In which of the following the solution of AgSCN will be unsaturated?

Options

A. `[Ag^(+)][SCN^(-)] = K_(sp)`
B. `[Ag^(+)] xx [SCN^(-)] lt K_(sp)`
C. `[Ag^(+)] xx [SCN^(-)] gt K_(sp)`
D. `[Ag^(+)] [SCN]^(2) lt K_(sp)`

Answer

To determine in which solution the concentration of AgSCN will be unsaturated, we need to understand the concepts of saturated and unsaturated solutions, particularly in relation to the solubility product constant (Ksp).

### Step-by-Step Solution:

1. **Understand Saturated vs. Unsaturated Solutions**:
- A **saturated solution** is one in which the maximum amount of solute has dissolved in a solvent at a given temperature. In this case, the concentration of the solute ions (Ag⁺ and SCN⁻) is equal to the solubility product constant (Ksp).
- An **unsaturated solution** is one where less solute is present than the maximum amount that can dissolve. Here, the concentration of the solute ions is less than the Ksp.

2. **Identify the Ksp of AgSCN**:
- The dissociation of AgSCN in water can be represented as:
\[ \text{AgSCN (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{SCN}^- (aq) \]
- The Ksp expression for this equilibrium is:
\[ Ksp = [\text{Ag}^+][\text{SCN}^-] \]
- For a solution to be saturated, the product of the concentrations of Ag⁺ and SCN⁻ must equal the Ksp value.

3. **Evaluate Given Options**:
- We need to evaluate the given options to see which one results in a concentration of Ag⁺ and SCN⁻ that is less than the Ksp.
- If any option provides a concentration of Ag⁺ and SCN⁻ that, when multiplied, is less than the Ksp, that solution will be unsaturated.

4. **Conclusion**:
- After evaluating the options, we find that option 2 provides a scenario where the concentration of Ag⁺ and SCN⁻ is indeed less than the Ksp value.
- Therefore, the solution of AgSCN in option 2 is unsaturated.

### Final Answer:
The solution of AgSCN will be unsaturated in option 2.