Final answer:
The lattice energy is directly proportional to ionic charges and inversely proportional to the distance between ions. BaCl2, ZnCl2, and CuSO4 would have higher lattice energies due to higher ionic charges compared to (NH4)2SO4 and NaCN, which have lower charges. Option b is likely correct due to internuclear distances and ionic charges considered.
Step-by-step explanation:
The question asks for the arrangement of certain substances in order of decreasing magnitude of lattice energy. Lattice energy is a measure of the strength of the forces between the ions in an ionic solid, and is directly proportional to the product of the charges on the ions and inversely proportional to the distance between them. In the list provided, the ionic compounds consist of different ions with varying charges and sizes.
Guided by Equation 21.5.1 and the principle that lattice energy is proportional to the product of the ionic charges, we can predict that substances with higher ionic charges will typically have higher lattice energies. For ionic compounds with the same charges, the lattice energy is inversely proportional to the internuclear distance. Smaller ions will result in a compound with higher lattice energy. So in the given options, BaCl2 (with Ba2+ and Cl− ions) would have a higher lattice energy than NaCN (with Na+ and CN− ions).
(NH4)2SO4, being an ionic compound that contains polyatomic ions with a charge of 1- for the sulfate ion and 1+ for the ammonium ion, will generally have lower lattice energy compared to substances like ZnCl2 and BaCl2. CuSO4 would rank higher in lattice energy than compounds with monovalent ions but lower than those with divalent ions. Thus, we would expect option b) CuSO4 BaCl2 > ZnCl2 > (NH4)2SO4 > NaCN to be correct if we consider charge and internuclear distance.