In chromium (III) chloride `CrCl_(3)` chloride ions have cubic close packed arrangement and Cr (III) ions present in the octahedral voids. What fraction of the octahedral void is occupied ? What fraction of the total number of voids is occupied?

Explanation

To solve the problem, we need to determine two fractions: the fraction of octahedral voids occupied by Cr(III) ions and the fraction of the total number of voids that are occupied.

### Step-by-Step Solution:

1. **Understanding the Arrangement**:
- In chromium (III) chloride (CrCl₃), the chloride ions (Cl⁻) are arranged in a cubic close-packed (CCP) structure.

2. **Identifying the Number of Ions**:
- In a CCP arrangement, for every 1 unit cell, there are 4 chloride ions (since each unit cell contains 8 corner atoms and 6 face-centered atoms, contributing to 4 whole atoms).

3. **Calculating the Number of Voids**:
- For each chloride ion in a CCP structure:
- There are 2 tetrahedral voids.
- There is 1 octahedral void.
- Therefore, for 4 chloride ions:
- Total tetrahedral voids = 4 ions × 2 = 8 tetrahedral voids.
- Total octahedral voids = 4 ions × 1 = 4 octahedral voids.
- Thus, the total number of voids = 8 (tetrahedral) + 4 (octahedral) = 12 voids.

4. **Determining the Number of Cr(III) Ions**:
- In CrCl₃, there is 1 Cr(III) ion for every 3 Cl⁻ ions. Thus, in the arrangement with 4 Cl⁻ ions, there will be:
- Number of Cr(III) ions = 4 Cl⁻ ions / 3 = 1.33 (approximately 1 Cr(III) ion for practical purposes).

5. **Calculating the Fraction of Octahedral Voids Occupied**:
- Since there are 4 octahedral voids and 1 Cr(III) ion occupies 1 of these voids:
- Fraction of octahedral voids occupied = Number of Cr(III) ions / Total octahedral voids = 1 / 4.

6. **Calculating the Fraction of Total Voids Occupied**:
- The total number of voids is 12 (as calculated earlier).
- Fraction of total voids occupied = Number of Cr(III) ions / Total voids = 1 / 12.

### Final Answers:
- Fraction of octahedral voids occupied by Cr(III) ions = **1/4**.
- Fraction of total voids occupied = **1/12**.