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

Statement (a) is not correct; Frenkel defects do not change crystal density.

Step 1: Understand Each Type of Defect

First, let's understand what Frenkel and Schottky defects are. A Frenkel defect involves a displacement of an ion from its lattice position to an interstitial site within the crystal. This typically does not affect the density because the number of atoms in the crystal remains unchanged. A Schottky defect involves a pair of vacancies, one cation and one anion, and leads to a decrease in the density of the crystal, as there are fewer ions present in the same volume.

Step 2: Analyze Statement (a)

Statement (a) claims that the density of a crystal with a Frenkel defect is less than a perfect crystal. Since Frenkel defects involve no loss of ions, they do not change the crystal's density. Therefore, statement (a) is incorrect.

Step 3: Analyze Statement (b)

Statement (b) suggests Schottky defects are common in ionic compounds with high coordination numbers and small ion sizes. This is correct because Schottky defects require the removal of pairs of ions, which is feasible when ions are small and can fit into high-coordination environments.

Step 4: Analyze Statement (c)

Statement (c) claims that Frenkel defects are not found in alkali halides. This is correct, as alkali halides typically have ions that are too large for interstitial positions, making Frenkel defects energetically unfavorable.

Step 5: Analyze Statement (d)

Statement (d) states that the density of a crystal with Schottky defects is less than that of a perfect crystal. This is correct because removing ions decreases the mass but the volume remains unchanged, leading to lower density.

Key Concepts

Frenkel Defect

The Frenkel defect is a type of point defect in crystalline solids. It occurs when an ion is displaced from its original lattice site to an interstitial site. This causes a vacancy at the original position while the ion remains within the lattice structure.

This defect mainly occurs in ionic crystals where there is a significant size difference between the anions and cations.

• The smaller ion, often a cation, moves into an interstitial space.
• The larger anion remains in its lattice position.

Importantly, the Frenkel defect does not change the overall number of ions within the crystal. Because of this, the defect does not affect the overall density. The number of atoms remains constant, so mass and volume are unchanged. The defect is more common in compounds where the cations are much smaller than the anions.

Schottky Defect

The Schottky defect is another common point defect but it involves the removal of a pair of ions from the crystal lattice. To maintain electrical neutrality, a cation-anion pair is removed:

• This decreases the overall number of ions within the crystal.
• The result is a drop in the crystal's density since both mass and volume are affected.

The Schottky defect is prevalent in ionic compounds where the ions are similar in size and able to be removed in pairs. It is also characteristic of systems with high coordination numbers. Examples include alkali halides like sodium chloride. The defect is especially significant at higher temperatures where ion mobility increases.

Ionic Compounds

Ionic compounds are chemical compounds composed of ions held together by electrostatic forces known as ionic bonds.

• They form a crystalline lattice that maximizes the interaction between opposite charges.
• Consistency in the orderly arrangement of ions gives rise to well-defined lattice structures.

The stability and properties of ionic compounds are influenced by the lattice energy, which depends on ion size, charge, and arrangement. Defects in the lattice, like Frenkel and Schottky defects, can significantly alter the physical properties such as density and electrical conductivity of these compounds. Ionic compounds exhibit high melting and boiling points due to the strong attraction between ions.

Alkali Halides

Alkali halides are a class of ionic compounds formed by an alkali metal and a halogen. Examples include sodium chloride (NaCl) and potassium bromide (KBr). These compounds are highly ionic due to the significant difference in electronegativity between the alkali metals and halogens.

• They usually have a high melting point and crystalline structure.
• Their crystals are generally cubic, allowing efficient packing of ions.

In alkali halides, Frenkel defects are uncommon because the large size of the ions makes it difficult for them to occupy interstitial sites. Schottky defects are more common as the similar size and opposite charges of the ions allow for the removal of ion pairs without greatly disturbing the crystal structure. Such defects can influence properties like color and ionic conductivity.