The precipitate of `Ag_(2)CrO_(4)(K_("sp") = 1.9 xx 10^(-12))` is obtained when equal volumes of the following are mixed.

Options

A. `10^(-4)M Ag^(+) + 10^(-4) M CrO_(4)^(2-)`
B. `10^(-2)M Ag^(+) + 10^(-3) M`
C. `10^(-5)M Ag^(+)+ 10^(-3) M`
D. `10^(-4)M Ag^(+) + 10^(-5) M`

Explanation

To determine when the precipitate of `Ag2CrO4` will form upon mixing equal volumes of solutions containing `Ag^+` and `CrO4^2-`, we need to calculate the ionic product (IP) and compare it with the solubility product constant (Ksp) of `Ag2CrO4`.

### Step-by-Step Solution:

1. **Understand the Reaction**:
The formation of the precipitate can be represented by the following equilibrium:
\[ Ag^+ + CrO_4^{2-} \rightleftharpoons Ag_2CrO_4 (s) \]

2. **Write the Expression for Ksp**:
The solubility product expression for `Ag2CrO4` is given by:
\[ K_{sp} = [Ag^+]^2 [CrO_4^{2-}] \]
Given that \( K_{sp} = 1.9 \times 10^{-12} \).

3. **Define Molar Solubility**:
Let the molar solubility of `Ag2CrO4` be \( S \). When `Ag2CrO4` dissolves, it produces:
- 2 moles of `Ag^+` for every mole of `Ag2CrO4`
- 1 mole of `CrO4^{2-}` for every mole of `Ag2CrO4`

Therefore, at equilibrium:
\[ [Ag^+] = 2S \quad \text{and} \quad [CrO_4^{2-}] = S \]

4. **Mixing Equal Volumes**:
When equal volumes of solutions are mixed, the concentrations of the ions will be halved. If the initial concentrations of `Ag^+` and `CrO4^{2-}` are \( C_{Ag} \) and \( C_{CrO4} \) respectively, after mixing:
\[ [Ag^+] = \frac{C_{Ag}}{2} \quad \text{and} \quad [CrO_4^{2-}] = \frac{C_{CrO4}}{2} \]

5. **Calculate the Ionic Product (IP)**:
The ionic product can be calculated using the concentrations after mixing:
\[ IP = \left(\frac{C_{Ag}}{2}\right)^2 \left(\frac{C_{CrO4}}{2}\right) \]
Simplifying gives:
\[ IP = \frac{C_{Ag}^2}{4} \cdot \frac{C_{CrO4}}{2} = \frac{C_{Ag}^2 \cdot C_{CrO4}}{8} \]

6. **Compare IP with Ksp**:
For precipitation to occur, the ionic product must exceed the solubility product:
\[ IP > K_{sp} \]
Substitute the calculated IP into this inequality to determine if precipitation occurs.

7. **Evaluate Different Cases**:
You will need to evaluate the concentrations given in the options to find the correct one where \( IP > K_{sp} \).