For a solution of 0.89 g of mercurous chloride in 50 g of `HgCl_(2)(l)` the freezing point depression id `1.24^(@)`C. `K_(f)` for `HgCl_(2)` is 34.3 . What is the state of mercurous chloride in `HgCL_(2)`? (Hg-200, Cl-35.5).

Options

A. as `Hg_2Cl_2` molecules
B. as `HgCl` molecules
C. as `Hg^+` and `Cl^(-)` ions
D. as `Hg_2^2+ and Cl^(-)` ions

Explanation

To solve the problem, we need to determine the state of mercurous chloride (Hg2Cl2) in a solution of mercurous chloride in mercuric chloride (HgCl2) based on the freezing point depression observed.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Mass of mercurous chloride (Hg2Cl2) = 0.89 g
- Mass of mercuric chloride (HgCl2) = 50 g
- Freezing point depression (ΔTf) = 1.24 °C
- Cryoscopic constant (Kf) for HgCl2 = 34.3 °C kg/mol
- Molar mass of Hg = 200 g/mol
- Molar mass of Cl = 35.5 g/mol

2. **Calculate the Molar Mass of Mercurous Chloride (Hg2Cl2):**
\[ \text{Molar mass of Hg2Cl2} = 2 \times 200 + 2 \times 35.5 = 400 + 71 = 471 \text{ g/mol} \]

3. **Calculate the Number of Moles of Mercurous Chloride:**
\[ \text{Number of moles of Hg2Cl2} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.89 \text{ g}}{471 \text{ g/mol}} \approx 0.00189 \text{ mol} \]

4. **Convert the Mass of Solvent (HgCl2) to kg:**
\[ \text{Mass of HgCl2 in kg} = \frac{50 \text{ g}}{1000} = 0.050 \text{ kg} \]

5. **Calculate the Molality (m) of the Solution:**
\[ m = \frac{\text{number of moles of solute}}{\text{mass of solvent in kg}} = \frac{0.00189 \text{ mol}}{0.050 \text{ kg}} \approx 0.0378 \text{ mol/kg} \]

6. **Use the Freezing Point Depression Formula:**
\[ \Delta T_f = i \cdot K_f \cdot m \]
Rearranging for \(i\):
\[ i = \frac{\Delta T_f}{K_f \cdot m} = \frac{1.24}{34.3 \cdot 0.0378} \]

7. **Calculate \(i\):**
\[ i \approx \frac{1.24}{1.29534} \approx 0.958 \]

8. **Interpret the Value of \(i\):**
Since \(i \approx 1\), this indicates that mercurous chloride does not dissociate or associate in the solution, meaning it remains as Hg2Cl2.

### Conclusion:
The state of mercurous chloride in HgCl2 is that it remains as the intact molecule Hg2Cl2.