Strengths of Ionic and Covalent Bonds

Learning Objectives

By the end of this section, you will be able to:

  • Describe the energetics of covalent and ionic bond formation and breakage
  • Use average covalent bond energies to estimate enthalpies of reaction

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. In this section, you will learn about the bond strength of covalent bonds, and then compare that to the strength of ionic bonds, which is related to the lattice energy of a compound.

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 (see Figure 1). The stronger a bond, the greater the energy required to break it.

A graph is shown with the x-axis labeled, “Internuclear distance ( p m )” while the y-axis is labeled, “Energy ( J ).” One value, “0,” is labeled midway up the y-axis and two values: “0” at the far left and “0.74” to the left, are labeled on the x-axis. The point “0.74” is labeled, “H bond H distance.” A line is graphed that begins near the top of the y-axis and to the far left on the x-axis and drops steeply to a point labeled, “negative 7.24 times 10 superscript negative 19 J” on the y-axis and 0.74 on the x-axis. This low point on the graph corresponds to a drawing of two spheres that overlap considerably. The line then rises to zero on the y-axis and levels out. The point where it almost reaches zero corresponds to two spheres that overlap slightly. The line at zero on the y-axis corresponds to two spheres that are far from one another.

Figure 1. The potential energy of two separate hydrogen atoms (right) decreases as they approach each other, and the single electrons on each atom are shared to form a covalent bond. The bond length is the internuclear distance at which the lowest potential energy is achieved.

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, DX–Y, is defined as the standard enthalpy change for the endothermic reaction:

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

For example, the bond energy of the pure covalent H–H bond, DH–H, is 436 kJ per mole of H–H bonds broken:

[latex]{\text{H}}_{2}\left(g\right)\rightarrow 2\text{H}\left(g\right){\text{D}}_{\text{H-H}}=\Delta {H}^{\circ}=436\text{ 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 CH4, 1660 kJ, is equal to the standard enthalpy change of the reaction:

A reaction is shown with Lewis structures. The first structure shows a carbon atom single bonded to four hydrogen atoms with the symbol, “( g )” written next to it. A right-facing arrow points to the letter “C” and the symbol “( g ),” which is followed by a plus sign. Next is the number 4, the letter “H” and the symbol, “( g ).” To the right of this equation is another equation: capital delta H superscript degree symbol equals 1660 k J.

The average C–H bond energy, DC–H, 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 Table 1, and a comparison of bond lengths and bond strengths for some common bonds appears in Table 2. When one atom bonds to various atoms in a group, the bond strength typically decreases as we move down the group. For example, C–F is 439 kJ/mol, C–Cl is 330 kJ/mol, and C–Br is 275 kJ/mol.

Table 1. Bond Energies (kJ/mol)
Bond Bond Energy Bond Bond Energy Bond Bond Energy
H–H 436 C–S 260 F–Cl 255
H–C 415 C–Cl 330 F–Br 235
H–N 390 C–Br 275 Si–Si 230
H–O 464 C–I 240 Si–P 215
H–F 569 N–N 160 Si–S 225
H–Si 395 [latex]\text{N}=\text{N}[/latex] 418 Si–Cl 359
H–P 320 [latex]\text{N}\equiv \text{N}[/latex] 946 Si–Br 290
H–S 340 N–O 200 Si–I 215
H–Cl 432 N–F 270 P–P 215
H–Br 370 N–P 210 P–S 230
H–I 295 N–Cl 200 P–Cl 330
C–C 345 N–Br 245 P–Br 270
[latex]\text{C}=\text{C}[/latex] 611 O–O 140 P–I 215
[latex]\text{C}\equiv \text{C}[/latex] 837 [latex]\text{O}=\text{O}[/latex] 498 S–S 215
C–N 290 O–F 160 S–Cl 250
[latex]\text{C}=\text{N}[/latex] 615 O–Si 370 S–Br 215
[latex]\text{C}\equiv \text{N}[/latex] 891 O–P 350 Cl–Cl 243
C–O 350 O–Cl 205 Cl–Br 220
[latex]\text{C}=\text{O}[/latex] 741 O–I 200 Cl–I 210
[latex]\text{C}\equiv \text{O}[/latex] 1080 F–F 160 Br–Br 190
C–F 439 F–Si 540 Br–I 180
C–Si 360 F–P 489 I–I 150
C–P 265 F–S 285
Table 2. Average Bond Lengths and Bond Energies for Some Common Bonds
Bond Bond Length (Å) Bond Energy (kJ/mol)
C–C 1.54 345
[latex]\text{C}=\text{C}[/latex] 1.34 611
[latex]\text{C}\equiv \text{C}[/latex] 1.20 837
C–N 1.43 290
[latex]\text{C}=\text{N}[/latex] 1.38 615
[latex]\text{C}\equiv \text{N}[/latex] 1.16 891
C–O 1.43 350
[latex]\text{C}=\text{O}[/latex] 1.23 741
[latex]\text{C}\equiv \text{O}[/latex] 1.13 1080

