To determine which of the metal sulfides (CuS, FeS, MnS, and CdS) will precipitate when saturated with H2S in a 0.1 M HCl solution, we need to compare the ion product of each salt with its solubility product (Ksp). The ion product is calculated using the concentration of the sulfide ion (S2-) and the concentration of the metal ion in solution.
Understanding the Ion Product
The ion product (Q) for a salt like MX (where M is a metal and X is the anion) is given by the formula:
Here, [M^n+] is the concentration of the metal ion, and [S^2-] is the concentration of the sulfide ion. If Q exceeds the Ksp of the salt, precipitation occurs.
Given Data
From the problem, we have:
- [S^2-] = 10-23 M
- [M^n+] for each salt = 0.01 M
- Ksp for CuS = 10-44
- Ksp for FeS = 10-14
- Ksp for MnS = 10-15
- Ksp for CdS = 10-26
Calculating the Ion Products
Now, let's calculate the ion products for each metal sulfide:
1. For CuS
QCuS = [Cu2+][S2-] = (0.01)(10-23) = 10-25
Since QCuS (10-25) is greater than Ksp (10-44), CuS will precipitate.
2. For FeS
QFeS = [Fe2+][S2-] = (0.01)(10-23) = 10-25
Here, QFeS (10-25) is greater than Ksp (10-14), so FeS will also precipitate.
3. For MnS
QMnS = [Mn2+][S2-] = (0.01)(10-23) = 10-25
In this case, QMnS (10-25) is greater than Ksp (10-15), indicating that MnS will precipitate as well.
4. For CdS
QCdS = [Cd2+][S2-] = (0.01)(10-23) = 10-25
For CdS, QCdS (10-25) is greater than Ksp (10-26), which means CdS will precipitate too.
Summary of Precipitation
Based on the calculations:
- CuS will precipitate.
- FeS will precipitate.
- MnS will precipitate.
- CdS will precipitate.
All four metal sulfides will precipitate when saturated with H2S in a 0.1 M HCl solution, as their ion products exceed their respective solubility products. This illustrates the importance of understanding solubility equilibria in predicting precipitation reactions in chemistry.
