On rising temperature and decreasing pressure in CsCl solid

Options

A. C.N. of metal ion increases from 6 to 8
B. Number of formula unit per unit cell (Z) changes from one to four
C. Density of unit cell is increased
D. `(r_(+))/(r_(-))` (radius ratio) is increased

Answer

### Step-by-Step Solution:

1. **Understanding the Structure of CsCl**:
- CsCl (Cesium Chloride) has a coordination number of 8. This means that each cesium ion (Cs⁺) is surrounded by 8 chloride ions (Cl⁻) and vice versa.

**Hint**: Recall that coordination number indicates how many ions of opposite charge surround a central ion in a crystal lattice.

2. **Effect of Temperature and Pressure**:
- When the temperature increases and pressure decreases, the structure of CsCl can transition to NaCl (Sodium Chloride). NaCl has a coordination number of 6.

**Hint**: Consider how changes in temperature and pressure can affect the stability and arrangement of ions in a crystal lattice.

3. **Change in Coordination Number**:
- The coordination number decreases from 8 (in CsCl) to 6 (in NaCl). This indicates a transition from a higher coordination structure to a lower coordination structure.

**Hint**: Remember that a decrease in coordination number typically means a change in the arrangement of ions.

4. **Formula Units per Unit Cell (Z)**:
- In CsCl, there is 1 formula unit per unit cell (Z = 1). In NaCl, there are 4 formula units per unit cell (Z = 4). Thus, as the structure changes from CsCl to NaCl, Z changes from 1 to 4.

**Hint**: Keep track of how the number of formula units in a unit cell relates to the structure of the solid.

5. **Density of the Unit Cell**:
- The density of a unit cell is given by the formula:
\[ \text{Density} = \frac{Z \cdot M}{N_A \cdot V} \]
where Z is the number of formula units per unit cell, M is the molar mass, \(N_A\) is Avogadro's number, and V is the volume of the unit cell. Since Z increases from 1 to 4, the density will also increase.

**Hint**: Density is directly proportional to the number of formula units per unit cell (Z).

6. **Radius Ratio and Coordination Number**:
- The radius ratio for coordination number 8 is between 0.732 and 1, while for coordination number 6, it is between 0.414 and 0.732. Since the coordination number is decreasing from 8 to 6, the radius ratio will also decrease.

**Hint**: Understand how the radius ratio relates to the stability of the coordination number in ionic compounds.

7. **Conclusion**:
- The correct statements regarding the changes in CsCl as temperature rises and pressure decreases are:
- The number of formula units per unit cell (Z) changes from 1 to 4 (Correct).
- The density of the unit cell increases (Correct).
- The coordination number decreases from 8 to 6 (Incorrect statement in the options).
- The radius ratio decreases (Incorrect statement in the options).

### Final Answer:
- The correct options are:
- Number of formula units per unit cell (Z) changes from 1 to 4.
- Density of the unit cell increases.