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

In this expression, the symbol Ʃ 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 (like Table 2) 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}\left(g\right)+{\text{Cl}}_{2}\left(g\right)\rightarrow 2\text{HCl}\left(g\right)[/latex]
or
[latex]\text{H-H}\left(g\right)+\text{Cl-Cl}\left(g\right)\rightarrow 2\text{H-Cl}\left(g\right)[/latex]

To form two moles of HCl, 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:

[latex]\begin{array}{lll}\hfill \Delta H& =& {\Sigma{D}}_{\text{bonds broken}}-{\Sigma{D}}_{\text{bonds formed}}\hfill \\ \hfill \Delta H& =& \left[{\text{D}}_{\text{H-H}}+{\text{D}}_{\text{Cl-Cl}}\right]-2{\text{D}}_{\text{H-Cl}}\hfill \\ & =& \left[436+243\right]-2\left(432\right)=-185\text{ kJ}\hfill \end{array}[/latex]

This excess energy is released as heat, so the reaction is exothermic. Standard Thermodynamic Properties for Selected Substances gives a value for the standard molar enthalpy of formation of HCl(g), [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.

Example 1: Using Bond Energies to Calculate Approximate Enthalpy Changes

Methanol, CH3OH, may be an excellent alternative fuel. The high-temperature reaction of steam and carbon produces a mixture of the gases carbon monoxide, CO, and hydrogen, H2, from which methanol can be produced. Using the bond energies in Table 2, calculate the approximate enthalpy change, ΔH, for the reaction here:

[latex]\text{CO}\left(g\right)+2{\text{H}}_{2}\left(g\right)\rightarrow{\text{CH}}_{3}\text{OH}\left(g\right)[/latex]

Check Your Learning

Ethyl alcohol, CH3CH2OH, was one of the first organic chemicals deliberately synthesized by humans. It has many uses in industry, and it is the alcohol contained in alcoholic beverages. It can be obtained by the fermentation of sugar or synthesized by the hydration of ethylene in the following reaction:

A set of Lewis structures show a chemical reaction. The first structure shows two carbon atoms that are double bonded together and are each single bonded to two hydrogen atoms. This structure is followed by a plus sign, then an oxygen atom with two lone pairs of electrons single bonded to two hydrogen atoms. A right-facing arrow leads to a carbon atom single bonded to three hydrogen atoms and a second carbon atom. The second carbon atom is single bonded to two hydrogen atoms and an oxygen atom with two lone pairs of electrons. The oxygen atom is single bonded to a hydrogen atom as well.

Using the bond energies in Table 2, calculate an approximate enthalpy change, ΔH, for this reaction.

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}\left(s\right)\rightarrow{\text{M}}^{n\text{+}}\left(g\right)+{\text{X}}^{n-}\left(g\right)\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, ΔHlattice = 769 kJ. Thus, it requires 769 kJ to separate one mole of solid NaCl into gaseous Na+ and Cl ions. When one mole each of gaseous Na+ and Cl ions form solid NaCl, 769 kJ of heat is released.

The lattice energy ΔHlattice 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{k}\left({\text{Q}}^{\text{+}}\right)\left({\text{Q}}^{-}\right)}{{\text{d}}}[/latex]

in which k is a constant that depends on the type of crystal structure; Q+ and Q are the charges on the ions; and d 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 LiF (Z+ and Z = 1) is 1023 kJ/mol, whereas that of MgO (Q+ and Q = 2) is 3900 kJ/mol (d 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 MgF2 (2957 kJ/mol) to that of MgI2 (2327 kJ/mol) to observe the effect on lattice energy of the smaller ionic size of F as compared to I.

