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

To analyze the effects of rising temperature and decreasing pressure on cesium chloride (CsCl) solid, we can break down the problem into a series of steps:

### Step 1: Understand the Structure of CsCl
- Cesium chloride (CsCl) has a body-centered cubic (BCC) structure.
- In this structure, the coordination number of the cesium ion (Cs⁺) is 8, and the coordination number of the chloride ion (Cl⁻) is 6.
- The number of formula units (Z) per unit cell for CsCl is 1.

**Hint:** Recall the basic structure of CsCl and its coordination numbers.

### Step 2: Effect of Increasing Temperature
- Increasing temperature generally leads to an increase in the kinetic energy of the particles, which can lead to a decrease in the coordination number.
- For CsCl, as temperature rises, it can transition to a structure similar to sodium chloride (NaCl), which has a coordination number of 6 for Na⁺ and 6 for Cl⁻.

**Hint:** Consider how temperature affects particle movement and coordination numbers.

### Step 3: Effect of Decreasing Pressure
- Decreasing pressure tends to favor structures with higher coordination numbers because particles can spread out more and occupy more space.
- Therefore, while temperature decreases coordination number, decreasing pressure can increase it.

**Hint:** Think about how pressure influences the arrangement of particles in a solid.

### Step 4: Analyze the Options
1. **Coordination number of metal ion increases from 6 to 8**: This is incorrect because increasing temperature decreases the coordination number.

2. **Number of formula units per unit cell (Z) changes from 1 to 4**: This is correct. As CsCl transitions to NaCl-like structure, Z changes from 1 (in BCC) to 4 (in FCC).

3. **Density of unit cell is increased**: This is correct. Since Z increases from 1 to 4, and density (D) is directly proportional to Z, the density of the unit cell will also increase.

4. **r⁺/r⁻ (radius ratio) increases**: This is incorrect. The radius ratio for coordination number 6 is maximum at 0.732, while for coordination number 8, it is less than this value. Thus, the radius ratio decreases with increasing temperature.

**Hint:** Evaluate each statement based on the effects of temperature and pressure on the solid state.

### Conclusion
- The correct statements are:
- The number of formula units per unit cell (Z) changes from 1 to 4.
- The density of the unit cell increases.

**Final Answer:** Options 2 and 3 are correct.