Problem 103 - A Complete Resource Book in Chemistry for JEE Main

Question

The ionic radii of \(\mathrm{Rb}^{+}\)and \(\mathrm{I}^{-}\)are \(1.46 \AA\) and \(2.16 \AA\) respectively. The most probable type of structure exhibited by it is (a) \(\mathrm{CaF}_{2}\) type (b) \(\mathrm{ZnS}\) type (c) \(\mathrm{CsCl}\) type (d) \(\mathrm{NaCl}\) type

Step-by-Step Solution

Answer

\( \mathrm{NaCl} \) type structure is most likely for \( \mathrm{RbI} \).

Step 1: Understand the Ionic Radii

The ionic radii of \(\mathrm{Rb}^{+}\) and \(\mathrm{I}^{-}\) are given as \(1.46 \text{ Å}\) and \(2.16 \text{ Å}\), respectively. These radii are crucial in determining the type of crystal structure that \(\mathrm{RbI}\) will form.

Step 2: Calculate the Ionic Radius Ratio

Calculate the radius ratio using the formula: \[ \text{Radius Ratio} = \frac{\text{Radius of } \mathrm{Rb}^{+}}{\text{Radius of } \mathrm{I}^{-}} = \frac{1.46 \text{ Å}}{2.16 \text{ Å}} \approx 0.68 \] This ratio helps identify the crystal structure.

Step 3: Identify the Structure Type Using the Radius Ratio

Radius ratios are used to predict the possible crystal structures: - For \(\text{Radius Ratio} < 0.414\), coordination is typically 4 (\(\mathrm{ZnS}\) type).- For \(0.414 \leq \text{Radius Ratio} < 0.732\), coordination is typically 6 (\(\mathrm{NaCl}\) type).- For \(0.732 \leq \text{Radius Ratio}\), coordination is typically 8 (\(\mathrm{CsCl}\) type).Since 0.68 falls within the range of 0.414 to 0.732, \( \mathrm{NaCl} \) type structure is most likely for \( \mathrm{RbI} \).

Key Concepts

Ionic Radii

Ionic radii are a measure of the size of an ion in a crystal lattice. They are pivotal when examining how ions fit together in inorganic compounds.
In our exercise, we have

• Rubidium ion (Rb⁺): possesses an ionic radius of \(1.46 \text{ Å}\)
• Iodide ion (I^-): possesses an ionic radius of \(2.16 \text{ Å}\).

These values indicate how the ions pack together within the crystal. Larger radii mean larger ions, affecting the spacing and the symmetry within the crystal. Understanding these values is crucial to discerning why certain crystal structures like those seen in RbI take the forms they do.

Ionic Radius Ratio

The ionic radius ratio is the ratio of the radii of the cation to the anion. This simple calculation provides valuable insight into the possible arrangement of ions in a crystalline network.
For RbI, the radius ratio is calculated as follows:
\[\text{Radius Ratio} = \frac{\text{Radius of } \mathrm{Rb}^{+}}{\text{Radius of } \mathrm{I}^{-}} = \frac{1.46 \text{ Å}}{2.16 \text{ Å}} \approx 0.68\]
The radius ratio not only hints at the geometry of the packing but also guides us to the appropriate coordination number, impacting the overall structure.

Coordination Number

The coordination number is the number of ions directly surrounding a given ion in a crystal lattice. It's closely linked to the ionic radius ratio.
The coordination number can decide features such as:

• Stability of the lattice
• Type of chemical bonds formed
• Physical properties like hardness and melting point

For RbI, with a radius ratio of 0.68, the most probable coordination number is 6.
This coordination is also typical of the NaCl-type structure, where each ion is surrounded by six oppositely charged ions, forming a symmetrical and stable lattice.

RbI Structure

In the case of RbI, the structure it adopts is influenced greatly by the main factors discussed: ionic radii, radius ratio, and coordination number. Given a radius ratio of 0.68, RbI is most likely to assume a face-centered cubic lattice similar to that of NaCl, in which each Rb⁺ ion is surrounded by six I^- ions and vice versa.
This arrangement equates to a balanced and energetically favorable configuration.
The

• "6:6 coordination"
• "type NaCl structure"

model benefits from strong ionic bonds and a cubic close-packed design, providing robust properties essential for various applications.