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 can use the formula for freezing point depression:

\[ \Delta T_f = i \cdot K_f \cdot m \]

Where:
- \(\Delta T_f\) = change in freezing point
- \(i\) = van't Hoff factor (number of particles the solute dissociates into)
- \(K_f\) = freezing point depression constant of the solvent
- \(m\) = molality of the solution

Since the concentration is given in molarity (0.1 M), we will consider \(m\) as 0.1 for our calculations. The freezing point depression constant \(K_f\) is a property of the solvent and will remain constant for all solutions, so we can focus on maximizing the value of \(i\) to find the solution with the lowest freezing point.

### Step-by-Step Solution:

1. **Identify the compounds and their dissociation:**
- **Compound 1:** A double salt (e.g., \(Fe(NH_4)(SO_4)_2\)) dissociates into 5 ions: \(Fe^{3+} + 2NH_4^+ + 2SO_4^{2-}\) → \(i = 5\).
- **Compound 2:** A coordination complex (e.g., \(CrCl_2(NH_3)\)) dissociates into 2 ions: \(CrCl_2 + 2NH_3\) → \(i = 2\).
- **Compound 3:** Another complex (e.g., \(K_3[Fe(CN)_6]\)) dissociates into 4 ions: \(3K^+ + [Fe(CN)_6]^{3-}\) → \(i = 4\).
- **Compound 4:** Another coordination complex (e.g., \(CoCl_2(NH_3)_5\)) dissociates into 3 ions: \(Co^{2+} + 2Cl^-\) → \(i = 3\).

2. **Calculate the van't Hoff factor (i) for each compound:**
- Compound 1: \(i = 5\)
- Compound 2: \(i = 2\)
- Compound 3: \(i = 4\)
- Compound 4: \(i = 3\)

3. **Determine which compound has the highest van't Hoff factor:**
- The highest \(i\) is for Compound 1, which has \(i = 5\).

4. **Conclusion:**
- Since the freezing point depression \(\Delta T_f\) is directly proportional to \(i\), the compound with the highest \(i\) will have the lowest freezing point. Therefore, the 0.1 M solution of Compound 1 will have the lowest freezing point.

### Final Answer:
The 0.1 M solution of the double salt (Compound 1) will have the lowest freezing point.

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