As you work through this section, if you find that you need a bit more background material to help you understand the topics at hand, you can consult “Chemistry: The Molecular Science” (5th ed. Moore and Stanitski) Chapter 6-6 through 6-8 and Chapter 6-10, and/or Chapter 5.1-5.6 in the Additional Reading Materials section.

D10.1 Covalent Bonds: Bond Length and Bond Enthalpy

In D6.1, you learned that as two atoms approach each other, electrons are shared between the nuclei and energy decreases. Bond length is the distance between two atomic nuclei at the minimum in a graph of energy versus nuclear separation. For example, the bond length in a H₂ molecule is 74 pm, as shown in Figure 1.

Bond enthalpy (also called bond energy) is the enthalpy change when the a chemical bond is broken; that is, when two bonded atoms are separated to a very large distance. For example, Figure 1 shows that the bonded hydrogen atoms have energy of −436 kJ/mol relative to the separated atoms. This means that the energy of the molecule must be increased by 436 kJ/mol to separate the atoms (break the bond) so the bond enthalpy for H₂ is 436 kJ/mol.

Bond lengths can be estimated by using the covalent radii (D5.1) of the bonded atoms.  For example, if we add the covalent radius of C (77 pm) to that of O (74 pm), we obtain an estimate for the length of the C―O bond, 151 pm. (This is an estimate because covalent radii are averaged over many molecules and therefore are not exact for a specific molecule.) In general, the bigger the atoms are, the longer the bond between them will be.

Bond length also depends on bond order. For example, the N—O single bond length is 136 pm, but a N=O double bond is 115 pm long and a triple bond between N and O is 108 pm long.

You can find tables of average bond length and bond enthalpy in the appendix. Comparison of these two tables show a general trend where shorter bond lengths correspond to larger bond enthalpies.

D10.2 Reaction Enthalpy Change

The enthalpy change for a chemical reaction, Δ_rH, is approximately equal to the sum of the enthalpies required to break each of the bonds in the reactant molecules (energy in, positive sign) plus the sum of the enthalpies released when each of the bonds in the product molecules forms (energy out, negative sign). This can be expressed mathematically:

Δ_rH = ∑E_{bonds broken} – ∑E_{bonds formed}

Because the bond enthalpy values provided in the Appendix are averages over many different molecules for a type of bond, this calculation provides a rough estimate, not an exact value, for the enthalpy of reaction. It is also important that bond enthalpy calculations assume that all molecules are far from each other (which means that reactants and products must be in the gas phase). There would be additional enthalpy changes if the molecules came together and condensed to a liquid or formed a solid.

Consider this reaction, in which one H₂ molecule and one Cl₂ molecule react to form two HCl molecules:

H₂(g) + Cl₂(g) → 2HCl(g)

To form two H-Cl bonds (431 kJ/mol each), one H–H bond (436 kJ/mol) and one Cl–Cl bond (242 kJ/mol) are broken:

Δ_rH = [E_H-H + E_Cl-Cl] – 2E_H-Cl = [436 kJ/mol + 242 kJ/mol] – 2(431 kJ/mol) = -184 kJ/mol

Because the bonds in the products are stronger than those in the reactants, the reaction has a net release of 184 kJ energy for every mole of reaction. The energy release increases the temperature of the surroundings (the reaction is exothermic). The experimental value for the quantity of energy released is 184.614 kJ/mol, slightly different from the value estimated using bond energies.

Based on bond enthalpy arguments, we can state general rules to predict qualitatively whether a chemical reaction releases energy (is exothermic):

• If there are more bonds in the product molecules than in the reactant molecules and the bonds have about the same strength, the reaction will be exothermic.
• If there are stronger bonds in the product molecules than in the reactant molecules and the number of bonds is the same in reactants and products, the reaction will be exothermic.

D10.3 Covalent Bonds: Bond Polarity

If the atoms that form a covalent bond are identical, as in H₂ or Cl₂, then the electrons in the bond must be shared equally. We refer to this as a pure covalent bond. Electrons shared in pure covalent bonds have an equal probability of being near each nucleus.

When different atoms are linked by a covalent bond, the bonding electrons can be more attracted by one atom than the other. This unequal distribution of bond electrons is known as a polar covalent bond. For example, in HCl, the Cl atom attracts the bond pair of electrons slightly more than does the H atom, and electron density of the H–Cl bond is shifted toward the chlorine atom. The chlorine atom, which has 17 protons, has electron density equivalent to 17.28 electrons and a partial negative charge, δ^– = −0.28. The hydrogen atom has a partial positive charge, δ⁺ = +0.28.

This unequal distribution of charge on two bonded atoms produces a bond dipole moment, the magnitude of which is represented by µ (Greek letter mu). The dipole moment is equal to:

μ = Qr

where Q is the magnitude of the partial charges (for HCl this is 0.28 times the charge of an electron) and r is the distance between the charges (the bond length).

The bond dipole moment has both direction and magnitude and can be represented as a vector. A dipole vector is shown as an arrow with a small + sign on the partially positive end and a point at the partially negative end. The length of the arrow is proportional to the dipole moment, µ.

D10.4 Electronegativity

The polarity of a covalent bond is determined by the difference in electronegativity of the bonded atoms. Electronegativity (EN) is the tendency of an atom to attract bond electron density. Thus, the more electronegative atom in a bond is the one with the δ– charge. The greater the difference in electronegativity between two bonded atoms the more the electron density in the bond shifts toward the more electronegative atom and the larger the partial charges on the atoms are.

