are comfortable with them.
3-3 Charge Distribution in Molecules. Electronegativity. The electronegativity of an atom was defined by Pauling as "the ability of the atom in a molecule to attract electrons to itself." Unlike the molar volume and ionization energy, the electronegativity is not a directly measurable physical property of an atom. Rather, it is defined in a somewhat vague and qualitative way. Several ways of assigning a numerical value to the electronegativity of an atom have been developed. The most commonly used scale of electronegativity is that of Pauling, based on the experimentally measured values of bond energies. We will not concern ourselves with the details of how the scale was established. We will instead present the scale, make some general statements about the variation of electronegativity with position in the periodic table, and then proceed to use the electronegativity where appropriate. Suffice it to say at this point that the electronegativity of an atom, symbolized c, is roughly proportional to the first ionization energy of the atom. In other words, the more difficult it is to remove the outermost electron from an atom, the more likely it is that the atom will attract additional electrons to itself.
The Pauling electronegativities of the elements are presented in Figure 3-18. The following trends can be extracted:
Electronegativity is the primary concept on which we base our understanding of electron distributions among atoms in a molecule.
Bond Dipoles and Dipole Moment. The distribution of electrons in a molecule determines its shape. One frequent consequence of shape is that the centers of positive and negative charge in the molecule are displaced from one another, so that the molecule has a positive end and a negative end. Such molecules are said to possess total molecular dipole moments. It is important to be able to assess whether or not a molecule is polar; that is, whether it has a total molecular dipole moment. In this section, we will take some time to discuss the origins of total molecular dipole moments so that you will be equipped to do this assessment.
An arrangement in which a positive charge q+ and an equal negative charge q- are separated by a fixed distance, r, is called an electric dipole. The electric dipole is a vector quantity that is by convention taken to point from the positive to the negative end of the dipole, as shown in Figure 3-19a. The magnitude (length) of the vector is the product of the charge, q+, and the distance between the positive and negative centers:
The electric dipole has units of charge times distance. For a dipole consisting of a charge of 1 electronic charge unit separated from an equal and opposite charge by a distance of 1 * 10-10 m, the dipole moment has the value 1.6 * 10-29 C-m.
The total molecular dipole moment of a molecule is in general the vector sum of various local electric dipoles that exist in the molecule. These local electric dipoles are of two types that we will call bond dipoles and lone pair dipoles. Local bond dipoles are generally larger in magnitude, hence more important, than lone pair dipoles. They are thus the major contributors to the total molecular dipole moment, and we will discuss them first. A bond between two atoms, X and Y, in which the bond pair is unequally shared is called a polar bond. A polar bond gives rise to a local bond dipole. Unequal sharing occurs when X and Y have different electronegativities; the shared electron pair is on average closer to the more electronegative atom. Consequently, the local bond dipole points along the bond, from the less electronegative atom (positive end) to the more electronegative atom (negative end). Assessment of the polarity of a bond is simple: if the two atoms involved in the bond are different either in identity or environment, the bond is polar. Only bonds between identical atoms in identical environments are non-polar. A heteronuclear diatomic molecule such as HCl provides an example of a local bond dipole. Heteronuclear means that the two atoms of the molecule are different. Chlorine is more electronegative than hydrogen, so the bond electrons between them are closer to Cl than to H. This makes the Cl atom slightly negative and the hydrogen atom slightly positive. The H-Cl bond is polar, with the electrons biased toward Cl. This polarity gives rise to a local bond dipole that points along the bond from H (positive) to Cl (negative). This local bond dipole is pictured in Figure 3-19b.
The second type of local electric dipole is the lone pair dipole, which exists at any atom having one or more lone electron pairs. A local lone pair dipole points, as expected, from the nucleus of the atom (positive) to the lone pair (negative). Although strictly speaking there is a lone pair dipole generated by each lone pair in a molecule, the major contribution to the total molecular dipole is made by lone pairs on the central atom. Consequently, in examining a molecule for local lone pair dipoles, we will consider only lone pairs on the central atom, ignoring those on terminal atoms. In addition to its local bond dipole, HCl contains three local lone pair dipoles, one associated with each of the lone pairs on the chlorine atom. One of these is shown in Figure 3-19c. The total molecular dipole moment of a molecule is the vector sum of all local electric dipoles (bond dipoles and central atom lone pair dipoles). The total molecular dipole moment of HCl is 0.36 x 10-29 C-m. This is due primarily to the bond dipole; the lone pair dipoles make a minor contribution, as is generally true.
