To understand why a 1.0 M KOH solution has the least boiling point among the given options, we need to consider the properties of the solute and its effect on boiling point elevation.


Boiling point elevation is a colligative property that depends on the number of solute particles present in a solution. When a non-volatile solute is dissolved in a solvent, the boiling point of the resulting solution increases compared to the pure solvent.


Electrolytes, which dissociate into ions in solution, have a greater effect on boiling point elevation compared to non-electrolytes. This is because electrolytes produce more solute particles per formula unit when they dissociate.


Let's compare the given solutions to determine which one will have the least boiling point:

1.0 M KOH:
- KOH is an electrolyte that dissociates into K⁺ and OH⁻ ions in solution.
- The dissociation equation is: KOH → K⁺ + OH⁻.
- For every mole of KOH, it produces one mole of K⁺ and one mole of OH⁻ ions.
- Therefore, the solution contains three particles for every mole of KOH: one KOH molecule, one K⁺ ion, and one OH⁻ ion.

1.0 M (NH₄)₂SO₄:
- (NH₄)₂SO₄ is an electrolyte that dissociates into NH₄⁺ and SO₄^2- ions in solution.
- The dissociation equation is: (NH₄)₂SO₄ → 2NH₄⁺ + SO₄^2-.
- For every mole of (NH₄)₂SO₄, it produces two moles of NH₄⁺ ions and one mole of SO₄^2- ions.
- Therefore, the solution contains three particles for every mole of (NH₄)₂SO₄: one (NH₄)₂SO₄ molecule, two NH₄⁺ ions, and one SO₄^2- ion.

1.0 M K₂CO₃:
- K₂CO₃ is an electrolyte that dissociates into 2K⁺ and CO