Final answer:
Pure distilled water will have the highest freezing point among the options given because it has no dissolved particles, and therefore does not experience freezing point depression unlike the other solutions listed which contain solutes that lower their freezing points.
Step-by-step explanation:
The student is asking about the relative freezing points of various solutions compared to pure water. In order to determine which solution has the highest freezing point, we turn to the principle that the freezing point of a solution is dependent on the concentration of dissolved particles it contains. Freezing point depression is the effect where the freezing point of a liquid (a solvent) is lowered by adding another compound to it (a solute), which makes the solvent less likely to go into a solid phase.
Pure water's freezing point is 0°C, so solutions with dissolved particles will have a lower freezing point depending on the concentration of the particles. For ionic compounds, such as LiClO₄ and CaSO₄, each unit dissociates into multiple ions; thus, they have a greater effect on lowering the freezing point than a compound like C₆H₁₂O₆, which does not dissociate into ions. For the given solutions, pure distilled water will have the highest freezing point because it does not contain any solutes, and therefore has no freezing point depression. Comparatively, the 1.0 m LiClO₄ solution will produce two particles per formula unit, the 1.0 m CaSO₄ will produce three particles per formula unit, and the 0.75 m (NH₄)₃PO₄ will produce four particles per formula unit, hence these solutions will all have lower freezing points than distilled water.
The 2.0 m C₆H₁₂O₆ solution, although having a higher molality, will not produce additional particles since sucrose does not ionize. Therefore, its freezing point depression will be less than those of ionic compounds, yet still lower than that of pure water. Conclusively, pure distilled water will have the highest freezing point among the options given due to absence of solutes.