Understanding the Chemistry
* Gold(I) Chloride (AuCl): AuCl is a sparingly soluble ionic compound. It dissolves in water to a small extent, forming gold(I) ions (Au+) and chloride ions (Cl-).
* Common Ion Effect: The presence of NaCl (a source of chloride ions) in the solution will decrease the solubility of AuCl. This is because the added chloride ions shift the equilibrium of the dissolution reaction to the left, favoring the formation of solid AuCl.
Calculations
1. Equilibrium: Write the equilibrium reaction for the dissolution of AuCl:
```
AuCl(s) <=> Au+(aq) + Cl-(aq)
```
2. Solubility Product: We need the solubility product constant (Ksp) for AuCl. This value is not readily available as AuCl is not a very common compound. You'll likely need to look it up in a specialized reference. For this example, let's assume a hypothetical Ksp value of 1.0 x 10^-10.
3. ICE Table: Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations:
| | Au+ | Cl- |
|--------------|--------|------------|
| Initial | 0 | 0.2 |
| Change | +s | +s |
| Equilibrium | s | 0.2 + s |
* "s" represents the molar solubility of AuCl.
4. Ksp Expression: Write the Ksp expression:
```
Ksp = [Au+][Cl-]
```
5. Substitute and Solve: Substitute the equilibrium concentrations from the ICE table into the Ksp expression and solve for "s":
```
1.0 x 10^-10 = (s)(0.2 + s)
```
Since Ksp is very small, we can make the simplifying assumption that 0.2 + s ≈ 0.2. This simplifies the calculation:
```
1.0 x 10^-10 = (s)(0.2)
s = 5.0 x 10^-10 M
```
Conclusion
The solubility of AuCl in a 0.2 M NaCl solution is approximately 5.0 x 10^-10 M. This value is significantly lower than the solubility of AuCl in pure water, demonstrating the common ion effect.
Important Notes:
* Finding Ksp: The Ksp value for AuCl is crucial for this calculation. It is important to locate a reliable source for this information.
* Assumptions: The assumption that 0.2 + s ≈ 0.2 is valid because Ksp is very small. If Ksp were larger, a more rigorous solution using the quadratic formula would be necessary.
* Real-World Considerations: The solubility of AuCl can be affected by other factors like pH, temperature, and the presence of other complexing agents.
