This chapter extends the ideas introduced in Chapter 7 and discusses the fundamental forces which hold atoms and ions together in chemical compounds - the chemical bond.

The two major types of bonds are ionic and covalent. The bonding between atoms in metals is different from these two general types and is called a metallic bond. This topic is discussed in chapter 10.

Ionic bonds
Ionic bonds are simply the attractive forces between oppositely-charged ions. Ionic compounds contain cations (which can be either monatomic or polyatomic) and anions (which can be either monatomic or polyatomic.) Remember that ions are formed by the loss or gain of electrons. For monatomic cations, the electrons which are lost first in the formation of the ion are always the outermost (valence) electrons. For example, you already know that the 4s subshell is at lower energy than the 3d subshell in a neutral atom. This is why the 4s subshell fills before the 3d. For ions, however, the order of orbital energies approaches that for a hydrogen ion, where all subshells in a given main shell have the same energy. For this reason, the 4s electrons are lost before the 3d electrons when a cation is formed from a transition metal. For example, the configuration of a neutral cobalt atom is [Ar]4s²3d⁷, but the configuration of a cobalt(III) ion is [Ar]3d⁶.

A simple view of the formation of an ionic compound is that the electrons lost by the cation are gained by the anion; in other words, a formal transfer of electrons can be envisioned. This is why the total positive charge from the cations must be balanced by the total negative charge from the anions - no free electrons are floating around. This gives rise to the formula Al₂O₃ for aluminum oxide rather than AlO₃, AlO, Al₃O₂, or other incorrect formulas.

Electronegativity
Electronegativity is a measure of the tendency of an atom to attract the bonding electrons in a chemical bond toward itself. It is not a precisely-defined quantity like ionization potential or electron affinity, which can be measured accurately. In fact, there are more than a dozen scales of electronegativity. Luckily, for introductory courses only one scale is really needed to put the concept to use: this is the Pauling scale, named after the two-time Nobel prize winning chemist Linus Pauling. According to this scale, fluorine is the most electronegative element, with a Pauling electronegativity of 4.0. The least electronegative element is cesium, with a Pauling electronegativity of 0.7. Thus, there is a range of about 3.3 Pauling units between the electronegativities of the most and least electronegative elements. Be sure you understand the two periodic trends in electronegativity and the rule for getting the electronegativity of any second-period element just by memorizing the value of 4.0 for fluorine:

1. Electronegativity increases from left to right in a given period.
2. Electronegativity decreases from top to bottom in a given group.
3. To get the electronegativity of a second-period element, start at fluorine (4.0) and subtract 0.5 Pauling unit for each step to the left in the second period. Thus, oxygen has an electronegativity of 3.5, nitrogen has an electronegativity of 3.0, etc.

Although the electronegativity values themselves differ from one electronegativity scale to another, the first two trends listed above work for all scales.

Covalent bonds
Covalent bonds are bonds formed by the sharing of electrons, in contrast to the transfer which can be envisioned for an ionic bond. Covalent bonds are formed when the electronegativity difference between the two elements involved in the bond is small, indicating that the two atoms have similar attractions for the electrons.

On the other hand, large differences in electronegativities give rise to ionic bonds. Half of the range (3.3) of Pauling electronegativity values is about 1.7. This value can be used as a ballpark dividing line between ionic and covalent bonds: if the difference in electronegativities between the two atoms is greater than 1.7, then the bond is predominately ionic; if the difference is less than 1.7, then it is predominately covalent; if it is 1.7, then the bond has approximately 50% ionic and 50% covalent character.

It is unusual, however, that you'll need to make such quantitative determinations, especially since they are only approximate. For example, the electronegativity difference between Li and I is 2.5-1.0, or 1.5. This would imply more covalent than ionic character, but most chemists would classify lithium iodide as an ionic compound because it is composed of a metal and a nonmetal. Now you can see the origin of the rule you learned in chapter 2: that ionic compounds are formed between metals and nonmetals, whereas covalent compounds are formed between nonmetals. The simple reason is that metals are on the left side of the periodic table and nonmetals are on the right side, giving a fairly large difference in electronegativities. Nonmetals, on the other hand, are in the same general region of the periodic table and thus there are small electronegativity differences between two nonmetals.

The only purely covalent compounds are those where the electronegativity difference is zero - and this occurs for homonuclear diatomic molecules like N₂, O₂, H₂, etc.

