The concentration of suphide ion in `0.1 M HCl` solution saturated with hydrogen sulphide is `1.0xx10^(-19)M`. If `10 mL` of this is added to `5 mL` of `0.04 M` solution of the following: `FeSO_(4), MnCl_(2), ZnCl_(z)` and `CdCl_(2)`. In which of these solutions precipitation will take place?

Explanation

To solve the problem, we need to determine whether precipitation occurs when a solution containing sulfide ions is mixed with solutions of various metal salts. The precipitation condition is met when the reaction quotient (Qsp) is greater than the solubility product constant (Ksp) for the respective metal sulfides.

### Step-by-Step Solution:

1. **Identify the Concentration of Sulfide Ion (S²⁻):**
The concentration of sulfide ions in the saturated solution is given as \(1.0 \times 10^{-19} \, M\).

2. **Calculate the New Concentration of Sulfide Ion After Mixing:**
When 10 mL of the sulfide ion solution is added to 5 mL of the metal salt solution, the total volume becomes 15 mL. The new concentration of sulfide ions can be calculated as follows:
\[ \text{New Concentration of } S^{2-} = \frac{(1.0 \times 10^{-19} \, M) \times 10 \, mL}{15 \, mL} = \frac{1.0 \times 10^{-18}}{15} = 6.67 \times 10^{-20} \, M \]

3. **Determine the Concentration of Metal Ions (M²⁺):**
The concentration of the metal ions (Fe²⁺, Mn²⁺, Zn²⁺, Cd²⁺) in the 5 mL solution is:
\[ \text{Concentration of } M^{2+} = \frac{(0.04 \, M) \times 5 \, mL}{15 \, mL} = \frac{0.2}{15} = 0.0133 \, M \]

4. **Calculate the Reaction Quotient (Qsp):**
The Qsp for the precipitation of metal sulfides (e.g., \(M^{2+} + S^{2-} \rightarrow MS\)) is given by:
\[ Qsp = [M^{2+}][S^{2-}] = (0.0133 \, M) \times (6.67 \times 10^{-20} \, M) = 8.87 \times 10^{-22} \]

5. **Compare Qsp with Ksp Values:**
We need to compare Qsp with the Ksp values for the respective metal sulfides:
- \(Ksp \, \text{for } FeS = 6.3 \times 10^{-18}\)
- \(Ksp \, \text{for } MnS = 2.5 \times 10^{-13}\)
- \(Ksp \, \text{for } ZnS = 1.6 \times 10^{-24}\)
- \(Ksp \, \text{for } CdS = 8.0 \times 10^{-27}\)

6. **Determine Precipitation:**
- For \(FeS\): \(Qsp = 8.87 \times 10^{-22} < Ksp = 6.3 \times 10^{-18}\) (No precipitation)
- For \(MnS\): \(Qsp = 8.87 \times 10^{-22} < Ksp = 2.5 \times 10^{-13}\) (No precipitation)
- For \(ZnS\): \(Qsp = 8.87 \times 10^{-22} > Ksp = 1.6 \times 10^{-24}\) (Precipitation occurs)
- For \(CdS\): \(Qsp = 8.87 \times 10^{-22} > Ksp = 8.0 \times 10^{-27}\) (Precipitation occurs)

### Conclusion:
Precipitation will take place in the solutions of **ZnCl₂** and **CdCl₂**.