Problem 107 - A Complete Resource Book in Chemistry for JEE Main

Question

In a compound XY, the ionic radii \(\mathrm{X}^{+}\)and \(\mathrm{Y}^{-}\)are \(88 \mathrm{pm}\) and \(200 \mathrm{pm}\) respectively. What is the coordination number of \(\mathrm{X}^{+} ?\) (a) 4 (b) 6 (c) 8 (d) 10

Step-by-Step Solution

Answer

The coordination number of \( \mathrm{X}^{+} \) is 6.

Step 1: Identify the Ratios of Ionic Radii

To determine the coordination number of \( \mathrm{X}^{+} \), we first calculate the ratio of the ionic radii, \( r \), where: \[ r = \frac{\text{radius of } \mathrm{X}^{+}}{\text{radius of } \mathrm{Y}^{-}} = \frac{88 \text{ pm}}{200 \text{ pm}} = 0.44 \]

Step 2: Determine Coordination Number Based on Ratio

Using the derived ratio \( r = 0.44 \), we compare it against standard coordination number thresholds. Generally, a ratio of: 1. \( r < 0.414 \) implies a coordination number of 4.2. \( 0.414 \leq r < 0.732 \) implies a coordination number of 6.3. \( 0.732 \leq r \) implies a coordination number of 8 or higher.Since \( r = 0.44 \) falls within the range \( 0.414 \leq r < 0.732 \), the coordination number is likely 6.

Key Concepts

Ionic Radii

Ionic radii refer to the size of the ions in an ionic compound. They are typically measured in picometers (pm), a unit suitable for expressing atomic-scale dimensions. An ion’s radius depends largely on its charge and electronic configuration. When an atom becomes an ion, by either losing or gaining electrons, its size will change accordingly.
The positive ion, or cation, usually decreases in size due to the loss of electrons, resulting in a greater pull of the remaining electrons towards the nucleus. In contrast, the negative ion, or anion, typically increases in size because the addition of electrons decreases the overall pull of electrons towards the nucleus.

• The observed ionic radii for different ions are essential in predicting ionic compound properties.
• They influence lattice structures and the stability of ionic compounds.
• Understanding ionic radii helps determine the coordination number, which in turn affects the overall chemistry of a compound.

By taking into account ionic radii, chemists can better understand and predict how ions will tend to arrange themselves in a crystalline lattice, which is crucial in determining various physical and chemical properties of an ionic compound.

Coordination Chemistry

Coordination chemistry investigates the geometry and structures regarding the arrangement of atoms around a central atom, particularly in complex ions comprised of a metal and surrounding ligands. A fundamental aspect of this is the **coordination number**, which is defined as the number of ligand atoms that are directly bonded to the central atom.
When we refer to coordination numbers in the context of ionic compounds, we are essentially talking about how many ions or molecules surround a particular ion in the crystal lattice. This concept helps in understanding crystal structures and properties of materials.

• A higher coordination number suggests a more closely packed arrangement with potentially increased stability.
• This number can vary based on ionic sizes, charge, and the intended geometry of the crystalline arrangement.
• Common coordination numbers include 4 (tetrahedral or square planar), 6 (octahedral), and 8 (cubic), among others.

Thus, knowing the coordination number is critical for the design and synthesis of new materials that involve metal complexes or are used in catalysis, electronics, and pharmaceuticals.

Ionic Compounds

Ionic compounds are formed from the electrostatic attractions between positively charged ions (cations) and negatively charged ions (anions). These interactions result in a crystal lattice, which is a highly organized structure characterizing these compounds. Several important characteristics define ionic compounds:
They generally have high melting and boiling points due to the strong attraction between the ions. In addition, ionic compounds often dissolve in water and other polar solvents, as the ions interact favorably with the solvent molecules.

• The shape and strength of ionic compounds depend significantly on the ion charges and their radii.
• The **coordination number** of the ions within the lattice determines almost everything from structural stability to electrical conductivity.
• Ionic compounds are usually brittle and can conduct electricity when dissolved or melted, due to the free movement of ions.

Understanding these subtle attributes of ionic compounds paves the way for many applications, including the development of solid-state batteries and other electronic components, as well as a vast array of chemical reactions pertinent in various industries.