Question

Predict coordination number of the cation in crystals of the following compounds: 1\. \(\mathrm{MgO}: r_{c}=0.65 \AA ; r_{a}=1.40 \AA\) 2\. \(\mathrm{MgS}: r_{c}=0.65 \AA ; r_{a}=1.84 \AA\) (a) 6,4 (b) 4,6 (c) 3,4 (d) 6,8

Short answer

(a) 6,4

Step-by-step solution

Understand Coordination Number

The coordination number of a cation in a crystal is the number of anions that surround the cation. It can be estimated by considering the ratio of the ionic radii, which is known as the ionic radius ratio (irr).

Calculate Ionic Radius Ratio for MgO

For MgO, use the given ionic radii of Mg (cation, rc) and O (anion, ra) to calculate the ionic radius ratio: \[ irr = \frac{r_c}{r_a} = \frac{0.65 \mathring{A}}{1.40 \mathring{A}} = 0.4643 \]

Predict Coordination Number for MgO

Using the calculated ionic radius ratio and known geometrical relationships, predict the coordination number for MgO. An irr of 0.4643 typically corresponds to a coordination number of 6.

Calculate Ionic Radius Ratio for MgS

For MgS, use the given ionic radii of Mg (cation, rc) and S (anion, ra) to calculate the ionic radius ratio: \[ irr = \frac{r_c}{r_a} = \frac{0.65 \mathring{A}}{1.84 \mathring{A}} = 0.3533 \]

Predict Coordination Number for MgS

Using the calculated ionic radius ratio and known geometrical relationships, predict the coordination ensure you are summarizing rather than copying- pasting text)number for MgS. An irr of 0.3533 typically corresponds to a coordination number of 4.

Key concepts

Ionic Radius Ratio

The ionic radius ratio (IRR) is a fundamental concept when exploring ionic compounds and their structures. It represents the ratio of the radii between a cation (positively charged ion) and an anion (negatively charged ion). Why is this important? It helps us predict how ions will pack together in a solid crystal structure. For example, in the case of magnesium oxide (MgO), the radius of the Mg cation is given as 0.65 angstroms and that of the oxygen anion is 1.40 angstroms, leading to an IRR of approximately 0.4643. This ratio suggests a certain way the ions arrange themselves, known as the coordination number, which in this case turns out to be 6. Thus, the IRR tells us how snugly a cation fits into the gap between surrounding anions.

Furthermore, different IRR ranges correspond to different coordination numbers, which can be matched to standard geometric configurations such as linear, triangular, or octahedral arrangements. Understanding this helps in visualizing and deducing the three-dimensional arrangements of ions in a solid crystal - an essential skill for chemistry students, particularly when studying for competitive exams like the JEE in India.

Crystal Structure

Crystal structure embodies the ordered three-dimensional arrangement of atoms or ions within a crystal. It is akin to the architectural blueprint of a building, dictating stability, and physical properties such as melting point, hardness, and solubility. The arrangement is determined by several factors, including ionic sizes and electrostatic forces. In the exercise, we consider cations surrounded by anions. The pattern of this arrangement is often discussed in terms of the coordination number, the number of nearest neighbour ions surrounding a cation.

For students preparing for the JEE Chemistry paper, visualizing these structures is vital. They need to understand the common crystal structures like face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP). Grasping the underlying principles of these structures can greatly aid in predicting the properties of materials and in solving complex problems on crystallography.

JEE Chemistry

JEE Chemistry is a segment of the Joint Entrance Examination, which is mandatory for admission into engineering colleges in India. The curriculum encompasses a variety of topics, including Physical, Organic, and Inorganic Chemistry. One of the concept pillars in Inorganic Chemistry is the study of crystal structures and the interactions of ions within those structures. A firm understanding of topics like IRR and coordination number can significantly enhance a student's problem-solving skills, enabling them to tackle complex questions efficiently.

Concepts like ionic radius ratio and coordination number are not just theoretical; they form the basis of many JEE problems, where students may need to predict crystal structures or properties. Students preparing for JEE should focus on understanding rather than memorizing these concepts, as comprehension will allow them to apply knowledge to a variety of contexts and questions.

Cation and Anion Interaction

The dance between cations and anions is the defining feature of ionic crystals. Positive cations and negative anions are attracted to one another due to electrostatic forces, with cations often becoming surrounded by a specific number of anions - their coordination number. This coordination number depends on the relative size of the ions, explained by the ionic radius ratio discussed earlier. For instance, in the given examples of MgO and MgS, Mg²⁺ would be coordinated differently, which is predicted using the IRR.

Understanding these interactions allows us to predict the crystal structure and the resultant properties of the material, such as its solubility, melting point, and hardness. Such knowledge is essential not just academically for passing exams like the JEE but also for practical applications in material science, pharmaceuticals, and engineering.