59 Strengths of Ionic and Covalent Bonds

A bond’s strength describes how strongly each atom is joined to another atom, and therefore how much energy is required to break the bond between the two atoms.

It is essential to remember that energy must be added to break chemical bonds (an endothermic process), whereas forming chemical bonds releases energy (an exothermic process). In the case of [latex]\text{H}_2[/latex], the covalent bond is very strong; a large amount of energy, 436 kJ, must be added to break the bonds in one mole of hydrogen molecules and cause the atoms to separate:

[latex]\text{H}_2 (g) \ \longrightarrow \ \text{2H} (g) \ \ \ \ \ \ \ \ \text{bond energy = 436  kJ}[/latex]

Conversely, the same amount of energy is released when one mole of [latex]\text{H}_2[/latex] molecules forms from two moles of H atoms:

[latex]\text{2H} (g) \ \longrightarrow \ \text{H}_2(g) \ \ \ \ \ \ \ \ \text{bond energy = -436 kJ}[/latex]

Bond Strength: Covalent Bonds

Stable molecules exist because covalent bonds hold the atoms together. We measure the strength of a covalent bond by the energy required to break it, that is, the energy necessary to separate the bonded atoms. Separating any pair of bonded atoms requires energy. The stronger a bond, the greater the energy required to break it.

The energy required to break a specific covalent bond in one mole of gaseous molecules is called the bond energy or the bond dissociation energy. The bond energy for a diatomic molecule, [latex]\text{D}_\text{X-Y}[/latex], is defined as the standard enthalpy change for the endothermic reaction:

[latex]\text{XY} (g) \longrightarrow \text{X} (g) \text{ + Y} (g) \ \ \ \ \ \text{D}_\text{X-Y} = \Delta H^{\circ}[/latex]

For example, the bond energy of the pure covalent H–H bond, [latex]\text{D}_\text{H-H}[/latex], is 436 kJ per mole of H–H bonds broken:

[latex]\text{H}_2 (g) \longrightarrow \text{2H} (g) \ \ \ \ \ \text{D}_\text{H-H} = \Delta H^{\circ} = \text{436 kJ}[/latex]

Molecules with three or more atoms have two or more bonds. The sum of all bond energies in such a molecule is equal to the standard enthalpy change for the endothermic reaction that breaks all the bonds in the molecule. For example, the sum of the four C–H bond energies in [latex]\text{CH}_4[/latex], 1660 kJ, is equal to the standard enthalpy change of the reaction:

The average C–H bond energy, [latex]\text{D}_\text{C-H}[/latex], is 1660/4 = 415 kJ/mol because there are four moles of C–H bonds broken per mole of the reaction. Although the four C–H bonds are equivalent in the original molecule, they do not each require the same energy to break; once the first bond is broken (which requires 439 kJ/mol), the remaining bonds are easier to break. The 415 kJ/mol value is the average, not the exact value required to break any one bond.

The strength of a bond between two atoms increases as the number of electron pairs in the bond increases. Generally, as the bond strength increases, the bond length decreases. Thus, we find that triple bonds are stronger and shorter than double bonds between the same two atoms; likewise, double bonds are stronger and shorter than single bonds between the same two atoms. Average bond energies for some common bonds appear in the table below, and a comparison of bond lengths and bond strengths for some common bonds appears in the following table. When one atom bonds to various atoms in a group, the bond strength typically decreases as we move down the group. For example, [latex]\text{C–F}[/latex] is 439 kJ/mol, [latex]\text{C–Cl}[/latex] is 330 kJ/mol, and [latex]\text{C–Br}[/latex] is 275 kJ/mol.

The bond energy is the difference between the energy minimum (which occurs at the bond distance) and the energy of the two separated atoms. This is the quantity of energy released when the bond is formed. Conversely, the same amount of energy is required to break the bond. For the [latex]\text{H}_2[/latex] molecule shown in the table above, at the bond distance of 74 pm the system is 7.24 × 10⁻¹⁹ J lower in energy than the two separated hydrogen atoms. This may seem like a small number. However, as we will learn in more detail later, bond energies are often discussed on a per-mole basis. For example, it requires 7.24 × 10⁻¹⁹ J to break one H–H bond, but it takes 4.36 × 10⁵ J to break 1 mole of H–H bonds. A comparison of some bond lengths and energies is shown in the tables above. We can find many of these bonds in a variety of molecules, and this table provides average values. For example, breaking the first C–H bond in [latex]\text{CH}_4[/latex] requires 439.3 kJ/mol, while breaking the first C–H bond in [latex]\text{H–CH}_2\text{C}_6\text{H}_5[/latex] (a common paint thinner) requires 375.5 kJ/mol.

As seen in the tables above, an average carbon-carbon single bond is 347 kJ/mol, while in a carbon-carbon double bond, the [latex]\pi[/latex] bond increases the bond strength by 267 kJ/mol. Adding an additional [latex]\pi[/latex] bond causes a further increase of 225 kJ/mol. We can see a similar pattern when we compare other [latex]\sigma[/latex] and [latex]\pi[/latex] bonds. Thus, each individual [latex]\pi[/latex] bond is generally weaker than a corresponding [latex]\sigma[/latex] bond between the same two atoms. In a [latex]\pi[/latex] bond, there is a greater degree of orbital overlap than in a [latex]\pi[/latex] bond.

