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 the Born-Haber cycle to compute lattice energies for ionic compounds
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, D_X–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, D_H–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, D_C–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]

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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.

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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 (ΔH_lattice) 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, ΔH_lattice = 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 ΔH_lattice 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}\left({\text{Z}}^{\text{+}}\right)\left({\text{Z}}^{-}\right)}{{\text{R}}_{\text{o}}}[/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 LiF (Z⁺ and Z^– = 1) is 1023 kJ/mol, whereas that of MgO (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 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?

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Check Your Understanding

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

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The Born-Haber Cycle

It is not possible to measure lattice energies directly. However, the lattice energy can be calculated using the equation given in the previous section or by using a thermochemical cycle. The Born-Haber cycle is an application of Hess’s law that breaks down the formation of an ionic solid into a series of individual steps:

[latex]\Delta{H}_{\text{f}}^{\circ},[/latex] the standard enthalpy of formation of the compound
IE, the ionization energy of the metal
EA, the electron affinity of the nonmetal
[latex]\Delta{H}_{s}^{\circ},[/latex] the enthalpy of sublimation of the metal
D, the bond dissociation energy of the nonmetal
ΔH_lattice, the lattice energy of the compound

Figure 2 diagrams the Born-Haber cycle for the formation of solid cesium fluoride.

A diagram is shown. An upward facing arrow is drawn to the far left of the chart and is labeled “H increasing.” A horizontal line is drawn at the bottom of the chart. A downward-facing, vertical arrow to the left side of this line is labeled, “Overall change.” Beside this arrow is another label, “capital delta H subscript f, equals negative 553.5 k J per mol, ( Enthalpy of formation ).” Three horizontal lines, one above the other, and all above the bottom line, are labeled, from bottom to top, as: “C s ( s ), plus sign, one half F subscript 2, ( g ),” “C s ( g ), plus sign, one half F subscript 2, ( g ),” and “C s, superscript positive sign, ( g ), plus sign, one half F subscript 2, ( g ).” Each of these lines is connected by an upward-facing vertical arrow. Each arrow is labeled, “capital delta H subscript 1, equals 76.5 k J per mol, ( Enthalpy of sublimation ),” “capital delta H subscript 2, equals 375.7 k J per mol, ( ionization energy ),” and “capital delta H subscript 3 equals 79.4 k J / mol ( one half dissociation energy ).” Another horizontal line is drawn in the center top portion of the diagram and is labeled “C s, superscript positive sign, ( g ), plus sign, F, ( g ).” There is one more horizontal line drawn to the right of the overall diagram and located halfway down the image. An arrow connects the top line to this line and is labeled, “capital delta H equals negative 328.2 k J / mol ( electron affinity ).” The line is labeled, “C s superscript positive sign ( g ) plus F superscript negative sign ( g ).” The arrow connecting this line to the bottom line is labeled, “negative capital delta H subscript lattice equals negative 756.9 k J / mol.” The arrow points to a label on the bottom line which reads, “C s F ( s ).”

We begin with the elements in their most common states, Cs(s) and F₂(g). The [latex]\Delta{H}_{s}^{\circ}[/latex] represents the conversion of solid cesium into a gas, and then the ionization energy converts the gaseous cesium atoms into cations. In the next step, we account for the energy required to break the F-F bond to produce fluorine atoms. Converting one mole of fluorine atoms into fluoride ions is an exothermic process, so this step gives off energy (the electron affinity) and is shown as decreasing along the y-axis. We now have one mole of Cs cations and one mole of F anions. These ions combine to produce solid cesium fluoride. The enthalpy change in this step is the negative of the lattice energy, so it is also an exothermic quantity. The total energy involved in this conversion is equal to the experimentally determined enthalpy of formation, [latex]\Delta{H}_{\text{f}}^{\circ},[/latex] of the compound from its elements. In this case, the overall change is exothermic.

Hess’s law can also be used to show the relationship between the enthalpies of the individual steps and the enthalpy of formation. Table 3 shows this for cesium chloride, CsCl₂.

