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 Ionic Radii

The given ionic radii are for the ions \( \mathrm{X}^+ \) and \( \mathrm{Y} \). \( \mathrm{X}^+ \) has a radius of \( 88 \mathrm{pm} \), and \( \mathrm{Y} \) has a radius of \( 200 \mathrm{pm} \).

Step 2: Calculate the Radius Ratio

The radius ratio is calculated by dividing the radius of the smaller ion by that of the larger ion: \[ \text{Radius Ratio} = \frac{R_{\mathrm{X}^+}}{R_{\mathrm{Y}}} = \frac{88 \mathrm{pm}}{200 \mathrm{pm}} = 0.44 \]

Step 3: Determine Coordination Number from the Radius Ratio

Analyze the radius ratio of \(0.44\) using standard ranges for ionic compounds:- For radius ratios between \(0.225\) and \(0.414\), the coordination number is \(4\).- For radius ratios between \(0.414\) and \(0.732\), the coordination number is \(6\).- For radius ratios greater than \(0.732\), the coordination number is \(8\) or higher.Since \(0.44\) falls within the \(0.414\) to \(0.732\) range, the coordination number is \(6\).

Key Concepts

Understanding Ionic Radii

Ionic radii refer to the size of an ion in a crystal lattice. When atoms lose or gain electrons to form ions, their size changes. The ionic radius of cations, which are positively charged ions, usually decreases compared to their original atoms. This is because they lose an outer electron shell, resulting in a smaller size. Anions, or negatively charged ions, typically increase in size upon gaining electrons due to the added electron-electron repulsion in the outer shell.
A clear understanding of ionic radii helps predict how ions will pack together in a solid. It plays a crucial role in determining the crystal structure of ionic compounds, which relates to their physical properties. Knowing the size of ions can help determine their possible coordination numbers, which define how an ion will interact with surrounding ions in a crystal lattice.

Exploring the Radius Ratio

The radius ratio is a key concept in understanding ionic compounds. It involves the ratio of the radius of a smaller ion to the radius of a larger ion within a compound. This simple calculation can provide significant insights into the geometry of the compound. For example, for the compound XY with ionic radii of 88 pm and 200 pm, the radius ratio is calculated as \[ \text{Radius Ratio} = \frac{88 \mathrm{pm}}{200 \mathrm{pm}} = 0.44 \] The radius ratio helps in predicting the most stable coordination number and hence the geometry of the compound.

• A smaller radius ratio generally results in a lower coordination number.
• If the ratio falls in specific ranges, it suggests the number of anions surrounding a cation.

Understanding this concept helps in predicting how compounds might form and their potential properties.

Introduction to Coordination Chemistry

Coordination chemistry revolves around the concept of coordination numbers. The coordination number describes the number of ligand atoms that can bond to a central metal atom or ion. In ionic crystals, the coordination number indicates how many nearest neighbor ions surround a particular ion, giving insight into the arrangement and structure of the compound.
For instance, consider a compound with a radius ratio of 0.44. In general, this falls within the range of 0.414 to 0.732, suggesting a coordination number of six. This means that each central ion is typically surrounded by six oppositely charged ions, leading to a stable octahedral geometry.

• Coordination chemistry enables understanding of structural arrangements in complex ions.
• It helps explain properties like color, magnetism, and reactivity of compounds.

Grasping coordination in chemistry allows better predictions of how compounds form and function in various conditions.