We can use bond energies to calculate approximate enthalpy changes for reactions where enthalpies of formation are not available. Calculations of this type will also tell us whether a reaction is exothermic or endothermic. An exothermic reaction (ΔH negative, heat produced) results when the bonds in the products are stronger than the bonds in the reactants. An endothermic reaction (ΔH positive, heat absorbed) results when the bonds in the products are weaker than those in the reactants.

The enthalpy change, ΔH, for a chemical reaction is approximately equal to the sum of the energy required to break all bonds in the reactants (energy “in”, positive sign) plus the energy released when all bonds are formed in the products (energy “out,” negative sign). This can be expressed mathematically in the following way:

[latex]\Delta H= \Sigma \text{D}_\text{bonds broken}- \Sigma \text{D}_\text{bonds formed}[/latex]

In this expression, the symbol [latex]\Sigma[/latex] means “the sum of” and D represents the bond energy in kilojoules per mole, which is always a positive number. The bond energy is obtained from a table and will depend on whether the particular bond is a single, double, or triple bond. Thus, in calculating enthalpies in this manner, it is important that we consider the bonding in all reactants and products. Because D values are typically averages for one type of bond in many different molecules, this calculation provides a rough estimate, not an exact value, for the enthalpy of reaction.

Consider the following reaction:

[latex]\text{H}_2 (g) + \text{Cl}_2 (g) \longrightarrow \text{2HCl} (g)[/latex]

or

[latex]\text{H-H} (g) + \text{Cl-Cl} (g) \longrightarrow \text{2H-Cl} (g)[/latex]

To form two moles of [latex]\text{HCl}[/latex], one mole of H–H bonds and one mole of Cl–Cl bonds must be broken. The energy required to break these bonds is the sum of the bond energy of the H–H bond (436 kJ/mol) and the Cl–Cl bond (243 kJ/mol). During the reaction, two moles of H–Cl bonds are formed (bond energy = 432 kJ/mol), releasing 2 × 432 kJ; or 864 kJ. Because the bonds in the products are stronger than those in the reactants, the reaction releases more energy than it consumes:

This excess energy is released as heat, so the reaction is exothermic. Appendix G gives a value for the standard molar enthalpy of formation of [latex]\text{HCl} (g)[/latex], [latex]\Delta H_\text{f}^{\circ}[/latex], of –92.307 kJ/mol. Twice that value is –184.6 kJ, which agrees well with the answer obtained earlier for the formation of two moles of HCl.

Ionic Bond Strength and Lattice Energy

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid MX, the lattice energy is the enthalpy change of the process:

[latex]\text{MX} (s) \longrightarrow \text{M}^{n+} (g) + \text{X}^{n-} (g) \ \ \ \ \Delta H_\text{lattice}[/latex]

Note that we are using the convention where the ionic solid is separated into ions, so our lattice energies will be endothermic (positive values). Some texts use the equivalent but opposite convention, defining lattice energy as the energy released when separate ions combine to form a lattice and giving negative (exothermic) values. Thus, if you are looking up lattice energies in another reference, be certain to check which definition is being used. In both cases, a larger magnitude for lattice energy indicates a more stable ionic compound. For sodium chloride, [latex]\Delta H_\text{lattice} = \text{769 kJ}[/latex]. Thus, it requires 769 kJ to separate one mole of solid [latex]\text{NaCl}[/latex] into gaseous [latex]\text{Na}^+[/latex]  and [latex]\text{Cl}^-[/latex] ions. When one mole each of gaseous [latex]\text{Na}^+[/latex] and [latex]\text{Cl}^-[/latex] ions form solid [latex]\text{NaCl}[/latex], 769 kJ of heat is released.
The lattice energy [latex]\Delta H_\text{lattice}[/latex] of an ionic crystal can be expressed by the following equation (derived from Coulomb’s law, governing the forces between electric charges):

[latex]\Delta H_\text{lattice} = \frac{ \text{C(Z}^+\text{)(Z}^-) }{ \text{R}_\circ }[/latex]

in which C is a constant that depends on the type of crystal structure; Z⁺ and Z^– are the charges on the ions; and R_o is the interionic distance (the sum of the radii of the positive and negative ions). Thus, the lattice energy of an ionic crystal increases rapidly as the charges of the ions increase and the sizes of the ions decrease. When all other parameters are kept constant, doubling the charge of both the cation and anion quadruples the lattice energy. For example, the lattice energy of [latex]\text{LiF}[/latex] (Z⁺ and Z^– = 1) is 1023 kJ/mol, whereas that of [latex]\text{MgO}[/latex] (Z⁺ and Z^– = 2) is 3900 kJ/mol (R_o is nearly the same—about 200 pm for both compounds).
Different interatomic distances produce different lattice energies. For example, we can compare the lattice energy of [latex]\text{MgF}_2[/latex] (2957 kJ/mol) to that of [latex]\text{MgI}_2[/latex] (2327 kJ/mol) to observe the effect on lattice energy of the smaller ionic size of F^– as compared to I^–.