Assessment of the total molecular dipole of HCl is quite simple, because there are only two atoms. For larger molecules, we will use the following systematic approach.
To illustrate the system, we consider the water molecule, which according to spectroscopy (and VSEPR) is bent, with an angle of 104o. Oxygen is more electronegative than hydrogen, so the O-H bonds are polar with the electrons closer to the oxygen than to the hydrogen atom. Each O-H bond in the water molecule therefore has a local bond dipole that points from H to O. The bond dipoles are shown in Figure 3-19d, along with their vector addition to produce the net bond dipole. Because the water molecule is bent, the local bond dipoles add together to produce a non-zero net bond dipole that points from the center of the (imaginary) line connecting the hydrogen atoms (positive) to the oxygen atom (negative). Next, we find two lone pairs on the central oxygen atom. Each lone pair generates a lone pair dipole pointing from the oxygen nucleus to the lone pair. The lone pair dipoles and their vector sum are shown in Figure 3-19e. The result is a non-zero net lone pair dipole that points from the oxygen atom (positive) to the center of the (imaginary) line connecting the lone pairs (negative). The net lone pair dipole and the net bond dipole point in the same direction. The final step, shown in Figure 3-19f, is the vector addition of the net bond and lone pair dipoles to produce the total molecular dipole moment of water. The magnitude of the total molecular dipole moment is 0.615 * 10-29 C-m. This substantial dipole is a major factor in the ability of water to dissolve a variety of substances, notably including ionic compounds.
Although bonds between different atoms are polar to at least some extent, as we saw above, many highly symmetrical molecules have no net dipole moments due to exact cancellation of the bond and lone pair dipoles. An example is the CO2 molecule, which is linear. Each C-O bond is polar. Each therefore has a local bond dipole pointing directly along the bond from carbon (less electronegative) to oxygen (more electronegative). However, the two equal local bond dipoles point in opposite directions and cancel exactly. The central carbon atom has no lone pairs, so no lone pair dipoles need be considered. Thus the molecule as a whole has coincident centers of + and - charge. We will see later that dipole moments contribute to the attractive forces that molecules exert on one another. To understand the magnitudes of these forces, it is essential that we be able to determine whether or not a molecule possesses a total molecular dipole moment.
SO3. Each S-O bond is polar, with a local vector bond dipole pointing from S (less electronegative) to O (more electronegative. All S-O bonds are the same when resonance is taken into account. The three local bond dipoles thus point to the corners of an equilateral triangle. When added vectorially, the result is zero. There are no lone pairs on the central S atom, so local lone pair dipoles need not be considered. There is no net molecular dipole; SO3 is non-polar.
O3. Although the bonds in this molecule connect pairs of oxygen atoms, the two oxygen atoms of a bond are not in identical environments. Considering the bond between oxygens 1 and 2, we see that oxygen 1 is bonded only to oxygen 2, whereas oxygen 2 is bonded to oxygen 1, but in addition to oxygen 3. Oxygens 1 and 2 are in different environments, so the bond between them is polar. The difference between oxygens 1 and 2 is evident from their formal charges, which are 0 and 1+ in the resonance form shown. The formal charges also enable us to assign the direction of the local bond dipole, which points from oxygen 2 to oxygen 1. The molecule is bent, so the two identical local bond dipoles do not add to zero. They cancel horizontally, but not vertically. The local lone pair dipole pointing from oxygen atom 2 to its lone pair only partially cancels the vertical net bond dipole (recall our statement that in general bond dipoles are more important than lone pair dipoles). Ozone has a net molecular dipole running from the center oxygen through the center of the molecular angle.
CCl4. From the Lewis structure for CCl4, a perfect tetrahedral shape is expected (like methane, CH4). The local bond dipoles are non-zero, with the negative end toward Cl, but cancel when added vectorially. The central carbon atom has no lone pairs. There is no molecular dipole moment. The cancellation of local bond dipoles may not be obvious here because of the three-dimensionality of the figure. However, the following argument may be used. Molecules having total molecular dipole moments are inherently less symmetric than molecules with zero molecular dipole moments. For example, if you were to orient the ammonia molecule with the nitrogen lone pair pointing down rather than up, it is easy to tell that the molecule has been moved. In contrast, if you were to orient carbon tetrachloride with any of the three other chlorine atoms at the top, the molecule would look exactly the same as it does above; you would not be able to tell that it had been moved! Thus it has no dipole moment.
