Question

Coordination number of Na ion in \(\mathrm{NaCl}\) is 6 and that of cacsium ion in CsCl is 8 . This is because (1) IP of \(\mathrm{Cs}\) is less than \(\mathrm{Na}\) (2) Size of \(\mathrm{Na}^{\prime}\) is less than \(\mathrm{Cs}\) (3) Attraction of \(\mathrm{Na}\) is higher than \(\mathrm{Cs}^{\prime}\) (4) None

Short answer

The size of \(\text{Na}^+\) is less than \(\text{Cs}^+\). Option 2 is correct.

Step-by-step solution

Understand Coordination Number

The coordination number is the number of nearest neighbors surrounding a central atom in a crystal lattice. For \(\text{NaCl}\), the coordination number of \(\text{Na}^+\) is 6, while for \(\text{CsCl}\), the coordination number of \(\text{Cs}^+\) is 8.

Analyze Ion Size

The size of the ion affects its coordination number. \(\text{Cs}^+\) is larger than \(\text{Na}^+\). Larger ions can accommodate more neighbors around them compared to smaller ions.

Connect Ion Size to Coordination Number

Since \(\text{Cs}^+\) is larger, it has a higher coordination number, allowing 8 neighbors. Smaller \(\text{Na}^+\) can only accommodate 6 neighbors due to its smaller size.

Evaluate Given Options

Given the options, the correct one is that the size of \(\text{Na}^+\) is smaller than \(\text{Cs}^+\). Therefore, Option 2 is likely correct.

Key concepts

Crystal Lattice

A crystal lattice is a highly ordered structure composed of atoms, ions, or molecules arranged in a repeating pattern. This regular arrangement extends in all three spatial dimensions. In a crystal lattice, each particle is surrounded by others in a specific geometrical pattern, known as the coordination geometry. The efficiency and stability of this packing depend greatly on the size and nature of the atoms or ions involved.

In solid-state chemistry, understanding crystal lattices is crucial because they determine the material's physical properties, such as density, melting point, and electrical conductivity. For instance, in the case of \(\text{NaCl}\), the ions form a cubic lattice, leading to each sodium ion being surrounded by six chloride ions. Similarly, in \(\text{CsCl}\), a different cubic lattice structure results in each cesium ion being surrounded by eight chloride ions.

The arrangement within the lattice influences both the coordination number and the compactness of the structure. The crystal lattice is vital for explaining why certain ions have different coordination numbers, as the geometric arrangement must accommodate different ion sizes efficiently.

Ion Size

Ion size, or ionic radius, is the measure from the center of an ion to its outer electrons. It directly affects the ion's ability to fit into specific lattice positions and its coordination number. Larger ions can usually accommodate more neighboring ions, leading to a higher coordination number.

A comparison of the sodium ion \(\text{Na}^+\) and cesium ion \(\text{Cs}^+\) illustrates this point well. \(\text{Na}^+\) has a smaller ionic radius compared to \(\text{Cs}^+\). Due to this smaller size, \(\text{Na}^+\) can only fit six chloride ions around it within the crystal lattice, resulting in a coordination number of 6. In contrast, the larger \(\text{Cs}^+\) ion can fit eight chloride ions around it, leading to a higher coordination number of 8.

Understanding ion size helps predict and explain the structure and coordination geometry of different compounds. It is a key factor in determining how ions will arrange themselves within a crystal, which in turn affects the material's properties.

Coordination Chemistry

Coordination chemistry deals with the study of the structure and properties of complexes formed between central atoms or ions and surrounding molecules or anions, known as ligands. The number of these surrounding entities is called the coordination number.

In ionic crystals like \(\text{NaCl}\) and \(\text{CsCl}\), the coordination number is defined by the number of nearest neighboring ions of opposite charge surrounding a central ion. This concept helps explain why \(\text{Na}^+\) has a coordination number of 6 in \(\text{NaCl}\) and why \(\text{Cs}^+\) has a coordination number of 8 in \(\text{CsCl}\).

Coordination chemistry is not limited to simple salts but extends to more complex coordination compounds, which can involve various ligands and central atoms. These compounds often have interesting and useful properties, such as catalytic activity, color, and magnetism.

In summary, understanding the principles of coordination chemistry, like coordination numbers, is essential for grasping the structures and behaviors of ionic compounds and complexes. This knowledge is foundational for advancing in fields like material science, chemistry, and solid-state physics.