In general, electronegativity increases from left to right across a period in the periodic table and decreases down a group. Thus, elements in the upper right corner of the periodic table tend to have the highest electronegativities, with fluorine being the most electronegative element of all (EN = 4.0). (Note that we do not typically consider the EN values of noble gases because these atoms usually do not form molecules.) Also, it is hard to predict the electronegativity of hydrogen using the periodic table; based on its electronegativity of 2.1, H should be above and between B (1.9) and C(2.4), which is far from its typical location at the upper left corner.

Electronegativity values of most elements are tabulated in the appendix.

Electronegativity Differs from Electron Affinity

Electron affinity is an experimentally measurable physical quantity—the energy  absorbed when an isolated gas-phase atom acquires an electron—usually expressed in kJ/mol. Electronegativity describes how strongly an atom attracts electrons in a bond. It is calculated, not measured, has an arbitrary relative scale, and has no units.

Electronegativity and Bond Type

The difference in electronegativity (ΔEN) of two bonded atoms provides a rough estimate of the bond polarity to be expected and, thus, the bond type. When ΔEN is very small (or zero), the bond is covalent and nonpolar. When it is large, the bond is polar covalent or ionic.

ΔEN spans a continuous scale and serves as a general guide; there is no definitive cutoff that defines a bond type. For example, HF has a ΔEN of 1.9 and is considered a polar covalent molecule, while NaCl has a ΔEN of 1.8 and forms an ionic compound. When considering the covalent or ionic character of a bond, you should also take into account the types of atoms involved and their relative positions in the periodic table. Bonds between two nonmetals are usually described as covalent; bonding between a metal and a nonmetal is often ionic.

Some compounds contain both covalent and ionic bonds. For example, potassium nitrate, KNO₃, contains the K⁺ cation and the polyatomic NO₃⁻ anion.

D10.5 Formal Charge

The formal charge of an atom in a molecule is the charge the atom would have if the electrons in the bonds are evenly distributed between the atoms. It is calculated by considering the number of valence electrons of an atom, and subtracting from it the number of nonbonding electrons and half the number of bonding electrons associated with that atom in the Lewis structure of the molecule:

formal charge = # valence electrons in an unbonded atom – # lone-pair electrons – 0.5(# bonding electrons)

The sum of the formal charges of all atoms in an uncharged molecule must be zero; the sum of the formal charges in an ion should equal the charge of the ion.

The formal charge calculated for an atom is not the actual charge of the atom in the molecule. Formal charge is only a useful bookkeeping tool; it does not correspond to the actual partial charges such as those calculated in Figure 2.

Using Formal Charge to Predict Lewis Structure

In many cases, following the steps for writing Lewis structures may lead to more than one possible electron and/or atomic arrangement. Formal charge can be helpful in deciding which of the possible structures is most likely for a particular molecule:

• For an uncharged molecule a Lewis structure in which all formal charges are zero is preferable.
• The smaller the number of atoms with nonzero formal charges, the better.
• The smaller the magnitude of the formal charges, the better.
• A structure with formal charges of the same sign (both + or both −) on adjacent atoms is less stable.
• Structures with the negative formal charges on the more electronegative atoms are preferable.

For example, consider the following three possible Lewist structure of carbon dioxide, CO₂:

Comparing the three formal charges, we can identify the structure on the left as preferable because it has only formal charges of zero. the structure on the right is least likely because of the larger formal charges.

D10.6 Exceptions to the Octet Rule

Some covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories.

Odd-electron Molecules

A molecule that contains an odd number of electrons must have at least one electron unpaired. A molecule with at least one unpaired electron is called a  free radical. Nitric oxide, NO, is an example; it is produced in internal combustion engines when oxygen and nitrogen react at high temperatures.

To draw the Lewis structure for an odd-electron molecule, follow the same six steps as for other molecules (section 7.3), but recognize that an odd-electron molecule will have less than an octet on some atom. For example, the Lewis structure for NO is:

Forming a triple bond would cause either oxygen or nitrogen to exceed an octet. Placing the unpaired electron on N makes sense because the formal charges are zero on both atoms in this structure. (Too verify that the structure above is better, calculate the formal charges on N and O if N had two lone pairs and O had a lone pair and an unpaired electron.)

Electron-deficient Molecules

A few molecules contain a central atom that does not have a filled valence shell. Usually, these central atoms are from groups 2 (IIA) and 13 (IIIA). For example, the Lewis structure of beryllium dihydride, BeH₂, shows beryllium with only four electrons, and that of boron trifluoride, BF₃, shows boron with only six electrons.

It is possible to draw a structure for BF₃ with one B=F double bond, satisfying the octet rule, but experimental evidence tells us that the bond lengths are closer to that expected for B–F single bonds. (Such a structure would have a negative formal charge on B and a positive formal charge on the more electronegative F, which is not preferable.) The reactivity of BF₃ is also consistent with an electron deficient boron. BF₃ readily reacts with any molecule containing an atom with a lone pair of electrons. For example, NH₃ reacts with BF₃ with the lone pair on nitrogen (red) forming a bond (red) that completes the octet of the boron atom:

Hypervalent Molecules

Some Lewis structures show more than four pairs of electrons around the central atom. This usually happens when the central atom is in the third or a higher period (n ≥ 3). Molecules with more than an octet around the central atom are called hypervalent molecules. For example, in PCl₅, the central phosphorus atom is surrounded by five pairs of electrons. In SF₆, sulfur has six pairs of electrons.