0.1 M solution of which of the following compounds will have the lowest freezing point ?

Options

A. `FeSO_4.(NH_4)_2SO_4.6H_2O`
B. `[CrCl_2(NH_3)]Cl`
C. `K_3[Fe(CN)_6]`
D. `[Co(Cl)(NH_3)_5]Cl_2`

Answer

To determine which 0.1 M solution will have the lowest freezing point, we need to analyze the depression in freezing point (ΔTf) for each compound. The depression in freezing point is given by the formula:

\[ \Delta Tf = i \cdot Kf \cdot C \]

Where:
- ΔTf = depression in freezing point
- i = van 't Hoff factor (number of particles the solute dissociates into)
- Kf = cryoscopic constant of the solvent (which remains constant for the same solvent)
- C = concentration of the solution (0.1 M for all options)

Since the concentration (C) and Kf are the same for all solutions, the depression in freezing point will depend solely on the van 't Hoff factor (i). The higher the value of i, the greater the depression in freezing point, and thus the lower the freezing point.

Let's analyze the given compounds:

1. **CrCl2**: This compound dissociates into 3 ions:
\[ \text{CrCl}_2 \rightarrow \text{Cr}^{3+} + 2 \text{Cl}^- \]
Here, i = 3.

2. **K3[Fe(CN)6]**: This compound dissociates into 4 ions:
\[ \text{K}_3[\text{Fe(CN)}_6] \rightarrow 3 \text{K}^+ + \text{Fe(CN)}_6^{3-} \]
Here, i = 4.

3. **CoCl2·6H2O**: This compound dissociates into 3 ions:
\[ \text{CoCl}_2 \rightarrow \text{Co}^{2+} + 2 \text{Cl}^- \]
Here, i = 3.

4. **NH4Cl**: This compound dissociates into 2 ions:
\[ \text{NH}_4\text{Cl} \rightarrow \text{NH}_4^+ + \text{Cl}^- \]
Here, i = 2.

Now, we can summarize the van 't Hoff factors for each compound:
- CrCl2: i = 3
- K3[Fe(CN)6]: i = 4
- CoCl2·6H2O: i = 3
- NH4Cl: i = 2

Since K3[Fe(CN)6] has the highest van 't Hoff factor (i = 4), it will produce the greatest depression in freezing point.

Thus, the 0.1 M solution of **K3[Fe(CN)6]** will have the lowest freezing point.

### Summary of Steps:
1. Understand the formula for depression in freezing point.
2. Identify the van 't Hoff factor (i) for each compound.
3. Compare the values of i to determine which compound will have the lowest freezing point.
4. Conclude that K3[Fe(CN)6] has the lowest freezing point due to the highest i value.