`Hg_(2)Cl_(2)(g)` in saturated aqeous solution has equilibrium constant equal to `:`

Options

A. `[Hg^(+)][Cl^(-)]`
B. `[hg^(+)]^(2)[Cl^(-)]^(2)`
C. `[Hg_(2)^(+2)][Cl^(-)]^(2)`
D. `2[Hg^(+)]xx2[Cl^(-)]`

Answer

To find the equilibrium constant for the dissociation of \( \text{Hg}_2\text{Cl}_2 \) in a saturated aqueous solution, we can follow these steps:

### Step 1: Write the dissociation reaction
The dissociation of mercurous chloride (\( \text{Hg}_2\text{Cl}_2 \)) in water can be represented as:
\[ \text{Hg}_2\text{Cl}_2 (s) \rightleftharpoons \text{Hg}^{2+} (aq) + 2 \text{Cl}^- (aq) \]

### Step 2: Define the equilibrium constant expression
The equilibrium constant \( K \) for the reaction can be expressed in terms of the concentrations of the products and reactants. For the reaction above, the equilibrium constant expression is:
\[ K = \frac{[\text{Hg}^{2+}][\text{Cl}^-]^2}{[\text{Hg}_2\text{Cl}_2]} \]

### Step 3: Consider the state of the reactant
Since \( \text{Hg}_2\text{Cl}_2 \) is a solid, its concentration is constant and does not appear in the equilibrium expression. Therefore, we can simplify the expression to:
\[ K = [\text{Hg}^{2+}][\text{Cl}^-]^2 \]

### Step 4: Assume concentrations
In a saturated solution, the concentrations of \( \text{Hg}^{2+} \) and \( \text{Cl}^- \) can be represented as:
- Let \( [\text{Hg}^{2+}] = x \)
- Then, \( [\text{Cl}^-] = 2x \) (since two chloride ions are produced for each formula unit of \( \text{Hg}_2\text{Cl}_2 \))

### Step 5: Substitute into the equilibrium expression
Substituting these values into the equilibrium expression gives:
\[ K = (x)(2x)^2 = x(4x^2) = 4x^3 \]

### Step 6: Conclusion
The equilibrium constant \( K \) for the dissociation of \( \text{Hg}_2\text{Cl}_2 \) in a saturated aqueous solution is:
\[ K = 4x^3 \]
However, without specific values for \( x \), we cannot calculate a numerical value for \( K \). The expression \( K = 4x^3 \) is the final answer.