Table 3
Enthalpy of sublimation of Cs(s)	[latex]\text{Cs}\left(s\right)\rightarrow\text{Cs}\left(g\right)\Delta H=\Delta{H}_{s}^{\circ}=76.5\text{kJ}[/latex]
One-half of the bond energy of Cl₂	[latex]\frac{1}{2}{\text{Cl}}_{2}\text{(}g\text{)}\rightarrow\text{Cl}\left(g\right)\Delta H=\frac{1}{2}D=122\text{kJ}[/latex]
Ionization energy of Na(g)	[latex]\text{Na}\left(g\right)\rightarrow{\text{Na}}^{\text{+}}\text{(}g\text{)}+{\text{e}}^{-}\Delta H=IE=496\text{kJ}[/latex]
Negative of the electron affinity of Cl	[latex]\text{Cl}\left(g\right)+{\text{e}}^{-}\rightarrow{\text{Cl}}^{-}\text{(}g\text{)}\Delta H=-EA=-368\text{kJ}[/latex]
Negative of the lattice energy of NaCl(s)	[latex]{\text{Na}}^{\text{+}}\text{(}g\text{)}+{\text{Cl}}^{-}\text{(}g\text{)}\rightarrow\text{NaCl}\left(s\right)\Delta H=-{\Delta{H}}_{\text{lattice}}=?[/latex]
Enthalpy of formation of NaCl(s), add steps 1–5	[latex]\begin{array}{l}\Delta H=\Delta{H}_{f}^{\circ}=\Delta{H}_{s}^{\circ}+\frac{1}{2}D+IE+\left(-EA\right)+\left(-{\Delta{H}}_{\text{lattice}}\right)\\ \text{Na}\left(s\right)+\frac{1}{2}{\text{Cl}}_{2}\left(g\right)\rightarrow\text{NaCl}\left(s\right)=-411\text{kJ}\end{array}[/latex]

Thus, the lattice energy can be calculated from other values. For cesium chloride, using this data, the lattice energy is:

[latex]\Delta{H}_{\text{lattice}}=\left(411+109+122+496+368\right)\text{kJ}=770\text{kJ}[/latex]

The Born-Haber cycle may also be used to calculate any one of the other quantities in the equation for lattice energy, provided that the remainder is known. For example, if the relevant enthalpy of sublimation [latex]\Delta{H}_{s}^{\circ},[/latex] ionization energy (IE), bond dissociation enthalpy (D), lattice energy ΔH_lattice, and standard enthalpy of formation [latex]\Delta{H}_{\text{f}}^{\circ}[/latex] are known, the Born-Haber cycle can be used to determine the electron affinity of an atom.

Lattice energies calculated for ionic compounds are typically much higher than bond dissociation energies measured for covalent bonds. Whereas lattice energies typically fall in the range of 600–4000 kJ/mol (some even higher), covalent bond dissociation energies are typically between 150–400 kJ/mol for single bonds. Keep in mind, however, that these are not directly comparable values. For ionic compounds, lattice energies are associated with many interactions, as cations and anions pack together in an extended lattice. For covalent bonds, the bond dissociation energy is associated with the interaction of just two atoms.

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. Lattice energies are often calculated using the Born-Haber cycle, a thermochemical cycle including all of the energetic steps involved in converting elements into an ionic compound.

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 = ƩD_{bonds broken} – ƩD_{bonds 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{C}\left({\text{Z}}^{\text{+}}\right)\left({\text{Z}}^{-}\right)}{{\text{R}}_{\text{o}}}[/latex]

