Which solutions will have the highest boiling point?

1 M \(BaCl_2\) solution

The correct answer is option 1. 1 M \(BaCl_2\) solution.

To determine which solution has the highest boiling point, we need to consider the concept of boiling point elevation, which depends on the concentration of solute particles in the solution. The boiling point elevation is given by:

\(\Delta T_b = i \cdot K_b \cdot m\)

where:

\(\Delta T_b\) is the boiling point elevation

\(i\) is the van 't Hoff factor (the number of particles the solute dissociates into)

\(K_b\) is the ebullioscopic constant of the solvent,

\(m\) is the molality of the solution (which can be approximated as molarity for dilute solutions).

1. 1 M \(BaCl_2\) Solution:

van 't Hoff Factor (\(i\)): \(BaCl_2\) dissociates into 3 ions: \(Ba^{2+}\) and 2 \(Cl^-\). Therefore, \(i = 3\).

Boiling Point Elevation: This solution will have a significant boiling point elevation due to the high \(i\) value.

2. 1 M \(NaCl\) Solution

van 't Hoff Factor (\(i\)): \(NaCl\) dissociates into 2 ions: \(Na^+\) and \(Cl^-\). Therefore, \(i = 2\).

Boiling Point Elevation: This solution has a moderate boiling point elevation compared to \(BaCl_2\) due to the lower \(i\) value.

3. 1 M \(C_6H_{12}O_6\) Solution (Glucose):

van 't Hoff Factor (\(i\)): Glucose does not dissociate in solution; it remains as a single molecule. Therefore, \(i = 1\).

Boiling Point Elevation: This solution will have the least boiling point elevation because \(i\) is the smallest among the options.

4. 1 M \((NH_2)_2CO\) Solution (Urea):

van 't Hoff Factor (\(i\)): Urea does not dissociate in solution; it remains as a single molecule. Therefore, \(i = 1\).

Boiling Point Elevation: This solution will have the same boiling point elevation as the glucose solution, as \(i\) is the same.

Conclusion: The boiling point elevation is directly proportional to the van 't Hoff factor \(i\). Thus, the solution with the highest van 't Hoff factor will have the highest boiling point.

Given that:

\(BaCl_2\) has \(i = 3\),

\(NaCl\) has \(i = 2\),

Glucose and urea have \(i = 1\),

The solution with the highest boiling point will be the 1 M \(BaCl_2\) solution due to its highest van 't Hoff factor.

Thus, the correct answer is 1. 1 M \(BaCl_2\) solution.