NH3. NH3 has a trigonal pyramidal shape. The bonds are polar, with the negative end of the local bond dipole toward nitrogen. These will combine to give a non-zero net bond dipole colinear with an axis passing through the nitrogen atom and the center of the equilateral triangle defined by the H atoms. This is reinforced by the nitrogen local lone pair dipole. The molecule therefore has a molecular dipole moment with the nitrogen end of the dipole negative.
PF5. PF5 is trigonal bipyramidal. The bonds are very polar because F is the most electronegative element. However, the two axial local bond dipoles oppose and cancel, and cancellation occurs in the equatorial plane as well, exactly as in SO3 above (you should use trigonometry to prove this to yourself). There are no lone pairs on the central atom. There is no molecular dipole moment.
3-4 Reasoning by Analogy: the Isovalent Fragment Approach to Structure. We close this chapter by developing an approach to molecular structure based on analogical thinking. An oxygen atom has 6 valence electrons, so it requires 2 to achieve the octet. Suppose it gains 1 electron by forming a bond to hydrogen, giving the species H-O*. Here * represents the remaining odd electron on the oxygen atom that must pair with a second electron in bond formation. Because the species H-O* requires only 1 electron more, it is analogous to a halogen atom, for example, Cl*. Again, * represents the seventh chlorine electron, the one that is shown unpaired in the dot structure for the atom. Since the O atom in H-O* is capable of forming one bond, like Cl*, OH* and Cl* are isovalent (iso = same, so same valence). Further, we will call them fragments because they do not yet have electron octets. Finally, they are 1-bond fragments because they need form only one additional chemical bond. Combining terms, we will refer to HO* and Cl* as 1-bond isovalent fragments. To emphasize the 1-bond aspect of these fragments, we will write them as OH- and Cl-, where the dash represents an incipient bond, not a negative charge. You should convince yourself that the following species are also 1-bond fragments, isovalent with HO- and Cl-:
Note that the number of atoms attached to the central atom in these fragments increases by 1 for each 1-unit decrease in the group number of the central atom.
Compatible fragments can be united to give the central atom of each fragment the octet. Thus two 1-bond fragments can be united. We therefore expect the existence of molecules in which two of the fragments from those listed above are combined. In fact, all possible combinations of the 1-bond fragments above actually exist and are (within the framework of the fragment idea) related, or analogous. The following structures are illustrative:
| Cl-Cl | HO-OH | HO-Cl | H2N-OH | H3C-OH |
| chlorine | hydrogen peroxide | hypochlorous acid | hydroxyl amine | methyl alcohol |
In similar fashion, the oxygen atom itself can be viewed as a 2-bond fragment, represented O=, because by forming 2 bonds it can achieve the octet. The following species are 2-bond fragments isoelectronic with O=:
2-bond fragments are compatible; thus two of them can be united to give the central atom of each fragment the octet. The following molecules can be viewed as the union of two 2-bond fragments:
| O=O | dioxygen |
| H2C=CH2 | ethylene |
| CH2=O | formaldehyde |
| (CH3)2C=O | acetone |
Further, a 2-bond fragment is compatible (can unite) with two 1- bond fragments, as in the following molecules:
Finally, the nitrogen atom is a 3-bond fragment, requiring 3 electrons to achieve the octet. It may be represented as N(3). Isoelectronic 3-bond fragments are
Combination of such fragments gives the following molecules or ions:
A 3-bond fragment is compatible with three 1-bond fragments. You should generate some molecular formulas by combining 3-bond and 1-bond fragments.
A single 2-bond fragment may be viewed as equivalent to two 1-bond fragments (X= equivalent to 2 Y-), and may replace them in a formula. Thus phosgene, COCl2, may be "generated" from carbon tetrachloride, CCl4, by replacing two 1-bond Cl fragments with the 2-bond fragment, O=. CO2 follows from phosgene by a similar replacement of the remaining Cl- fragments. Similarly, X(3) is equivalent to 3 Y-. It is quite easy to go from a known Lewis structure to several others using this analogical approach. Figure 3-20 illustrates the generation of a family of sulfur compounds. Successive replacement of two 1-bond F fragments with the 2-bond fragment, O=, leads to sulfur trioxide via two oxofluorides. Replacement of O= by another 2-bond fragment, HN=, leads to the Lewis structure for S(NH)F4. Finally, replacement of three 1-bond F with one 3-bond fragment, N, generates the final molecule, SF3N.