Exercises

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
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]
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]
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:
How does the bond energy of HCl(g) differ from the standard enthalpy of formation of HCl(g)?
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.
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.
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)?
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)?
Complete the following Lewis structure by adding bonds (not atoms), and then indicate the longest bond:
Use the bond energy to calculate an approximate value of ΔH for the following reaction. Which is the more stable form of FNO₂?
Use principles of atomic structure to answer each of the following:¹
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.
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.
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
The reaction of a metal, M, with a halogen, X₂, proceeds by an exothermic reaction as indicated by this equation: [latex]\text{M}\left(s\right)+{\text{X}}_{2}\left(g\right)\rightarrow{\text{MX}}_{2}\left(s\right).[/latex] For each of the following, indicate which option will make the reaction more exothermic. Explain your answers.
1. a large radius vs. a small radius for M⁺²
2. a high ionization energy vs. a low ionization energy for M
3. an increasing bond energy for the halogen
4. a decreasing electron affinity for the halogen
5. an increasing size of the anion formed by the halogen
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.
Which compound in each of the following pairs has the larger lattice energy? Note: Mg²⁺ and Li⁺ have similar radii; O^2– and F^– have similar radii. Explain your choices.
1. MgO or MgSe
2. LiF or MgO
3. Li₂O or LiCl
4. Li₂Se or MgO
Which compound in each of the following pairs has the larger lattice energy? Note: Ba²⁺ and K⁺ have similar radii; S^2– and Cl^– have similar radii. Explain your choices.
1. K₂O or Na₂O
2. K₂S or BaS
3. KCl or BaS
4. BaS or BaCl₂
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
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
The lattice energy of KF is 794 kJ/mol, and the interionic distance is 269 pm. The Na–F distance in NaF, which has the same structure as KF, is 231 pm. Which of the following values is the closest approximation of the lattice energy of NaF: 682 kJ/mol, 794 kJ/mol, 924 kJ/mol, 1588 kJ/mol, or 3175 kJ/mol? Explain your answer.

Element	First Ionization Energy (kJ/mol)	Second Ionization Energy (kJ/mol)
K	419	3050
Ca	590	1140

Selected Answers

1. In general, a multiple bond between the same two elements is stronger than a single bond. The greater the electronegativity difference between two similar elements, the greater the bond energy

[latex]\text{C}=\text{C}[/latex]
[latex]\text{C}\equiv \text{N}[/latex]
[latex]\text{C}\equiv \text{O}[/latex]
H–F
O–H
C–O

3. The approximate enthalpy changes are as follows:

[latex]\begin{array}{ll}\hfill DH^{\circ}& ={\Sigma{D}}_{\text{bonds broken}}-{\Sigma{D}}_{\text{bonds formed}}\\ & =2{D}_{\text{Cl-Cl}}+3{D}_{\text{F-F}}-6{D}_{\text{Cl-F}}\\ & =-564\text{kJ}\end{array}[/latex]
[latex]\begin{array}{ll}\hfill DH^{\circ}& ={\Sigma{D}}_{\text{bonds broken}}-{\Sigma{D}}_{\text{bonds formed}}\\ & ={D}_{\text{C-C}}+4{D}_{\text{C-H}}+{D}_{\text{H-H}}-{D}_{\text{C-C}}-6{D}_{\text{C-H}}\\ & =611+4\left(415\right)+436-345-6\left(415\right)\\ & =-128\text{kJ}\end{array}[/latex]
[latex]\begin{array}{ll}\hfill DH^{\circ}& ={\Sigma{D}}_{\text{bonds broken}}-{\Sigma{D}}_{\text{bonds formed}}\\ & =2{D}_{\text{C-C}}+12{D}_{\text{C-H}}+7{D}_{\text{O-O}}-8{D}_{\text{C-O}}-12{D}_{\text{O-H}}\\ & =2\left(345\right)+12\left(415\right)+7\left(496\right)-8\left(741\right)-12\left(464\right)\\ & =-2354\text{kJ}\end{array}[/latex]

5. The bond energy involves breaking HCl into H and Cl atoms. The enthalpy of formation involves making HCl from H₂ and Cl₂ molecules.

7. This problem can be solved as follows:

[latex]{\text{CS}}_{2}\left(g\right)\rightarrow\text{C}\left(\text{graphite}\right)+2\text{S}\left(s\right){\Delta{H}}_{1}^{\circ}=\Delta{H}_{\text{f}\left[{\text{CS}}_{2}\left(g\right)\right]}^{\circ}[/latex]
[latex]\text{C}\left(\text{graphite}\right)\rightarrow\text{C}\left(g\right)\Delta{H}_{2}^{\circ }=\Delta{H}_{\text{fC}\left(g\right)}^{\circ}[/latex]
[latex]2\text{S}\left(s\right)\rightarrow 2\text{S}\left(g\right)2\Delta{H}_{3}^{\circ }=2\Delta{H}_{\text{fS}\left(g\right)}^{\circ}[/latex]