One final clarification is necessary: the bonding within a polyatomic ion is covalent, since the atoms in the ion are nonmetals (NH₄⁺, SO₄^2-, etc.). But compounds of these ions are ionic, since by definition an ionic bond is the electrostatic attraction between oppositely-charged ions in the crystal. Thus, sodium nitrate, NaNO₃, is an ionic compound, but the bonding within the nitrate ion is covalent.

Polar Molecules
You already know that covalent bonds represent shared electrons. This does not necessarily mean, however, that the electrons are shared equally. An unequal sharing of electrons results in a polar covalent bond (sometimes simply called a polar bond.) Such a bond results in a partial negative charge at one end of the bond and a partial positive charge at the other end. If a molecule consists of only one bond and the bond is polar, then the molecule must be polar. Examples of this situation are HF, HCl, ClF, etc. The partial negative charge resides on the end of the bond with the more electronegative atom, while the partial positive charge resides on the end with the less electronegative atom. The partial negative charge in the three molecules above is at the end with F, Cl, and F, respectively.

If a molecule has more than one bond, then the molecule as a whole is nonpolar only if the individual polarities of the bonds cancel each other. To decide if this happens, the geometry of the molecule must be known. For example, the carbon dioxide molecule is linear, with each C-O bond along the same line: O=C=O. Although each carbon-oxygen bond is polar, the molecule as a whole is nonpolar because the two equal polarities are in exactly opposite directions. Water, on the other hand, is a bent molecule. The two H-O polar bonds do not cancel each other, and as a result the molecule is polar. See Table 8.2 for a table listing three molecules which have polar bonds but which have no molecular dipole moment because the individual bond polarities cancel one another. The topic of molecular geometry is discussed in section 8.13 (and at the end of this document), which describes the VSEPR model.

Covalent Bond Energies
Bonds are stable because the ions in an ionic bond are at lower energy when they are close to one another in the crystal, and because the shared electrons in a covalent bond are attracted by the two nuclei of the bonded atoms. Thus, it takes energy to break ionic and covalent bonds. Covalent bond energies are average energies, each of which depends on the chemical environment of the bonded atom. For example, the successive bond dissociation energies for methane are shown on page 366 of the text. Although the four values (one for each C-H bond) are slightly different, their average value of 413 kJ/mol can be assumed to represent the energy of a covalent carbon-hydrogen bond.

A number of bond energies are shown in Table 8.4. Notice that the table is separated into single bond and multiple bond categories. Table 8.5 lists bond lengths for selected bonds. Notice that for a given pair of atoms, bond length decreases in the order

Since the formation of covalent bonds releases energy and the breaking of bonds requires energy, we can calculate the approximate the enthalpy change for a chemical reaction by using tabulated bond energies. The procedure is simple: first, break apart all the bonds in the reactants and determine how much energy is required (this is endothermic, and thus a positive value.) Then determine how much energy is released when the bonds in the products form (this is exothermic, and thus a negative value.) Add the two quantities to get the enthalpy change for the reaction.

Important note: It is essential that the type of bonds in the reactants and products are known. For example, simply looking at the formula N₂ might give one the impression that a single-bond N-N energy of 160 kJ per mole should be used. However, this will result in an incorrect answer, since there is a triple bond in the nitrogen molecule with a covalent bond energy of 941 kJ/mole.

The types of bonds in a molecule can be determined by drawing the Lewis electron-dot structure for the molecule.

Resonance
Although Lewis structures are very useful for a large number of molecules, there are some problems with using electron-dot structures to describe bonding:

1. One of the goals in drawing a Lewis structure is to pair up electrons. This is impossible for a molecule with an odd number of electrons, like NO or ClO₂. Which atom "has" the odd electron in these molecules? Chapter 9 describes the molecular orbital model, which overcomes this difficulty.
2. Another goal for obtaining a valid Lewis structure is to obtain a duet of electrons around hydrogen or a completed octet around other atoms. The fact, however, is that there are exceptions to the octet rule: Be in BeF₂ and B in BF₃ have only four and six electrons in the Lewis structure, respectively, instead of eight. Atoms in the third period and below are able to "expand" their octet and can thus have more than eight electrons in the Lewis structure. Some examples are SF₄ (10 e^- around sulfur) and XeF₄ (12 e^- around xenon). There are many more examples.
3. Sometimes a single Lewis structure for a molecule doesn't accurately explain the properties of the molecule. For example, the Lewis structure for sulfur dioxide, SO₂, has a single sulfur-oxygen bond, a double sulfur-oxygen bond, and a lone pair of electrons on the central sulfur atom. All electrons are paired, 18 valence electrons are used in the Lewis structure, and each atom has an octet. Thus, the Lewis structure is "correct", at least in a formal sense. The problem is that the electron-dot diagram implies that there should be two bond strengths in sulfur dioxide - an S-O single bond and a stronger S-O double bond. Furthermore, there should also be two different bond lengths - a longer S-O single bond and a shorter S-O double bond. Here's the problem: experimentally, it has been found that both sulfur-oxygen bonds have the same bond length and the same bond strength. The concept of resonance is used to overcome this sort of problem with Lewis structures.