3-5 The Importance of Molecular Stereochemistry. The importance of molecular shape cannot be overstated. It is the shape of the simple water molecule that determines its physical and chemical properties, and in particular makes it suitable for sustaining life (we will say more about the consequences of the shape of the water molecule in Chapter 6). Shape has far reaching consequences in chemistry, biology, and the technology of materials. It is probably not an exaggeration to say that virtually all important biological processes are grounded in molecular shape, and, in particular, the ability of molecules to recognize one another based on shape. A familiar and extremely important example is found in the the double helical structure of the DNA molecule, responsible for the transcription of genetic information in all living organisms. The double helix is maintained because molecules recognize one another's shapes. Figure 3-21 shows the molecular interactions responsible for maintaining the DNA double helix.
In 3-21a, the guanine and cytosine molecules engage in three attractive interactions that hold them in specific positions relative to one another. In biochemical jargon, this is called a base-pairing interaction; it occurs in the gap between the two DNA strands. In 3-21b, adenine and thymine are shown in their base-pairing engagement, this time involving two shape-specific interactions. Clearly, molecular shape plays a crucial role in enabling these life-sustaining interactions. Chemists are actively conducting research in the area of molecular recognition; that is, the manner in which molecules recognize each other based on shape. This area of research promises the development of new and useful polymers and plastics; and mechanical and electrical devices that can be used in the engineering of extremely small (nanoscale) machines and computers. It will also help to clarify the details of many biochemical processes that are currently only vaguely understood. Among these are the interaction(s) between enzymes and their substrates that lead to catalysis of substrate conversion to products; the role of retinal in vision; the mechanism of smell; and the mechanism of nerve transmission.
In Chapter 6, we will have more to say about the nature of interactions between molecules. For now, it is important only to realize that such interactions are shape-driven.
Because water is produced as a result of the linkage, the process is called a condensation reaction. The group of atoms shown in Figure 3-22c, consisting of the carbon and oxygen of the left amino acid and the nitrogen, hydrogen, and central carbon of the right amino acid, is collectively referred to as the peptide link. It is found experimentally that all of these atoms lie in the same plane--i.e., the peptide link is planar. It is our goal to provide a rationale for this observation in terms of the concepts of Lewis structure and VSEPR.
An acceptable Lewis structure for the peptide link is shown in Figure 3-22d. This is the structure arrived at by applying the systematic procedure, and minimizing formal charges. The structure places three electron groups around the peptide carbon atom. All of these groups are used to bond atoms, so the stereochemistry at this carbon atom is trigonal planar. The structure places 4 electron groups around the nitrogen atom, one of them a lone pair. This leads us to expect tetrahedral electron group distribution, and trigonal pyramidal stereochemistry at the nitrogen atom. However, this stereochemistry at the nitrogen atom would prevent some of the atoms in the peptide grouping from lying in the same plane with carbons 1 and 2 and the nitrogen atom. In particular, C3 and the proton attached to N could not simultaneously lie in the C1-C2-N plane in any arrangement of the molecule. How then do we explain planarity?
With some thought, we realize that there is another acceptable resonance form involving the N, C2, and O atoms of the peptide link. This is obtained by simultaneously moving the N lone pair in to form a double bond with C2, while moving the double bond pair between C2 and O out onto the oxygen atom as a lone pair. This form, shown in Figure 3-22e, is less acceptable than that in d because it places formal charges of 1+ and 1- on N and O, respectively. However, these are not unusual formal charges for these atoms, and they are not in conflict with electronegativities. The most important aspect of the structure in 3-22e is that there are now 3 electron groups around the nitrogen atom! Judging from this resonance form, trigonal planar stereochemistry is expected at N, and the planarity of the atoms C2, N, H, and C3 is required. Further, the double bond between N and C2 also requires C1 and O to be in this same plane. The planarity of the peptide link is understandable. The key question is this: when two resonance forms place different numbers of electron groups around an atom, what is the stereochemistry at that atom? Based on our earlier discussion of resonance, we know that the molecule is not rapidly switching back and forth between the two forms. Rather, there is a single molecular structure that may be considered as an average of the resonance forms. And, in point of fact, the actual stereochemistry at N is trigonal planar. We will find the following rule to be useful in all situations like this:
When the reasonable resonance forms for a molecule place different numbers of groups around a particular atom, the stereochemistry at that atom is consistent with the smallest number of electron groups in any resonance form.
Our final example teaches us an extremely important lesson. The principles of structure and stereochemistry that we developed from and applied to small molecules apply equally as well for large molecules. Thus the carbon, nitrogen, oxygen, and sulfur atoms in proteins follow the same bonding and stereochemical rules that apply in small molecules. In fact, the behavior and function of biomolecules is a consequence of the adherence to these rules. We will have more to say about biomolecules in a later chapter.