[latex]\begin{array}{ll}\\ \hfill {D}_{{\text{CS}}_{2}}& =\Delta H^{\circ}=-{\Delta{H}}_{\text{f}\left[\left({\text{CS}}_{2}\left(g\right)\right)\right]}^{\circ}+\Delta{H}_{\text{fC}\left(g\right)}^{\circ}+2\Delta{H}_{\text{fS}\left(g\right)}^{\circ}\\ \hfill & =-116.9+716.681+2\left(278.81\right)\\ \hfill & =1157.4\text{ kJ}{\text{mol}}^{-1}\\ \hfill {D}_{\text{C }=\text{S}}& =\frac{1157.4}{2}=578.7\text{kJ}{\text{mol}}^{-1}\text{of}\text{C=S}\text{ bonds}\end{array}[/latex]

9. This problem can be solved as follows:

[latex]{\text{PCl}}_{3}\left(g\right)\rightarrow\frac{1}{4}{\text{P}}_{4}\left(s\right)+\frac{3}{2}{\text{Cl}}_{2}\left(g\right)\Delta{H}_{1}^{\circ}=-{\Delta{H}}_{\text{f}\left[\left({\text{PCl}}_{3}\left(g\right)\right)\right]}^{\circ}[/latex]

[latex]\frac{1}{4}{\text{P}}_{4}\left(s\right)\rightarrow\text{P}\left(g\right)\Delta{H}_{2}^{\circ}=\Delta{H}_{\text{fP}\left(g\right)}^{\circ}[/latex]

[latex]\frac{3}{2}{\text{Cl}}_{2}\left(g\right)\rightarrow 3\text{Cl}\left(g\right)3\Delta{H}_{3}^{\circ}=3\Delta{H}_{\text{fCl}\left(g\right)}^{\circ}[/latex]

[latex]\begin{array}{ll}\\{D}_{{\text{PCl}}_{3}}& =\Delta H^{\circ}=-{\Delta{H}}_{\text{f}\left[\left({\text{PCl}}_{3}\left(g\right)\right)\right]}^{\circ}+\Delta{H}_{\text{fP}\left(g\right)}^{\circ}+3\Delta{H}_{\text{fCl}\left(g\right)}^{\circ}\\ \hfill & =287.0+314.64+3\left(121.3\right)=965.54{\text{kJ mol}}^{-\text{1}}\\ \hfill {D}_{{\text{PCl}}_{3}}& =\frac{965.54\text{kJ}}{3}=321.8{\text{kJ per mol}}^{{-1}}\text{of bonds}\end{array}[/latex]

Proceeding in the same manners, [latex]-{\Delta{H}}_{{\text{f[PCl}}_{\text{5}}\text{(g)]}}=\text{374.9 kJ}{\text{mol}}^{-1}[/latex]. The P(g) and the 5Cl(g) contribute 921.14 kJ; then [latex]{\text{DF}}_{{\text{PCl}}_{\text{5}}}=\text{1296.04 kJ}[/latex] and [latex]{D}_{\text{P-Cl}}=\frac{\text{1296.04 kJ/mol}}{5}=\text{259.2 kJ/mol}[/latex] of bonds. The P–Cl bond in PCl₃ is stronger.

10.The C–C single bonds are longest.

11. the left hand arrangement: [latex]\text{O}=\text{N}[/latex] not listed, N-F 270, N-O 200; the right hand arrangement: [latex]\text{O}=\text{N}[/latex] not listed, N-O 200, O-F 185; the bond energy of [latex]\text{O}=\text{N}[/latex] does not matter because it must be the same in both cases, the form on the right has a bond energy of X +470; that on the right, X +385; the form on the left is more stable.

