Answer :
The 0.5M [tex]MgCl_{2}[/tex]2 solution has the lowest boiling point among the given options. The boiling point elevation is a colligative property that depends on the concentration of solute particles in a solution.
The greater the concentration of solute particles, the higher the boiling point of the solution compared to the pure solvent. In this case, we compare four solutions: 1.5M C_{2}H_{6} solution, 0.75M MgCl_{2} solution, 0.5M MgCl_{2}solution, and 1.5M [tex]C_{3}H_{8}[/tex] solution. Both [tex]C_{2}H_{6}[/tex] and C_{3}H_{8} are non-electrolytes, which means they do not dissociate into ions in solution. Therefore, their effect on boiling point elevation is relatively small compared to ionic solutes. On the other hand, MgCl_{2} is an ionic compound that dissociates into Mg^{+2} and 2[tex]Cl^{-}[/tex] ions in solution, resulting in three particles for every formula unit of MgCl_{2}. The concentration of ions significantly affects boiling point elevation.
Comparing the three MgCl_{2} solutions, the one with the lowest concentration, 0.5M, has the fewest solute particles and thus the lowest boiling point elevation. Therefore, the 0.5MMgCl_{2} solution has the lowest boiling point among the given options.
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