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.

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 H₂, 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:

Conversely, the same amount of energy is released when one mole of H₂ molecules forms from two moles of H atoms:

Reference: https://www.youtube.com/watch?v=5AOblYlknBc

Bond Strength: Covalent Bonds

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.

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.

Strengths of Covalent Bonds

Bond dissociation energy or bond energy is the energy required to break a bond. Usually we mean bond dissociation enthalpy, the enthalpy change for this reaction:
A—B → A(g) + B(g)
For example, H—Cl → H•(g) + Cl•(g)
The • represents an unpaired electron, called a radical. When measuring the bond enthalpy, we break the bond so that half the bonding electrons go to each atom. Breaking a bond is always an endothermic process, so the bond energy is always positive. We use the symbol D(A—B) to represent the bond enthalpy of an A—B bond.

Bond energy is similar, but is the average energy required to break all the bonds in a molecule. For instance, C-H bond energy is the enthalpy of atomization of methane divided by 4. This is different from the energy required to break the first C-H bond in CH₄ because breaking the second bond might be easier or harder than breaking the first.

Some approximate average bond enthalpies, in kcal/mol (use this table to get a sense of which bonds are relatively weak or strong)

How do we measure?

As you might guess from the discussion above about bond energy vs. bond dissociation energy, it’s actually quite complicated to measure these! There are a lot of complications to consider, and you can’t always measure directly the heat of reaction that you want.

Why does it matter?

Having a general knowledge of bond strengths lets us understand the structures of molecules and predict reactions. For instance, when we guess the arrangement of atoms to make a Lewis structure, we will probably do better if we avoid making weak bonds. N-N and O-O single bonds are pretty weak, so usually we try not to put them in Lewis structures, unless nothing else makes sense. The structure will be better if we can make a multiple bond or put some other atom in between.

We can also use bond strength knowledge to predict what direction reactions will go and how fast they will go. If the product has stronger bonds than the reactants, the reaction is likely to be exothermic, and exothermic reactions often go forward. If the reactant has strong bonds, you might need to use a lot of energy to get the reaction started, even if it is exothermic. Combustion reactions are an example: C-C and C-H bonds are pretty strong, so we need a spark or a match to start the burning.

Another example is “nitrogen fixation”: we need N to make proteins and other important molecules in our bodies, but it is very hard to get N from N₂ because of the strong triple bond. This is why we have to use fertilizer in agriculture, and making nitrogen fertilizer uses roughly 1% of the world’s energy. Another example is teflon or PTFE, which makes a very slippery and non-reactive coating that is used in non-stick pans, containers for reactive chemicals, etc. PTFE has only C-C and C-F bonds, both of which are very strong, so it doesn’t easily react even at high temperature when you cook with it. In contrast, if a reactant has some very weak bonds, it might be very easy to start a reaction. For instance, hydrogen peroxide (HOOH) can be used as a bleach or disinfectant because the weak O-O single bond can easily break, helping it oxidize whatever is nearby. Hydrogen peroxide and hydrazine (N₂H₄) can both be used as rocket fuel because they react easily and exothermically (they have weak bonds, and they form products with stronger bonds).

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 following Table-1, and a comparison of bond lengths and bond strengths for some common bonds appears in the following 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)

Reference: https://chem.libretexts.org/Courses/University_of_Kentucky/UK%3A_General_Chemistry/07%3A_Chemical_Bonding_and_Molecular_Geometry/7.5%3A_Strengths_of_Ionic_and_Covalent_Bonds

Table-2 Average Bond Lengths and Bond Energies for Some Common Bonds.

References: https://chem.libretexts.org/Courses/University_of_Kentucky/UK%3A_General_Chemistry/07%3A_Chemical_Bonding_and_Molecular_Geometry/7.5%3A_Strengths_of_Ionic_and_Covalent_Bonds

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:

In this expression, the symbol ΣΣ 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:

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:

This excess energy is released as heat, so the reaction is exothermic. where it gives a value for the standard molar enthalpy of formation of HCl(g), ΔH∘fΔHf∘, 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.

