A solution is found to contain `[CI^(Theta)] = 1.5 xx 10^(-1)M, [Br^(Theta)] = 5.0 xx 10^(-4)M, [CrO_(4)^(2-)] = 1.9xx 10^(-2)M`.
A solution of `AgNO_(3)` (100 % dissociated) is added to the above solution drop by drop. Which silver salt will precipiate first ? Given: `K_(sp) (AgCI) = 1.5 xx 10^(-10), K_(sp) (AgBr) = 5.0 xx 10^(-13),K_(sp) (Ag_(2)CrO_(4)) =1.9 xx 10^(-12)`.

Options

A. `AgCI`
B. `AgBr`
C. `Ag_(2)CrO_(4)`
D. `AgCI` and `AgBr` togther

Explanation

To determine which silver salt will precipitate first when adding AgNO₃ to the given solution, we need to calculate the concentration of Ag⁺ required to start the precipitation of each silver salt based on their solubility product constants (Ksp).

### Step-by-Step Solution:

1. **Identify the given concentrations and Ksp values:**
- \([Cl^-] = 1.5 \times 10^{-1} \, M\)
- \([Br^-] = 5.0 \times 10^{-4} \, M\)
- \([CrO_4^{2-}] = 1.9 \times 10^{-2} \, M\)
- \(K_{sp}(AgCl) = 1.5 \times 10^{-10}\)
- \(K_{sp}(AgBr) = 5.0 \times 10^{-13}\)
- \(K_{sp}(Ag_2CrO_4) = 1.9 \times 10^{-12}\)

2. **Calculate the concentration of Ag⁺ required for precipitation of AgCl:**
- The Ksp expression for AgCl is:
\[ K_{sp} = [Ag^+][Cl^-] \]
- Rearranging gives:
\[ [Ag^+] = \frac{K_{sp}}{[Cl^-]} = \frac{1.5 \times 10^{-10}}{1.5 \times 10^{-1}} = 1.0 \times 10^{-9} \, M \]

3. **Calculate the concentration of Ag⁺ required for precipitation of AgBr:**
- The Ksp expression for AgBr is:
\[ K_{sp} = [Ag^+][Br^-] \]
- Rearranging gives:
\[ [Ag^+] = \frac{K_{sp}}{[Br^-]} = \frac{5.0 \times 10^{-13}}{5.0 \times 10^{-4}} = 1.0 \times 10^{-9} \, M \]

4. **Calculate the concentration of Ag⁺ required for precipitation of Ag₂CrO₄:**
- The Ksp expression for Ag₂CrO₄ is:
\[ K_{sp} = [Ag^+]^2[CrO_4^{2-}] \]
- Rearranging gives:
\[ [Ag^+]^2 = \frac{K_{sp}}{[CrO_4^{2-}]} = \frac{1.9 \times 10^{-12}}{1.9 \times 10^{-2}} = 1.0 \times 10^{-10} \]
- Taking the square root gives:
\[ [Ag^+] = \sqrt{1.0 \times 10^{-10}} = 1.0 \times 10^{-5} \, M \]

5. **Compare the concentrations of Ag⁺ required for precipitation:**
- For AgCl: \(1.0 \times 10^{-9} \, M\)
- For AgBr: \(1.0 \times 10^{-9} \, M\)
- For Ag₂CrO₄: \(1.0 \times 10^{-5} \, M\)

6. **Conclusion:**
- The lowest concentration of Ag⁺ required for precipitation is \(1.0 \times 10^{-9} \, M\) for both AgCl and AgBr. Therefore, both AgCl and AgBr will precipitate first when AgNO₃ is added to the solution.

### Final Answer:
Both AgCl and AgBr will precipitate first.