The problem mentioned above is not a problem with the molecule - it is a problem with the limited ability of a simple notation like a Lewis structure to describe a complicated concept like the bonding in a molecule. It is rather like trying to describe a real, three-dimensional object by drawing it on a two-dimensional piece of paper; the problem isn't with the object - it is with our limited resources for making the drawing.

The best way to describe the bonding in molecules like SO₂ is to draw two or more Lewis structures and say that the actual molecule is a hybrid, or combination, of the separate structure; this is indicated by drawing double-headed arrows between the structures (see page 379.)

Each of the separate structures is called a resonance structure, and the actual molecule is described as a resonance hybrid of the resonance structures. It is important to remember two rules for drawing resonance structures:

1. The positions of all atoms in all resonance structures of a given molecule must be the same. In other words, atoms are not moved when a different resonance structure is drawn from an existing one; rather, electron pairs are moved.
2. Do not think that the actual structure results from an oscillation among the resonance structures. For example, each of the two resonance structures for sulfur dioxide has a single bond and a double bond: the difference is in the location of each. Don't think that at a particular instant there is a single bond between the sulfur and one of the oxygens and that in the next instant the bond becomes a double bond, with continual "flipping" back and forth. This is not the correct interpretation of resonance. Both bonds in SO₂ are identical, and the bonds are neither single nor double bonds. Each bond has properties intermediate between a single and double bond.

The resonance hybrid can be compared to a mule, which is a hybrid between a horse and a donkey. The mule has its own unique properties, and it exists in its own right -- it isn't a horse half the time and a donkey the other half of the time.

Formal Charge
Unlike oxidation number, which can be determined from a formula like Na₂SO₄, the formal charge of an atom in a covalent molecule or polyatomic ion can only be determined from the Lewis structure. Formal charge is calculated by splitting the bonding electrons equally between the bonded atoms, and assigning all nonbonding electrons to the atom which "owns" them, then comparing the resulting number of electrons with the number of valence electrons the atom would have if it were neutral. Formal charges are shown as a positive number or negative number (e.g. +2 or -1) inside a circle and placed next to the atomic symbol in the Lewis structure. Recall that oxidation numbers are written without the circle.

For example, the Lewis structure for carbon dioxide shows two carbon-oxygen double bonds and two nonbonding pairs of electrons on each of the oxygen atoms. (Draw the Lewis structure now, before continuing to read this paragraph.) The carbon atom has four bonding pairs of electrons (two double bonds, or eight electrons) around it. The central carbon atom is assigned four of these eight electrons and each oxygen is assigned two of them. The formal charge of carbon is therefore

Each oxygen atom "owns" two nonbonding pairs of electrons (four electrons) and was assigned two of the bonding electrons, giving a total of six electrons. The formal charge is therefore 6-6= a formal charge of zero.

Now draw one of the resonance structures for sulfur dioxide, with one S-O single bond, one S-O double bond, and a nonbonding pair on the central sulfur atom (remember to complete the octets around the oxygen atoms.) Assigning the electrons as described above leads to a formal charge of +1 for the sulfur, -1 for the singly-bonded oxygen and zero for the doubly-bonded oxygen.

Let's look at one more example. Draw the Lewis structure for the sulfate ion, (SO₄)^2-, which has four single sulfur-oxygen bonds. Verify the formal charges of +2 for the central sulfur atom and -1 for each of the oxygen atoms.

Notice that in the CO₂, SO₂, and (SO₄)^2- examples above, the algebraic sum of the formal charges is equal to the charge on the molecule or ion. This must always be the case.

Remember that formal charges cannot be determined from a simple formula; the Lewis structure is needed.

Formal Charges and Resonance
Formal charges can be used to decide if a particular resonance structure is a "good" one - in other words, if the resonance structure contributes significantly to the actual structure. Here are the rules:

1. "Like" formal charges (plus/plus or minus/minus) should not reside on adjacent atoms.
2. "Unlike" formal charges (plus/minus) should not be unnecessarily separated.
3. Formal charges closer to zero usually represent more important resonance structures than those which have large formal charges.

