To determine which solute will lower the freezing point of water the most, we shall analyze each solute based on the principle of colligative properties. The freezing point depression is directly related to the number of particles the solute dissociates into in a solution. Let's break down each solute:
A. Sucrose [tex]$( C _{12} H _{22} O _{11})$[/tex]:
Sucrose is a molecular compound and doesn't dissociate into ions in an aqueous solution. It remains as a single molecule, thus producing only 1 particle in solution.
B. Magnesium sulfate [tex]$( MgSO _4)$[/tex]:
Magnesium sulfate is an ionic compound. When it dissolves in water, it dissociates into magnesium ions [tex]$( Mg^{2+})$[/tex] and sulfate ions [tex]$( SO_4^{2-})$[/tex]. Therefore, it produces 2 particles in the solution.
C. Lithium chloride [tex]$( LiCl)$[/tex]:
Lithium chloride is also an ionic compound. When dissolved in water, it dissociates into lithium ions [tex]$( Li^+)$[/tex] and chloride ions [tex]$( Cl^-)$[/tex], producing 2 particles in solution.
D. Calcium fluoride [tex]$( CaF _2)$[/tex]:
Calcium fluoride is an ionic compound. It dissociates into one calcium ion [tex]$( Ca^{2+})$[/tex] and two fluoride ions [tex]$( F^-)$[/tex], leading to a total of 3 particles in solution.
Colligative properties, such as the depression of the freezing point, depend on the number of particles in the solution. Since the freezing point is lowered more with an increasing number of particles:
- Sucrose yields 1 particle
- Magnesium sulfate yields 2 particles
- Lithium chloride yields 2 particles
- Calcium fluoride yields 3 particles
Among the given options, calcium fluoride (CaF_2) dissociates into the most particles (3 particles), meaning it will lower the freezing point of water the most.
Thus, the correct answer is:
D. the ionic compound calcium fluoride [tex]$( CaF _2)$[/tex].
