Problem 39 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements is not correct? (a) Heating of zinc oxide leads to the formation of a yellow coloured non- stoichiometric compound (b) The creation of cationic holes in ionic crystals imparts electrical conductivity to such crystals (c) The compound ferrous oxide can be prepared in its stoichiometric composition (d) Silver bromide shows both types of Schottky and Frenkel defects

Step-by-Step Solution

Answer

Statement (c) is not correct because ferrous oxide is difficult to prepare in its stoichiometric form.

Step 1: Understand Non-stoichiometric Compounds

Non-stoichiometric compounds occur when the ratio of elements in the compound deviates from simple whole numbers. Zinc oxide is known to form a non-stoichiometric compound, typically appearing yellow when heated due to excess zinc ions that lead to oxygen vacancies, altering the stoichiometry.

Step 2: Analyze Electrical Conductivity in Ionic Crystals

Ionic crystals can conduct electricity when there are defects in the crystal lattice. The creation of cationic holes, which are positive ion vacancies, allows ions to move and carry electrical current. Therefore, ionic crystals with such defects can display electrical conductivity.

Step 3: Investigate Stoichiometry of Ferrous Oxide

Ferrous oxide ( ext{FeO}) often forms with a non-stoichiometric composition due to an excess of iron ions, resulting in an formula like ext{Fe}_{1-x} ext{O}. This makes it difficult to consistently prepare it in a perfect 1:1 stoichiometric ratio.

Step 4: Identify Common Defects in Silver Bromide

Silver bromide ( ext{AgBr}) is known to exhibit both Schottky and Frenkel defects. Schottky defects occur when equal numbers of anions and cations are missing from the lattice, whereas Frenkel defects occur when an ion is displaced from its lattice site to an interstitial site.

Step 5: Determine the Incorrect Statement

Review each statement based on your analysis: - Statement (a) is true as zinc oxide forms a yellow non-stoichiometric compound when heated. - Statement (b) is true since creation of cationic holes can lead to electrical conductivity. - Statement (c) implies ferrous oxide can be prepared with stoichiometric accuracy, which is often not the case due to non-stoichiometry. - Statement (d) correctly describes silver bromide showing both Schottky and Frenkel defects. The only incorrect statement is (c).

Key Concepts

Cationic Holes and Electrical Conductivity

Ionic crystals are typically known for their robust and ordered structures. However, they're not insulators. They can surprisingly conduct electricity, and this is due to a phenomenon known as cationic holes. So what exactly happens here?
A cationic hole is a type of defect in the crystal lattice where a positively charged ion is missing from its normal position. This vacancy creates the possibility for adjacent ions to move into the vacant position, thus allowing ions to migrate through the crystal. This process enables the flow of an electrical current, as any excess charge can propagate across these holes.
It's like playing a sliding puzzle; when one piece is missing, the others can move around. This type of movement within the lattice grants the crystal a degree of electrical conductivity, making some ionic crystals act similarly to semiconductors.

• Cationic holes: missing positive ions.
• Facilitate ion movement.
• Grant electrical conductivity.

Understanding such defects provides insight into how some materials, like certain ceramics and mixed metal oxides, can be engineered for conductivity in high-temperature environments.

Schottky and Frenkel Defects

When it comes to ionic crystals, not all defects are the same. Schottky and Frenkel defects represent two principal types of imperfection that can affect the properties of these materials. Let's explore each.

**Schottky Defects**
This type of defect arises when there are equal numbers of missing cations and anions in the crystal lattice. Imagine a neat array of soldiers, but with several gaps in line where soldiers (ions) should be standing. This uniform absence preserves electrical neutrality but alters the density. Such defects can lead to increased ionic conductivity as vacancies facilitate ion movement.

• Equal cation and anion vacancies.
• Preserves overall neutrality.
• Impacts density and conductivity.

**Frenkel Defects**
In contrast, Frenkel defects occur when an ion leaves its regular position and occupies an interstitial site—gaps usually between ions. This kind of defect doesn't affect the overall density as much as Schottky defects do, but still maintains neutrality while increasing the likelihood of ion movement within the crystal.

• Ion displacement to interstitial site.
• Maintains crystal neutrality.
• Enhances mobility without changing density much.

Both types of defects underline how imperfection can paradoxically enhance certain properties, like conductivity, within ionic compounds.

Stoichiometry in Ionic Compounds

Stoichiometry speaks to the precise balance of elements in a compound. It's like making sure every recipe ingredient is measured perfectly for the dish you're creating. With ionic compounds, this concept ensures that the ratio of cations to anions matches their respective charges, presenting a chemically stable structure.

However, in real-world scenarios, compounds like ferrous oxide (\( \text{FeO} \)) often deviate from this perfect stoichiometry. Such deviations occur due to various factors, including temperature, pressure, and the presence of crystallographic defects. A non-stoichiometric compound might have a formula like \( \text{Fe}_{1-x}\text{O} \), indicating an imbalance in the expected one-to-one ratio as some Fe ions are in excess. These adjustments are crucial in fields such as materials science where properties can be fine-tuned.

• Stoichiometry ensures balanced proportions.
• Deviations lead to non-stoichiometry.
• External conditions can affect stoichiometric balance.

Understanding stoichiometry's role allows researchers to harness material properties more effectively, using slight compositional changes to achieve desired results like increased conductivity or specific mechanical properties.