Energetics of Ionic Bond Formation

Ionic bonds are formed when positively and negatively charged ions are held together by electrostatic forces. Consider a single pair of ions, one cation and one anion. How strong will the force of their attraction be? According to Coulomb's Law, the energy of the electrostatic attraction (E ) between two charged particles is proportional to the magnitude of the charges and inversely proportional to the internuclear distance between the particles (r):

where each ion’s charge is represented by the symbol Q. The proportionality constant k is equal to 2.31 × 10⁻²⁸ J·m. This value of k includes the charge of a single electron (1.6022 × 10⁻¹⁹ C) for each ion. The equation can also be written using the charge of each ion, expressed in coulombs (C), incorporated in the constant. In this case, the proportionality constant, k, equals 8.999 × 109 J·m/C². In the example given, Q₁ = +1(1.6022 × 10⁻¹⁹ C) and Q₂ = −1(1.6022 × 10⁻¹⁹ C). If Q₁ and Q₂ have opposite signs (as in NaCl, for example, where Q₁ is +1 for Na⁺ and Q₂ is −1 for Cl⁻), then E is negative, which means that energy is released when oppositely charged ions are brought together from an infinite distance to form an isolated ion pair.

Energy is always released when a bond is formed and correspondingly, it always requires energy to break a bond.

As shown by the green curve in the lower half of Figure 1 , the maximum energy would be released when the ions are infinitely close to each other, at r = 0. Because ions occupy space and have a structure with the positive nucleus being surrounded by electrons, however, they cannot be infinitely close together. At very short distances, repulsive electron–electron interactions between electrons on adjacent ions become stronger than the attractive interactions between ions with opposite charges, as shown by the red curve in the upper half of Figure 1. The total energy of the system is a balance between the attractive and repulsive interactions. The purple curve in Figure 1

shows that the total energy of the system reaches a minimum at r₀, the point where the electrostatic repulsions and attractions are exactly balanced. This distance is the same as the experimentally measured bond distance.

Figure 1 : A Plot of Potential Energy versus Internuclear Distance for the Interaction between a Gaseous Na⁺ Ion and a Gaseous Cl⁻ Ion. The energy of the system reaches a minimum at a particular distance (r₀) when the attractive and repulsive interactions are balanced.

Consider the energy released when a gaseous Na+ ion and a gaseous Cl− ion are brought together from r = ∞ to r = r₀. Given that the observed gas-phase internuclear distance is 236 pm, the energy change associated with the formation of an ion pair from an Na+(g) ion and a Cl−(g) ion is as follows:

The negative value indicates that energy is released. Our convention is that if a chemical process provides energy to the outside world, the energy change is negative. If it requires energy, the energy change is positive. To calculate the energy change in the formation of a mole of NaCl pairs, we need to multiply the energy per ion pair by Avogadro’s number:

This is the energy released when 1 mol of gaseous ion pairs is formed, not when 1 mol of positive and negative ions condenses to form a crystalline lattice. Because of long-range interactions in the lattice structure, this energy does not correspond directly to the lattice energy of the crystalline solid. However, the large negative value indicates that bringing positive and negative ions together is energetically very favorable, whether an ion pair or a crystalline lattice is formed.

We summarize the important points about ionic bonding:

• At r₀, the ions are more stable (have a lower potential energy) than they are at an infinite internuclear distance. When oppositely charged ions are brought together from r = ∞ to r = r₀, the energy of the system is lowered (energy is released).
• Because of the low potential energy at r₀, energy must be added to the system to separate the ions. The amount of energy needed is the bond energy.
• The energy of the system reaches a minimum at a particular internuclear distance (the bond distance).