Concept: Lattice Energy

Lattice energy is the energy required to completely separate one mole of a solid ionic compound into gaseous ionic constituents. It is directly proportional to the product of the charges of the ions and inversely proportional to the sum of their ionic radii. This relationship is described by Born-Landé equation or qualitatively by Coulomb's Law.

The formula for lattice energy (U) is given by:

$U\propto \frac{q_1{q}_2}{r_0}$

where $q_1$ and $q_2$ are the charges of the ions, and $r_0$ is the internuclear distance (sum of ionic radii).

Why (C) CsF is correct:

In the given options (KF, NaF, CsF, RbF), the anion is common (F⁻). The cations are K⁺, Na⁺, Cs⁺, and Rb⁺. All these cations have a +1 charge. Therefore, the lattice energy will primarily depend on the size of the cation.

As we move down a group in the periodic table, the size of the ions increases. The order of ionic radii for these cations is: Na⁺ < K⁺ < Rb⁺ < Cs⁺.

Since lattice energy is inversely proportional to the sum of ionic radii ($r_0=r_{cation}+r_{anion}$), the compound with the largest cation will have the largest internuclear distance and thus the smallest lattice energy.

Cs⁺ is the largest cation among Na⁺, K⁺, Rb⁺, and Cs⁺. Therefore, CsF will have the largest internuclear distance and consequently the smallest lattice energy.

Option Analysis:

• A) KF: K⁺ is smaller than Rb⁺ and Cs⁺, leading to higher lattice energy than CsF and RbF.
• B) NaF: Na⁺ is the smallest cation among the options, resulting in the highest lattice energy.
• C) CsF: Cs⁺ is the largest cation, leading to the largest internuclear distance and thus the smallest lattice energy.
• D) RbF: Rb⁺ is smaller than Cs⁺, so RbF will have a higher lattice energy than CsF.

Correct Answer: (C)