Lengths of chemical bonds

The length of a chemical bond the distance between the centers of the two bonded atoms (the internuclear distance.) Bond lengths have traditionally been expressed in Ångstrom units, but picometers are now preferred (1Å = 10^-8 cm = 100 pm.) Bond lengths are typically in the range 1-2 Å or 100-200 pm. Even though the bond is vibrating, equilibrium bond lengths can be determined experimentally to within ±1 pm.

Figure 7.76 Bond energy vs. Bond Length

Bond lengths depend mainly on the sizes of the atoms, and secondarily on the bond strengths, the stronger bonds tending to be shorter. Bonds involving hydrogen can be quite short; The shortest bond of all, H–H, is only 74 pm. Multiply-bonded atoms are closer together than singly-bonded ones; this is a major criterion for experimentally determining the multiplicity of a bond. This trend is clearly evident in the above plot which depicts the sequence of carbon-carbon single, double, and triple bonds.

The most common method of measuring bond lengths in solids is by analysis of the diffraction or scattering of X-rays when they pass through the regularly-spaced atoms in the crystal. For gaseous molecules, neutron- or electron-diffraction can also be used.

The complete structure of a molecule requires a specification of the coordinates of each of its atoms in three-dimensional space. This data can then be used by computer programs to construct visualizations of the molecule as discussed above. One such visualization of the water molecule, with bond distances and the HOH bond angle superimposed on a space-filling model, is shown here. (It is taken from an excellent reference source on water). The colors show the results of calculations that depict the way in which electron charge is distributed around the three nuclei.

Figure 7.77 Water Molecule

Ionic Bond Strength and Lattice Energy

Multiple bonds are stronger than single bonds between the same atoms. 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.

Ions are atoms or molecules which are electrically charged. Cations are positively charged and anions are negatively charged. Ions form when atoms gain or lose valence electrons. Since electrons are negatively charged, an atom that loses one or more electrons will become positively charged; an atom that gains one or more electrons becomes negatively charged. Ionic bonding is the attraction between positively- and negatively-charged ions. These oppositely charged ions attract each other to form ionic networks, or lattices. Electrostatics explains why this happens: opposite charges attract and like charges repel. When many ions attract each other, they form large, ordered, crystal lattices in which each ion is surrounded by ions of the opposite charge. Generally, when metals react with non-metals, electrons are transferred from the metals to the non-metals. The metals form positively-charged ions and the non-metals form negatively-charged ions.

The properties of ionic compounds follow from the orderly crystal lattice arrangement of tightly bonded charged particles that make them up. Ionic compounds tend to have high melting and boiling points, because the attraction between ions in the lattice is very strong. Moving ions out of the lattice disrupts the structure, so ionic compounds tend to be brittle rather than malleable. Ionic compounds do not conduct electricity in the solid state because ions are not free to move around the lattice; however, when ionic compounds are dissolved, they may dissociate into individual ions which move freely through the solution and therefore conduct electricity well.

The Born-Haber Cycle

Born Haber cycle is a cycle of enthalpy change of process that leads to the formation of a solid crystalline ionic compound from the elemental atoms in their standard state and of the enthalpy of formation of the solid compound such that the net enthalpy becomes zero.

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:

• ΔHf ° , the standard enthalpy of formation of the compound

• IE, the ionization energy of the metal

• EA, the electron affinity of the nonmetal

• ΔHs ° , the enthalpy of sublimation of the metal

• D, the bond dissociation energy of the nonmetal

• ΔHlattice, the lattice energy of the compound

Reference: https://www.youtube.com/watch?v=jIyIhTzA4xI

EXAMPLE

Reference: https://www.youtube.com/watch?v=I61-N0GuSx8

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?

Solution

In these two ionic compounds, the charges Z⁺ and Z^– are the same, so the difference in lattice energy will depend upon Ro. The O^2– ion is smaller than the Se^2– ion. Thus, Al₂O₃ would have a shorter interionic distance than Al₂Se₃, and Al₂O₃ would have the larger lattice energy.

Check Your Learning

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

Answer: ZnO would have the larger lattice energy because the Z values of both the cation and the anion in ZnO are greater, and the interionic distance of ZnO is smaller than that of NaCl.                              

Reference: https://www.youtube.com/watch?v=DI-bwx8r3r8