MICSP - Lattice Energies and Potential Energy Curves (Lesson)

Lattice Energy and Potential Energy Curves

Lattice Energy of Ionic Compounds

When discussing ionic compounds an important concept to understand is that of lattice energy.  The lattice energy for an ionic compound is essentially the energy required to separate an entire mole of an ionic compound into its constituent elements in the gas phase as shown in the equation below:

NaCl(s)  $\longrightarrow$  Na⁺ (g) + Cl^$-$ (g)

The ions of sodium and chlorine can be related to simple point charges for the sake of comparison.  These ions can be considered as being not only charged but separated from each by a certain distance.  Because of these factors, Coulomb's law shown below becomes useful as a qualitative tool to help evaluate or compare lattice energies between two different ionic substances.

Potential Energy Curves for Covalent Bonds

Let's look at what happens when two hydrogen atoms join to form an H₂ molecule. As the two atoms get closer, the electron of each atom begins to feel the attraction of both nuclei. This causes the electron density around each nucleus to shift toward the region between the two atoms. Therefore, as the distance between the nuclei decreases, there is an increase in the probability of finding either electron near either nucleus. In effect as the molecule is formed each of the hydrogen atoms in the H₂ molecule acquires a share of two electrons.

This is a graph of chemical potential energy in relation to the distance between bonding particles. The values would be specific for each bonding pair based on the number of protons in the nucleus. While this shows hydrogen, any bonding pair of atoms would look similar in shape, but with different energy values and distances. 

Let's consider this relationship using the graph. Consider first the far right side in this graph of Energy vs Bond Length. On the right, the atoms are far apart and not yet 'bonding'. This is our starting energy we arbitrarily call zero. Moving to the left, the distance between the two nuclei grows smaller as the atoms come closer to one another, the energy of the system is lowered as each bonding atom gains the shared electrons in its energy levels. But remember, at the same time there is a nuclear repulsion of the two nuclei increasing as distance decreases. At some particular distance, there is a balance of attraction and repulsion, related to Coulomb's Law. The lowest part of this graph is where the balance between repulsion and attraction is in balance, and unique for each molecule that can be formed.

Don't be confused about the best fit curve being located in both the positive and negative quadrants for potential energy on this graph. This is a graph for the formation of a bond. As a bond forms, energy is released from the bonding atoms to the environment. At the farthest left, the increasing positive values seen as distance diminishes reflect that electrostatic repulsion exceeds the energy released in the bonding, reflecting distances that would not create a stable molecule.

The stable covalent bond is found where the energy profile is lowest.

Since every atom has its own unique amount of protons and electrons, each possible combination of atoms has its own balance of distance and force. That balance is the chemical bond. The distance is known as bond length. The amount of energy needed to separate these atoms is called the bond energy.

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