Problem 53 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{CaO}\) and \(\mathrm{NaCl}\) have same crystal structure and nearly the same ionic radii. If \(\mathrm{X}\) is the lattice energy of \(\mathrm{NaCl}\), the lattice energy of \(\mathrm{CaO}\) is very nealy (a) \(\mathrm{X}\) (b) \(2 \mathrm{X}\) (c) \(4 \mathrm{X}\) (d) \(\mathrm{X} / 4\)

Step-by-Step Solution

Answer

The lattice energy of CaO is very nearly 4X.

Step 1: Understand Lattice Energy

Lattice energy is the energy required to break an ionic solid into gaseous ions and is directly related to the charges on the ions and inversely related to the sum of the ionic radii in the crystal lattice.

Step 2: Analyze Ionic Charges for Lattice Energy Comparison

For NaCl, the ions are Na\(^+\) and Cl\(^-\), both with a charge of ±1. In CaO, the ions are Ca\(^{2+}\) and O\(^{2-}\), both with a charge of ±2. Since the lattice energy is proportional to the product of the charges, CaO will have a much higher lattice energy than NaCl.

Step 3: Calculate the Proportional Increase

The lattice energy for an ionic compound is proportional to the product of the charges on the ions. Thus, for CaO, where the charges are 2 and -2, the product is 4 times greater than in NaCl, where the charges are 1 and -1. Therefore, the lattice energy of CaO is approximately 4 times that of NaCl.

Step 4: Conclusion Based on Proportionality

Since the lattice energy of CaO is 4 times that of NaCl due to the greater charge product, the answer is very nearly (c) 4X.

Key Concepts

Crystal Structures

Crystal structures dictate the arrangement of ions in a solid. Think of them as three-dimensional patterns where each ion has a specific position. In both calcium oxide (CaO) and sodium chloride (NaCl), the structure is cubic, known as the face-centered cubic (FCC) system.

This means that the ions are situated in a lattice where each ion is surrounded by others in a symmetrical fashion, maximizing stability and minimizing repulsion.

• The uniformity of this structure allows for consistent physical and chemical properties across different compounds with the same crystal framework.
• This structural consistency explains why compounds like CaO and NaCl exhibit comparable features despite difference in charges.

Such crystal structures are crucial in determining properties like melting points, solubility, and lattice energy.

Ionic Charges

Ions are atoms or molecules that have lost or gained electrons, leading to a charge. The ionic charge affects how these particles interact in a compound.

In CaO, calcium ions have a charge of +2 (Ca\(^{2+}\)) and oxygen ions have a -2 charge (O\(^{2-}\)).
In contrast, NaCl consists of sodium ions with +1 charge (Na\(^+\)) and chloride ions with -1 charge (Cl\(^-\)).

• Lattice energy, the energy required to separate ions in a compound, is heavily influenced by these charges.
• Higher charges result in stronger attraction between ions, leading to a greater lattice energy.

This explains why CaO, with higher ionic charges, has a lattice energy that is approximately four times greater than that of NaCl.

Ionic Radii

Ionic radius refers to the size of an ion in a crystal lattice as it gains or loses electrons. It is a critical factor in determining the lattice energy of ionic compounds.

In both CaO and NaCl, the ionic radii are nearly identical. However, these small dimensions mean that charged ions can pack closely together, stronger interactions arising from their proximity.

• When ionic radii are smaller, ions are packed tightly, increasing the electrostatic forces between them.
• This closeness boosts lattice energy, as less distance between ions means stronger attractions.

Therefore, even though the radii of ions in CaO and NaCl are similar, the different charges significantly influence the resulting lattice energy.