Final answer:
To rank the lattice energies of CsCl, CsBr, and CsI, consider the size of the halide ions and their influence on internuclear distance. With identical charges, the size of the anions determines that CsCl has the most negative lattice energy and CsI the least, giving the order CsI, CsBr, CsCl.
Step-by-step explanation:
The question asks us to rank the lattice energies of CsCl, CsBr, and CsI, which all have the same crystal structure. To determine the order of lattice energies, we need to consider the factors affecting lattice energy. According to the principles of ionic bonding, lattice energy is directly proportional to the product of the ionic charges and inversely proportional to the internuclear distance between the ions. In the case of CsCl, CsBr, and CsI, all contain the Cs+ cation with a +1 charge, paired respectively with Cl-, Br-, and I- anions, each with a -1 charge. Therefore, since the ionic charges are identical, the determining factor is the size of the halide ions. The size of the halide ions increases from Cl- to Br- to I-, meaning that CsCl will have the smallest internuclear distance and thus the largest lattice energy. Conversely, CsI will have the largest internuclear distance and the smallest lattice energy. Therefore, the correct order from least negative (weakest) to most negative (strongest) lattice energy is CsI, CsBr, CsCl, which corresponds to answer choice (a).