Example 2: Lattice Energy Comparisons

The precious gem ruby is aluminum oxide, Al2O3, containing traces of Cr3+. The compound Al2Se3 is used in the fabrication of some semiconductor devices. Which has the larger lattice energy, Al2O3 or Al2Se3?

Check Your Understanding

Zinc oxide, ZnO, is a very effective sunscreen. How would the lattice energy of ZnO compare to that of NaCl?

Key Concepts and Summary

The strength of a covalent bond is measured by its bond dissociation energy, that is, the amount of energy required to break that particular bond in a mole of molecules. Multiple bonds are stronger than single bonds between the same atoms. The enthalpy of a reaction can be estimated based on the energy input required to break bonds and the energy released when new bonds are formed. For ionic bonds, the lattice energy is the energy required to separate one mole of a compound into its gas phase ions. Lattice energy increases for ions with higher charges and shorter distances between ions.

Key Equations

  • Bond energy for a diatomic molecule: [latex]\text{XY}\left(g\right)\rightarrow\text{X}\left(g\right)+\text{Y}\left(g\right){\text{D}}_{\text{X-Y}}=\Delta H^{\circ}[/latex]
  • Enthalpy change: ΔH = ƩDbonds broken – ƩDbonds formed
  • Lattice energy for a solid MX: [latex]\text{MX}\left(s\right)\rightarrow{\text{M}}^{n\text{+}}\left(g\right)+{\text{X}}^{n-}\left(g\right)\Delta{H}_{\text{lattice}}[/latex]
  • Lattice energy for an ionic crystal: [latex]\Delta{H}_{\text{lattice}}=\frac{\text{k}\left({\text{Q}}^{\text{+}}\right)\left({\text{Q}}^{-}\right)}{{\text{d}}}[/latex]

