Assertion:Addition of silver ions to a mixture of aqueos sodium chloride and sodium bromide solution will first precipitate AgBr than AgCl.
`K_(sp)` of `AgCl gt K_(sp)` of AgBr.

Options

A. If both assertion and reason are true and reason is the explaination of assertion.
B. If both assertion and reason are true but reason is not the correct explaination of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To solve the given assertion and reason question, we need to analyze both statements carefully.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that when silver ions are added to a mixture of aqueous sodium chloride (NaCl) and sodium bromide (NaBr), AgBr will precipitate first, followed by AgCl.

2. **Understanding the Reason**:
The reason provided states that the solubility product (Ksp) of AgCl is greater than that of AgBr.

3. **Analyzing the Solubility Products**:
- The solubility product (Ksp) of AgBr is given as \(5 \times 10^{-13}\).
- The solubility product (Ksp) of AgCl is given as \(5 \times 10^{-10}\).

4. **Comparing Ksp Values**:
Since \(Ksp\) of AgCl (\(5 \times 10^{-10}\)) is greater than \(Ksp\) of AgBr (\(5 \times 10^{-13}\)), this indicates that AgBr is less soluble than AgCl. Therefore, AgBr will precipitate first when silver ions are added to the solution.

5. **Conclusion on Assertion**:
The assertion is true because AgBr will indeed precipitate before AgCl due to its lower solubility.

6. **Conclusion on Reason**:
The reason is false because it incorrectly states that the solubility product of AgCl is greater than that of AgBr. In fact, AgBr has a lower Ksp, which means it is less soluble and will precipitate first.

7. **Final Evaluation**:
Since the assertion is true and the reason is false, the correct answer is that the assertion is true, but the reason is false.

### Final Answer:
The assertion is true, and the reason is false.