Problem 39 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Read the following statement (Assertion) and explanation (Reason) and answer each question as per the options given below : (a) If both assertion and reason are correct, and reason is the correct explanation of the assertion. (b) If both assertion and reason are correct, but reason is not the correct explanation of the assertion. (c) If assertion is correct but reason is incorrect. (d) If assertion is incorrect but reason is correct. Assertion : In any ionic solid \([M X]\) with Schottky defects, the number of positive and negative ions are same. Reason : Equal number of cation and anion vacancies are present.

Step-by-Step Solution

Answer

(a) Both assertion and reason are correct, and reason is the correct explanation of the assertion.

Step 1: Understand Schottky Defects

In ionic solids, Schottky defects occur when equal numbers of cations and anions are missing from their lattice sites. This maintains electrical neutrality as the overall charge remains balanced.

Step 2: Analyze the Assertion

The assertion states that in any ionic solid \([MX]\) with Schottky defects, the number of positive and negative ions are the same. Given that Schottky defects occur in pairs to preserve charge, the assertion is correct as these defects do not alter the stoichiometric balance of the compound.

Step 3: Evaluate the Reason

The reason provided states that equal numbers of cation and anion vacancies are present in a Schottky defect. This indeed describes a Schottky defect correctly because both cations and anions are absent in equal numbers.

Step 4: Relate Assertion and Reason

Both the assertion and the reason are correct. The reason directly explains why the number of positive and negative ions remains the same in an ionic solid with Schottky defects, as it is due to equal numbers of cation and anion vacancies.

Key Concepts

Ionic Solids

The structure of ionic solids is based on a lattice where alternating positive and negative ions, known as cations and anions, are arranged in a repetitive pattern. They are held together by strong electrostatic forces, which gives these solids high melting points and significant stability. In ionic solids, the ions are stacked in a way that maximizes ionic attractions and minimizes ionic repulsions. This precise arrangement needs to be maintained for the material to remain stable and brittle. If this ordered structure is disrupted, it can lead to defects like the Schottky defect, which involve missing ions from the lattice.

Lattice Sites

Lattice sites are the specific positions in the crystalline structure of a solid where ions are situated. Imagine a three-dimensional grid where each point represents the position of a cation or an anion. These sites form the framework within which the ions in an ionic solid reside. The arrangement of ions at these lattice sites is crucial for maintaining the solid's structure and properties. If some lattice sites are vacant, like in Schottky defects, it can change the physical properties of the solid, such as its density and conductivity.

Cation and Anion Vacancies

A cation vacancy occurs when a positively charged ion is missing from its designated lattice site. Similarly, an anion vacancy is when a negatively charged ion is absent. In the case of Schottky defects, both types of vacancies occur simultaneously. This means equal numbers of cations and anions are missing. This pairing is essential as it helps to maintain the charge neutrality of the solid. Vacancies alter the density of the solid, as missing ions reduce the overall mass without changing the volume significantly. Understanding vacancies helps in comprehending how solids respond to external conditions and pressure.

Electrical Neutrality

Electrical neutrality in ionic solids means that the total positive charge from the cations is perfectly balanced by the total negative charge from the anions. This balance maintains the solid's stability and prevents it from becoming electrically reactive. Schottky defects are one type of defect that ensures this neutrality is maintained even when some ions are missing. By having equal numbers of both cation and anion vacancies, Schottky defects do not disturb the overall charge balance within the solid. This characteristic is crucial for the practical application of ionic solids, ensuring they can function effectively without unwanted electrical conduction.