For example, draw one of the Lewis structures for nitrous oxide (laughing gas, N₂O - the skeletal structure is N-N-O). You should now be able to "push" electron pairs around to come up with a total of three resonance structures which obey the octet rule. Each of these resonance structures is described below.

Make sure you correctly determined these formal charges for all three of the resonance structures (Formal charges are listed in the following order: terminal nitrogen, central nitrogen, oxygen.)

1. N-N double bond, N-O double bond: formal charges are -1, +1, 0.
2. N-N triple bond, N-O single bond: formal charges are 0, +1, and -1.
3. N-N single bond, N-O triple bond: formal charges are -2, +1, and +1.

According to the rules mentioned above, resonance structures 1 and 2 are "good" structures and contribute significantly to the actual structure. Resonance structure 3 results in the placement of two positive formal charges on adjacent atoms, and thus does not contribute significantly to the actual structure.

The VSEPR Model
According to the Valence Shell Electron Pair Repulsion model, the geometry of a molecule or polyatomic ion is determined by repulsions between valence electron pairs in the molecule. The idea is simple: since electrons all have the same charge, electron pairs repel each other, resulting in a geometry in which these mutual repulsions are minimized.

The overall geometry is determined by the total number of "groups" around the central atom in the species. A "group" is any of the following: a single bond, double bond, triple bond, or nonbonding pair.

The molecular geometry is obtained by first determining the overall geometry, then ignoring any nonbonding pairs around the central atom and deciding what shape results.

A common abbreviation for representing a molecule or ion uses the symbol A for the central atom, X for an atom bonded to the central atom, and E for a nonbonding pair on the central atom. For example, methane (CH₄) can be represented by the general abbreviation AX₄, while ammonia (NH₃) and water can be generalized as AX₃E and AX₂E₂ types, respectively. [Draw the Lewis structures for these three molecules to make sure you reach the same conclusions.]

The following table lists some examples. Don't memorize the table - understand it!

Type	Overall Geometry	Molecular Geometry	Example(s)
AX2	linear	linear	BeF2, CO2
AX3	trigonal planar	trigonal planar	BCl3, H2CO
AX2E	trigonal planar	bent, angular, or V-shaped	SO2
AX4	tetrahedral	tetrahedral	CH4, (SO4)2-
AX3E	tetrahedral	trigonal pyramidal	NH3
AX2E2	tetrahedral	bent, angular, or V-shaped	H2O
AX5	trigonal bipyramidal	trigonal bipyramidal	PCl5
AX4E	trigonal bipyramidal	seesaw or distorted tetrahedral	SF4
AX3E2	trigonal bipyramidal	T-shaped	ClF3
AX2E3	trigonal bipyramidal	linear	XeF2
AX6	octahedral	octahedral	SF6
AX5E	octahedral	square pyramidal	IF5
AX4E2	octahedral	square planar	(BrF4)-, XeF4

Remember the following rules about using VSEPR to describe molecular geometries:

1. Electron pair repulsions decrease in the order
   1. (nonbonding-nonbonding) > (nonbonding-bonding) > (bonding-bonding) and
   2. triple bond > double bond > single bond
2. Nonbonding pairs occupy equatorial (radial) positions in a trigonal bipyramid.
3. Two nonbonding pairs in an overall octahedral structure occupy trans positions (across from one another)
4. Bond angles decrease with increasing electronegativity of the non-central atoms, provided that there is at least one nonbonding pair in the species. For example, the F-N-F bond angle in NF₃ is smaller than the H-N-H bond angle in ammonia. A simple way to understand this is to picture the bonding electrons in NF₃ as being closer to the more electronegative fluorine than the nitrogen, thereby allowing the nonbonding pair to "squeeze" the bonding pairs closer together, resulting in a smaller bond angle. In ammonia, the bonding electrons are closer to the more electronegative nitrogen than the hydrogen, and are therefore already close to one another. This doesn't allow the nonbonding pair to push the hydrogens as close together as it could for the fluorine atoms in NF₃.

   However, the F-B-F angles in BF₃ and the Cl-B-Cl angles in BCl₃ are all 120°, since there are no nonbonding pairs. In other words, the atoms can get farthest apart with a trigonal planar geometry, irregardless of the identity of the non-central atom.
   

Last modified June 16, 1997