Which of the following will have the highest boiling point at `1 atm` pressure?

Options

A. `0.1 M NaCl`
B. `0.1 M sucrose`
C. `0.1 M BaCl_(2)`
D. `0.1 M glucose`

Explanation

To determine which of the given substances will have the highest boiling point at 1 atm pressure, we can use the concept of boiling point elevation, which is influenced by the van 't Hoff factor (i). The boiling point elevation can be described by the formula:

\[ \Delta T_b = i \cdot K_b \cdot m \]

Where:
- \(\Delta T_b\) = boiling point elevation
- \(i\) = van 't Hoff factor (number of particles the solute dissociates into)
- \(K_b\) = ebullioscopic constant of the solvent
- \(m\) = molality of the solution

### Step-by-Step Solution:

1. **Identify the van 't Hoff factor (i)** for each solute:
- **NaCl**: Dissociates into 2 ions (Na\(^+\) and Cl\(^-\)), so \(i = 2\).
- **BaCl\(_2\)**: Dissociates into 3 ions (Ba\(^{2+}\) and 2 Cl\(^-\)), so \(i = 3\).
- **Glucose**: A non-electrolyte that does not dissociate, so \(i = 1\).
- **Cross**: Assuming this is another non-electrolyte, \(i = 1\).

2. **Compare the van 't Hoff factors**:
- NaCl: \(i = 2\)
- BaCl\(_2\): \(i = 3\)
- Glucose: \(i = 1\)
- Cross: \(i = 1\)

3. **Determine which substance has the highest van 't Hoff factor**:
- The highest \(i\) value is for BaCl\(_2\) with \(i = 3\).

4. **Conclusion**:
- Since the boiling point elevation (\(\Delta T_b\)) is directly proportional to \(i\), the substance with the highest boiling point at 1 atm pressure will be BaCl\(_2\).

Thus, the answer to the question is **BaCl\(_2\)**, which has the highest boiling point at 1 atm pressure.