To determine the boiling point of the solution, we need to follow these steps:
1. Identify the given data:
- Moles of solute ([tex]\( K_2SO_4 \)[/tex]): [tex]\( 0.60 \)[/tex] mol
- Mass of solvent (water): [tex]\( 1.0 \)[/tex] kg
- Boiling point elevation constant ([tex]\( K_b \)[/tex]) for water: [tex]\( 0.51 \)[/tex] [tex]\( ^\circ C \cdot kg/mol \)[/tex]
- Boiling point of pure water: [tex]\( 100 \)[/tex] [tex]\( ^\circ C \)[/tex]
2. Calculate the molality ([tex]\( m \)[/tex]) of the solution:
Molality is defined as moles of solute per kilogram of solvent.
[tex]\[
m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} = \frac{0.60 \text{ mol}}{1.0 \text{ kg}} = 0.6 \text{ mol/kg}
\][/tex]
3. Calculate the boiling point elevation ([tex]\( \Delta T_b \)[/tex]) using the formula:
[tex]\[
\Delta T_b = K_b \cdot m
\][/tex]
Substituting the given values:
[tex]\[
\Delta T_b = 0.51 \ ^\circ C \cdot kg/mol \times 0.6 \ \text{mol/kg} = 0.3 \ ^\circ C
\][/tex]
4. Determine the new boiling point of the solution:
The boiling point of the solution is the boiling point of pure water plus the boiling point elevation:
[tex]\[
\text{Boiling point of the solution} = 100 \ ^\circ C + 0.3 \ ^\circ C = 100.3 \ ^\circ C
\][/tex]
Therefore, the boiling point of the solution is [tex]\(\boxed{100.3}\ ^\circ C\)[/tex].
