Which of the following solution will have the highest freezing point and which will have the lowest freezing point and why ? (i) 0.1 M NaCl solution (ii) 0.1 M glucose solution (iii) 0.1 M `BaCl_(2)` solution

Explanation

To determine which solution has the highest and lowest freezing points among the given options, we need to analyze the freezing point depression, which is described by the formula:

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

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

Since all solutions have the same concentration (0.1 M) and are dissolved in the same solvent (water), we can focus on the van 't Hoff factor \(i\) to compare the freezing points.

### Step 1: Determine the van 't Hoff factor \(i\) for each solute

1. **For NaCl**:
- NaCl dissociates into 2 ions: Na\(^+\) and Cl\(^-\).
- Therefore, \(i = 2\).

2. **For glucose**:
- Glucose does not dissociate in solution; it remains as one molecule.
- Therefore, \(i = 1\).

3. **For BaCl\(_2\)**:
- BaCl\(_2\) dissociates into 3 ions: Ba\(^{2+}\) and 2 Cl\(^-\).
- Therefore, \(i = 3\).

### Step 2: Compare the values of \(i\)

- NaCl: \(i = 2\)
- Glucose: \(i = 1\)
- BaCl\(_2\): \(i = 3\)

### Step 3: Determine the freezing point depression \(\Delta T_f\)

Since \(\Delta T_f\) is directly proportional to \(i\), we can conclude:
- The solution with the highest \(i\) will have the lowest freezing point (most depression).
- The solution with the lowest \(i\) will have the highest freezing point (least depression).

### Step 4: Order the solutions based on freezing point depression

- BaCl\(_2\) has the highest \(i\) (3), so it will have the lowest freezing point.
- NaCl has the next highest \(i\) (2), so it will have a higher freezing point than BaCl\(_2\) but lower than glucose.
- Glucose has the lowest \(i\) (1), so it will have the highest freezing point.

### Conclusion

- **Highest freezing point**: Glucose solution (0.1 M)
- **Lowest freezing point**: BaCl\(_2\) solution (0.1 M)

### Summary of the order of freezing points:
1. Glucose (highest freezing point)
2. NaCl
3. BaCl\(_2\) (lowest freezing point)