1 `dm^(3)` solution `10^(-5)` moles each of `CI^(-)` ions and `CrO_(4)^(2-)` ions is treated with 10 moles of silver nitrate. Which one of the following observations is made?
`[K_(sp) Ag_(2) CrO_(4) = 4 xx 10^(-12)] & [K_(sp) AgCI = 1 xx 10^(-10)]`

Options

A. percipitation does not occur
B. silver chromate gets precipitated first
C. silver chloride gets precipitated first
D. Both silver chromate and silver chloride start precipitating simultaneously.

Answer

To solve the problem, we need to analyze the precipitation reactions of silver chloride (AgCl) and silver chromate (Ag2CrO4) when silver nitrate (AgNO3) is added to a solution containing chloride ions (Cl^-) and chromate ions (CrO4^2-).

### Step-by-Step Solution:

1. **Identify the Concentrations:**
- The solution contains \(10^{-5}\) moles of Cl^- ions and \(10^{-5}\) moles of CrO4^2- ions in 1 dm³ (1 L) of solution.
- Therefore, the concentrations of these ions are:
- \([Cl^-] = 10^{-5} \, \text{M}\)
- \([CrO4^{2-}] = 10^{-5} \, \text{M}\)

2. **Add Silver Nitrate:**
- We are adding 10 moles of AgNO3 to the solution. Since the volume of the solution is 1 L, the concentration of Ag^+ ions after adding AgNO3 will be:
- \([Ag^+] = 10 \, \text{M}\)

3. **Calculate Ionic Product for AgCl:**
- The ionic product (Q) for the precipitation of AgCl can be calculated as:
\[ Q_{AgCl} = [Ag^+][Cl^-] = (10)(10^{-5}) = 10^{-4} \]
- The solubility product (Ksp) for AgCl is given as \(1 \times 10^{-10}\).
- Since \(Q_{AgCl} = 10^{-4} > Ksp_{AgCl} = 10^{-10}\), a precipitate of AgCl will form.

4. **Calculate Ionic Product for Ag2CrO4:**
- The ionic product (Q) for the precipitation of Ag2CrO4 can be calculated as:
\[ Q_{Ag2CrO4} = [Ag^+]^2[CrO4^{2-}] = (10)^2(10^{-5}) = 10^{2} \times 10^{-5} = 10^{-3} \]
- The solubility product (Ksp) for Ag2CrO4 is given as \(4 \times 10^{-12}\).
- Since \(Q_{Ag2CrO4} = 10^{-3} > Ksp_{Ag2CrO4} = 4 \times 10^{-12}\), a precipitate of Ag2CrO4 will also form.

5. **Conclusion:**
- Both AgCl and Ag2CrO4 will precipitate when silver nitrate is added to the solution containing Cl^- and CrO4^2- ions.

### Final Observation:
Both silver chloride (AgCl) and silver chromate (Ag2CrO4) precipitates will form upon the addition of silver nitrate to the solution.

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