Exercises

  1. Which bond in each of the following pairs of bonds is the strongest?
    1. C–C or [latex]\text{C}=\text{C}[/latex]
    2. C–N or [latex]\text{C}\equiv \text{N}[/latex]
    3. [latex]\text{C}\equiv \text{O}[/latex] or [latex]\text{C}=\text{O}[/latex]
    4. H–F or H–Cl
    5. C–H or O–H
    6. C–N or C–O
  2. Using the bond energies in Table 1, determine the approximate enthalpy change for each of the following reactions:
    1. [latex]{\text{H}}_{2}\left(g\right)+{\text{Br}}_{2}\left(g\right)\rightarrow 2\text{HBr}\left(g\right)[/latex]
    2. [latex]{\text{CH}}_{4}\left(g\right)+{\text{I}}_{2}\left(g\right)\rightarrow{\text{CH}}_{3}\text{I}\left(g\right)+\text{HI}\left(g\right)[/latex]
    3. [latex]{\text{C}}_{2}{\text{H}}_{4}\left(g\right)+3{\text{O}}_{2}\left(g\right)\rightarrow 2{\text{CO}}_{2}\left(g\right)+2{\text{H}}_{2}\text{O}\left(g\right)[/latex]
  3. Using the bond energies in Table 1, determine the approximate enthalpy change for each of the following reactions:
    1. [latex]{\text{Cl}}_{2}\left(g\right)+3{\text{F}}_{2}\left(g\right)\rightarrow 2{\text{ClF}}_{3}\left(g\right)[/latex]
    2. [latex]{\text{H}}_{2}\text{C}={\text{CH}}_{2}\left(g\right)+{\text{H}}_{2}\left(g\right)\rightarrow{\text{H}}_{3}{\text{CCH}}_{3}\left(g\right)[/latex]
    3. [latex]2{\text{C}}_{2}{\text{H}}_{6}\left(g\right)+7{\text{O}}_{2}\left(g\right)\rightarrow 4{\text{CO}}_{2}\left(g\right)+6{\text{H}}_{2}\text{O}\left(g\right)[/latex]
  4. When a molecule can form two different structures, the structure with the stronger bonds is usually the more stable form. Use bond energies to predict the correct structure of the hydroxylamine molecule: Two Lewis structures are shows with the word “or” written in between them. The left structure shows a nitrogen atom with one lone pair of electrons single bonded to two hydrogen atoms. It is also bonded to an oxygen atom with two lone pairs of electrons. The oxygen atom is bonded to a hydrogen atom. The right structure shows a nitrogen atom single bonded to three hydrogen atoms and an oxygen atom with three lone pairs of electrons.
  5. How does the bond energy of HCl(g) differ from the standard enthalpy of formation of HCl(g)?
  6. Using the standard enthalpy of formation data in Standard Thermodynamic Properties for Selected Substances, show how can the standard enthalpy of formation of HCl(g) can be used to determine the bond energy.
  7. Using the standard enthalpy of formation data in Standard Thermodynamic Properties for Selected Substances, calculate the bond energy of the carbon-sulfur double bond in CS2.
  8. Using the standard enthalpy of formation data in Standard Thermodynamic Properties for Selected Substances, determine which bond is stronger: the S–F bond in SF4(g) or in SF6(g)?
  9. Using the standard enthalpy of formation data in Standard Thermodynamic Properties for Selected Substances, determine which bond is stronger: the P–Cl bond in PCl3(g) or in PCl5(g)?
  10. Complete the following Lewis structure by adding bonds (not atoms), and then indicate the longest bond:A Lewis structure is shown that is missing its bonds. It shows a horizontal row of six carbon atoms, equally spaced. Three hydrogen atoms are drawn around the first carbon, two around the second, one above the fifth, and two by the sixth.
  11. Use the bond energy to calculate an approximate value of ΔH for the following reaction. Which is the more stable form of FNO2?
    Two Lewis structures are shown with a right-facing arrow in between. The left structure shows a nitrogen atom double bonded to an oxygen atom with two lone pairs of electrons. It is also bonded to a fluorine atom and another oxygen atom, each with three lone pairs of electrons. The right structure shows an oxygen atom with two lone pairs of electrons double bonded to a nitrogen atom with one lone pair of electrons. This nitrogen atom is single bonded to an oxygen with two lone pairs of electrons. The oxygen atom is single bonded to a fluorine atom with three lone pairs of electrons.
  12. Use principles of atomic structure to answer each of the following:
    1. The radius of the Ca atom is 197 pm; the radius of the Ca2+ ion is 99 pm. Account for the difference.
    2. The lattice energy of CaO(s) is –3460 kJ/mol; the lattice energy of K2O is –2240 kJ/mol. Account for the difference.
    3. Given these ionization values, explain the difference between Ca and K with regard to their first and second ionization energies.
      Element First Ionization Energy (kJ/mol) Second Ionization Energy (kJ/mol)
      K 419 3050
      Ca 590 1140
    4. The first ionization energy of Mg is 738 kJ/mol and that of Al is 578 kJ/mol. Account for this difference.
  13. The lattice energy of LiF is 1023 kJ/mol, and the Li–F distance is 200.8 pm. NaF crystallizes in the same structure as LiF but with a Na–F distance of 231 pm. Which of the following values most closely approximates the lattice energy of NaF: 510, 890, 1023, 1175, or 4090 kJ/mol? Explain your choice.
  14. For which of the following substances is the least energy required to convert one mole of the solid into separate ions?
    1. MgO
    2. SrO
    3. KF
    4. CsF
    5. MgF2
  15. The lattice energy of LiF is 1023 kJ/mol, and the Li–F distance is 201 pm. MgO crystallizes in the same structure as LiF but with a Mg–O distance of 205 pm. Which of the following values most closely approximates the lattice energy of MgO: 256 kJ/mol, 512 kJ/mol, 1023 kJ/mol, 2046 kJ/mol, or 4090 kJ/mol? Explain your choice.
  16. Which compound in each of the following pairs has the larger lattice energy? Note: Mg2+ and Li+ have similar radii; O2– and F have similar radii. Explain your choices.
    1. MgO or MgSe
    2. LiF or MgO
    3. Li2O or LiCl
    4. Li2Se or MgO
  17. Which compound in each of the following pairs has the larger lattice energy? Note: Ba2+ and K+ have similar radii; S2– and Cl have similar radii. Explain your choices.
    1. K2O or Na2O
    2. K2S or BaS
    3. KCl or BaS
    4. BaS or BaCl2
  18. Which of the following compounds requires the most energy to convert one mole of the solid into separate ions?
    1. MgO
    2. SrO
    3. KF
    4. CsF
    5. MgF2
  19. Which of the following compounds requires the most energy to convert one mole of the solid into separate ions?
    1. K2S
    2. K2O
    3. CaS
    4. Cs2S
    5. CaO

Glossary

bond energy: (also, bond dissociation energy) energy required to break a covalent bond in a gaseous substance

lattice energy (ΔHlattice): energy required to separate one mole of an ionic solid into its component gaseous ions