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 whether the solution of AgSCN (Silver thiocyanate) is unsaturated, we need to analyze the solubility product constant (Ksp) and the reaction quotient (Q) of the dissolution process. Here’s a step-by-step solution:

### Step 1: Understand the Dissolution of AgSCN
When AgSCN dissolves in water, it dissociates into its ions:
\[ \text{AgSCN (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{SCN}^- (aq) \]

### Step 2: Write the Expression for Ksp
The solubility product constant (Ksp) for this equilibrium can be expressed as:
\[ K_{sp} = [\text{Ag}^+][\text{SCN}^-] \]

### Step 3: Define Q and Compare with Ksp
The reaction quotient (Q) is calculated using the same expression as Ksp, but it reflects the concentrations of the ions at any given moment, not necessarily at equilibrium:
\[ Q = [\text{Ag}^+][\text{SCN}^-] \]

### Step 4: Determine Conditions for Unsaturation
A solution is considered unsaturated if more solute can be added without causing precipitation. This occurs when:
\[ Q < K_{sp} \]
This means that the product of the concentrations of the ions is less than the solubility product, indicating that the solution can still dissolve more solute.

### Step 5: Identify the Correct Option
From the given options, we need to find the scenario where the concentration of Ag\(^+\) and SCN\(^-\) ions results in \( Q < K_{sp} \). The option that satisfies this condition will indicate that the solution of AgSCN is unsaturated.

### Conclusion
Based on the analysis, the solution of AgSCN will be unsaturated in the case where the ionic product (Q) is less than the Ksp value.