Addition of `CdCl_(2)` to AgCl yields solid solution where the divalent cations `Cd^(2+)` occupy the `Ag^(+)` sites. Which one of the following statements is true ?

Options

A. The no of cationic vacancies is equal to that of divalent ions added.
B. The no. of cationic vacancies is one half of the no. of that of divalent ions added.
C. The no. of anionic vacancies is equal in no. to that of divalent ions added.
D. No cationic or anionic vacancies are produced.

Explanation

To solve the question regarding the addition of `CdCl₂` to `AgCl` and the resulting solid solution, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Components**:
- `AgCl` is a compound where `Ag^+` ions are the cations and `Cl^-` ions are the anions.
- `CdCl₂` contains `Cd^2+` ions (divalent cations) and `Cl^-` ions.

2. **Substitution in the Crystal Lattice**:
- When `CdCl₂` is added to `AgCl`, the `Cd^2+` ions occupy the sites of `Ag^+` ions in the crystal lattice of `AgCl`.
- Since `Cd^2+` has a +2 charge, it will replace two `Ag^+` ions (each with a +1 charge) to maintain charge neutrality.

3. **Charge Balance**:
- For every `Cd^2+` ion that replaces `2 Ag^+` ions, there is a need to maintain the overall charge balance in the crystal structure.
- The replacement of `2 Ag^+` ions by `1 Cd^2+` ion creates a cation vacancy because the total positive charge needs to be balanced.

4. **Cation Vacancies**:
- The substitution of `1 Cd^2+` ion results in the generation of `1 cation vacancy` because it replaces `2 Ag^+` ions.
- Therefore, for every `n` divalent `Cd^2+` ions added, `n` cation vacancies are generated.

5. **Evaluating the Statements**:
- The question asks which statement is true regarding the relationship between the number of cation vacancies and the divalent ions added.
- The correct statement is that the number of cation vacancies is equal to the number of divalent ions added.

### Conclusion:
The true statement is: **The number of cation vacancies is equal to that of divalent ions added.**