Problem 38 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements is not correct? (a) The density of the crystal exhibiting Frenkel defect is less as compared to that of the perfect crystal (b) The Schottky defects are more common in ionic compounds with high coordination numbers and where the sizes of ions are small (c) In alkali halides, Frenkel defects are not found (d) The density of the crystal exhibiting Schottky defect is less as compared to that of the perfect crystal

Step-by-Step Solution

Answer

Option (a) is not correct.

Step 1: Understanding Options

To determine which statement is not correct, we need to first understand each option. Option (a) states that the density of a crystal exhibiting Frenkel defect is less than that of a perfect crystal. Option (b) specifies that Schottky defects are more common in ionic compounds with high coordination numbers and small ion sizes. Option (c) claims Frenkel defects are not found in alkali halides. Option (d) suggests the density of a crystal with Schottky defect is less than that of the perfect crystal.

Step 2: Analyzing Frenkel Defect and Density

Frenkel defects occur when an ion is displaced to an interstitial site, causing no change in density since no ions are missing. Hence, option (a) is incorrect because Frenkel defects do not reduce the crystal density.

Step 3: Examining Schottky Defects

Schottky defects involve the absence of ion pairs (both cation and anion), leading to a lower density of the crystal as there are fewer ions contributing to its mass and volume. Therefore, option (d) is correct about density decrease, and option (b) accurately identifies typical characteristics of Schottky defects.

Step 4: Addressing Frenkel Defects in Alkali Halides

Frenkel defects are unlikely in alkali halides since these crystals typically have similar cation and anion sizes, making movement to interstitial sites uncommon. Thus, option (c) correctly notes the absence of Frenkel defects in alkali halides.

Step 5: Concluding with the Incorrect Statement

Based on the analysis, option (a) is the incorrect statement since Frenkel defects do not affect the density of a crystal.

Key Concepts

Frenkel Defects

Frenkel defects are a type of point defect in crystalline solids. This defect occurs when an ion, typically a cation due to their smaller size, is dislocated from its regular position and instead occupies an interstitial site within the crystal lattice. Unlike vacancies, no ions are lost from the system. This rearrangement within the same crystal maintains the overall mass and volume, meaning the crystal density remains unchanged. Frenkel defects are more common in materials where the cation is much smaller than the anion, allowing it to fit into interstitial sites easily.

• Frenkel defects are typical in poor ionic conductors and non-stoichiometric compounds.
• Commonly seen in compounds like silver chloride (AgCl), where the cation can fit into interstitial spaces.

Due to the negligible effect on the crystal's density, Frenkel defects do not alter the observable properties of the crystal in terms of its mass per unit volume.

Schottky Defects

Schottky defects are another form of point defect but are distinctively different from Frenkel defects. These defects occur when both cations and anions are absent from their respective lattice sites, creating vacancies in the crystal. The absence of ion pairs results in a decrease in the crystal's density because the overall mass of the crystal is reduced while the volume remains constant. Schottky defects are prevalent in ionic compounds with high coordination numbers and relatively equal-sized ions, making these compounds suitable for ion mobility needed to form vacancies.

• Examples include sodium chloride (NaCl) and potassium chloride (KCl) where lattice ions completely leave their positions.
• The loss of ion pairs explains why the density of a crystal exhibiting Schottky defects is reduced compared to a perfect crystal.

While Schottky defects decrease the density, they do not affect the electric neutrality of the compound, as both types of ions are absent in equal numbers, preserving electrical balance.

Crystal Density

Crystal density is defined as the mass per unit volume of a crystal. It is an important property influencing the physical characteristics of the crystalline material. The presence of defects, such as Frenkel or Schottky defects, can alter the density of a crystal, impacting its structural and physical properties.

• When Frenkel defects occur, ions merely rearrange themselves, impacting the internal structure but not the density.
• Schottky defects cause a reduction in density due to the loss of mass from the missing ion pairs.

Understanding how defects affect density helps in predicting material behavior under various conditions, which is essential for applications in materials science and solid-state chemistry. Evaluating these defects is crucial for manipulating material properties intentionally for technological applications.