12. The answers are as follows:

When two electrons are removed from the valence shell, the Ca radius loses the outermost energy level and reverts to the lower n = 3 level, which is much smaller in radius.
The +2 charge on calcium pulls the oxygen much closer compared with K, thereby increasing the lattice energy relative to a less charged ion.
Removal of the 4s electron in Ca requires more energy than removal of the 4s electron in K, because of the stronger attraction of the nucleus and the extra energy required to break the pairing of the electrons. The second ionization energy for K requires that an electron be removed from a lower energy level, where the attraction is much stronger from the nucleus for the electron. In addition, energy is required to unpair two electrons in a full orbital. For Ca, the second ionization potential requires removing only a lone electron in the exposed outer energy level.
In Al, the removed electron is relatively unprotected and unpaired in a p orbital. The higher energy for Mg mainly reflects the unpairing of the 2s electron.

13. The lattice energy is given by [latex]U=C\left(\frac{{Z}^{+}{Z}^{-}}{{R}_{o}}\right),[/latex] where R_o is the interatomic distance. The charges are the same in both LiF and NaF. The major difference is expected to be the interatomic distance 2.008 Å versus 2.31 Å. From the data for LiF, with Z⁺Z^– = –1, [latex]C=\frac{U{R}_{\text{o}}}{{Z}^{+}{Z}^{-}}=\frac{1023\times 2.008}{-1}=-2054\text{ kJ}\text{A}{\text{mol}}^{-1}[/latex].

Then, [latex]{U}_{\text{NaF}}=\frac{-2054\text{kJ}\text{A}{\text{mol}}^{-1}\left(-1\right)}{2.31\text{A}}=889\text{kJ}{\text{mol}}^{-1}\text{or }890{\text{ kJ mol}}^{-1}[/latex].

14. The lattice energy, U, is the energy required to convert the solid into separate ions. U may be calculated from the Born-Haber cycle.

The values in kJ/mol are approximately (a) 3791; (b) 3223; (c) 821; (d) 740; and (e) 2957.

The answer is (d), which requires about 740 kJ/mol.

15. In each case, think about how it would affect the Born-Haber cycle. Recall that the more negative the overall value, the more exothermic the reaction is.

The smaller the radius of the cation, the shorter the interionic distance and the greater the lattice energy would be. Since the lattice energy is negative in the Born-Haber cycle, this would lead to a more exothermic reaction.
A lower ionization energy is a lower positive energy in the Born-Haber cycle. This would make the reaction more exothermic, as a smaller positive value is “more exothermic.”
As in part (b), the bond energy is a positive energy. The lower it is, the more exothermic the reaction will be.
A higher electron affinity is more negative. In the Born-Haber cycle, the more negative the electron affinity, the more exothermic the overall reaction.
The smaller the radius of the anion, the shorter the interionic distance and the greater the lattice energy would be. Since the lattice energy is negative in the Born-Haber cycle, this would lead to a more exothermic reaction.

16. 4008 kJ/mol; both ions in MgO have twice the charge of the ions in LiF; the bond length is very similar and both have the same structure; a quadrupling of the energy is expected based on the equation for lattice energy

17. The compounds with the larger lattice energy are

MgO; selenium has larger radius than oxygen and, therefore, a larger interionic distance and thus, a larger smaller lattice energy than MgO
MgO; the higher charges on Mg and O, given the similar radii of the ions, leads to a larger lattice energy
Li₂O; the higher charge on O^2– leads to a larger energy; additionally, Cl^– is larger than O^2–; this leads to a larger interionic distance in LiCl and a lower lattice energy
MgO; the higher charge on Mg leads to a larger lattice energy

18. The compounds with the larger lattice energy are

Na₂O; Na⁺ has a smaller radius than K⁺
BaS; Ba has a larger charge than K
BaS; Ba and S have larger charges
BaS; S has a larger charge

19. MgO

20. CaO

21. 924 kJ/mol

Glossary

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

Born-Haber cycle: thermochemical cycle relating the various energetic steps involved in the formation of an ionic solid from the relevant elements

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

Unit 4: Electronic Structure and Chemical Bonding

Learning Objectives

Bond Strength: Covalent Bonds

Example 1: Using Bond Energies to Calculate Approximate Enthalpy Changes

Check Your Learning

Ionic Bond Strength and Lattice Energy

Example 2: Lattice Energy Comparisons

Check Your Understanding

The Born-Haber Cycle

Key Concepts and Summary

Key Equations

Exercises

Glossary