Problem 19 - Chemistry: The Central Science

Question

(a) Define the term lattice energy. (b) Which factors govern the magnitude of the lattice energy of an ionic compound?

Step-by-Step Solution

Answer

Lattice energy is the energy change associated with the formation of an ionic compound from its constituting ions in their gaseous state. The magnitude of lattice energy of an ionic compound is governed by two factors: the charge of the ions and their ionic radii. Lattice energy is directly proportional to the product of the ionic charges (\(U \propto q_1q_2\)) and inversely proportional to the sum of the ionic radii (\(U \propto \dfrac{1}{r_1 + r_2}\)). The equation for lattice energy can be given by the modified form of Coulomb's law: \(U = k\dfrac{q_1q_2}{r_1 + r_2}\), where k is a proportionality constant.

Step 1: Define Lattice Energy

Lattice energy is the amount of energy required to break apart a crystal lattice of an ionic compound into its separate ions, or the energy released when the ions in a gaseous state combine to form a crystal lattice. In other words, it is the energy change associated with the formation of an ionic compound from its constituting ions in their gaseous state.

Step 2: Explain the Factors Governing Lattice Energy Magnitude

There are two main factors that govern the magnitude of the lattice energy of an ionic compound: the charge of the ions and their ionic radii. 1. Charge of the ions: The charge of the ions influences the electrostatic force between them. Greater the charge on the ions, stronger will be the electrostatic force of attraction between the positive and negative ions, and therefore greater will be the lattice energy. Mathematically, the lattice energy (U) is directly proportional to the product of the ionic charges (q1 and q2), represented as \(U \propto q_1q_2\). 2. Ionic radii: The size of the ions will also determine the strength of the electrostatic force between them and hence, the lattice energy. Larger ions will have weaker electrostatic forces compared to smaller ions since the distance between the charges is greater. Therefore, the greater the ionic radii, the lower the lattice energy. Mathematically, lattice energy (U) is inversely proportional to the sum of the ionic radii (r1 and r2), represented as \(U \propto \dfrac{1}{r_1 + r_2}\). These factors can be combined to form the equation for lattice energy, which is given by the modified form of Coulomb's law: \(U = k\dfrac{q_1q_2}{r_1 + r_2}\), where k is a proportionality constant.