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Answer :
Final answer:
The salt that would lower the freezing point the most is 1.25m Na₂SO₄, as it has the highest effective particle concentration when considering the van't Hoff factor (the number of ions each solute dissociates into) multiplied by the molality. So, the correct option is b) 1.25m Na₂SO₄.
Explanation:
Freezing Point Depression
The freezing point of a solvent is lowered when a solute is dissolved in it, and this effect is dependent on the number of particles the solute provides once dissociated. Colligative properties, such as freezing point depression, are properties that depend on the concentration of solute particles rather than the identity of the solute itself. The more particles dissolved in the solvent, the more the freezing point is lowered.
To determine which salt would lower the freezing point of a solvent the most, we need to consider both the concentration of the solution and how many ions each formula unit of the solute breaks into. For instance, NaCl breaks into 2 ions (Na+ and Cl-), Na2SO4 breaks into 3 ions (2 Na+ and SO42-), Li3PO4 breaks into 4 ions (3 Li+ and PO43-), and CaCl2 breaks into 3 ions (Ca2+ and 2 Cl-).
To find the solution that lowers the freezing point the most, we can multiply the van't Hoff factor (i.e., the number of ions the solute dissociates into) by the molality of the solution. This gives us the effective particle concentration, often referred to as the i-value:
NaCl: 1.5m x 2 = 3
Na2SO4: 1.25m x 3 = 3.75
Li3PO4: 0.4m x 4 = 1.6
CaCl2: 0.5m x 3 = 1.5
Based on the i-value, the salt that would lower the freezing point the most is 1.25m Na2SO4 since it results in the highest effective particle concentration.
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