Problem 106 - A Complete Resource Book in Chemistry for JEE Main

Question

Match List I with List II and select the correct answer: \(\begin{array}{ll}\text { List I } & \text { List II }\end{array}\) \(\begin{aligned}&\text { (Shape) } & \text { (Radius ratio) }\end{aligned}\) 1\. Planar triangle (i) \(0.732\) 2\. Square planar (ii) \(0.225\) 3\. Body-centred cubic (iii) \(0.155\) 4\. Tetrahedral (iv) \(0.414\) \(\begin{array}{llll}1 & 2 & 3 & 4\end{array}\) (a) (iii) (ii) (i) (iv) (b) (iii) (iv) (i) (ii) (c) (ii) (i) (iv) (iii) (d) (ii) (iv) (iii) (i)

Step-by-Step Solution

Answer

The correct option is (d).

Step 1: Understand the Relationship

The problem involves matching geometric shapes with their corresponding radius ratios. We must know the typical radius ratios associated with each of these geometric configurations to proceed.

Step 2: Match Shapes to Radius Ratios

1. Planar triangle is often associated with small ratio and less stable coordination: it typically corresponds to radius ratio (iii) 0.155. 2. Square planar configurations are usually more stable and have moderate radius ratios: they typically align with radius ratio (iv) 0.414. 3. Body-centred cubic structures are associated with a larger radius ratio: they correspond to (i) 0.732. 4. Tetrahedral structures are characterized by minimal ratio requirements consistent with (ii) 0.225.

Step 3: Verify Against Options

Now, verify if any options match our matching sequence: - Option (d) aligns with our sequence: (iii) for Planar triangle, (iv) for Square planar, (i) for Body-centred cubic, and (ii) for Tetrahedral.

Key Concepts

Geometric Shapes in Chemistry

Understanding geometric shapes in chemistry is crucial when predicting molecular behavior and properties. These shapes result from the arrangement of atoms around a central atom, influencing how molecules interact. Shapes in chemistry are determined by the spatial arrangement of atoms, which results from the minimization of electron pair repulsion according to the VSEPR (Valence Shell Electron Pair Repulsion) theory.

Some common geometric shapes include:

• **Linear:** Atoms are arranged in a straight line. An example is carbon dioxide,\( \text{CO}_2 \).
• **Planar triangle:** Three atoms form a triangle in a single plane, such as in boron trifluoride, \( \text{BF}_3 \).
• **Tetrahedral:** Atoms form a tetrahedron around the central atom, like in methane, \( \text{CH}_4 \).
• **Square planar:** Forms a square shape on a single plane, common in transition metal complexes, such as \( \text{PtCl}_4^{2-} \).

These shapes dictate molecular symmetry, dipole moments, and reactivity. They fundamentally influence how molecules participate in chemical reactions and form crystal structures.

Crystal Structures

The organization of atoms, ions, or molecules in a crystalline material results in what we know as the crystal structure. Understanding these structures is key to many fields, including materials science, physics, and chemistry.

Crystal structures are categorized by the pattern repeated throughout, which is defined by its unit cell - the smallest repeating unit that reflects the full symmetry of the arrangement. Here are some basic types of crystal structures:

• **Body-centred cubic (BCC):** Atoms are positioned at the corners of a cube with one atom at the center of the cube. This arrangement results in a large radius ratio of approximately 0.732. Metals like iron and tungsten commonly exhibit BCC structures.
• **Face-centred cubic (FCC):** Atoms occupy the corners and the centers of all the cube's faces. Gold and aluminum are examples of metals with this structure.
• **Hexagonal close-packed (HCP):** Atoms form two layers of hexagonally packed atoms, with another layer fitting into the crevices between. Zinc and magnesium have HCP structures.

Studying crystal structures helps in understanding the density, melting point, and strength of materials. Each type has its unique properties based on the tightness of atomic packing and connectivity between atoms or ions.

Coordination Geometry

Coordination geometry describes the spatial arrangement of ligands surrounding a central atom, most often observed in coordination compounds. The geometry is a reflection of the coordination number, which is the number of atoms bonded to the central atom.

Here's a look at several important coordination geometries:

• **Linear:** Often seen in compounds with a coordination number of 2. An example is \( \text{[Ag(NH}_3)_2]^+ \), where two ligands are at opposite ends.
• **Tetrahedral:** A coordination number of 4, forming a shape like that of methane. Common in many organometallic and transition metal complexes.
• **Square planar:** Another geometry for coordination number 4, typical for compounds of transition metals like palladium and platinum, providing stability with ligands placed in a square on the same plane.
• **Octahedral:** With a coordination number of 6, this is the most common geometry, especially for complex ions containing transition metals, such as \( \text{[Fe(CN}_6]^{3-} \).

The choice between different geometries is often dictated by the size of ligands and metals, as well as the electronic configuration and steric factors. Coordination geometry heavily influences the reactivity and properties of these compounds.