Problem: A solution is prepared by dissolving 456 g of sucrose (C12H22O11, molar mass 342 g/mol) in 764 g of water (18.02 g/mol; density 1.00 g/mL) calculate:d) How many grams of Ca 3 (PO4)2 must be added to 764g of water to have the same effect?

We’re being asked to calculate the mass of Ca₃(PO₄)₂ needed to achieve the freezing point of the solution as the one given with sucrose. 

Recall that the freezing point of a solution is lower than that of the pure solvent and the change in freezing point (ΔT­_f) is given by:

$\boxed{{\mathbf{\Delta T}}_{\mathbf{f}}\mathbf{=}{\mathbf{T}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{pure}\mathbf{ }\mathbf{solvent}}\mathbf{-}{\mathbf{T}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{solution}}}$

The change in freezing point is also related to the molality of the solution:

$\boxed{{\mathbf{\Delta T}}_{\mathbf{f}}\mathbf{=}{\mathbf{imK}}_{\mathbf{f}}}$

where:

i = van’t Hoff factor

m = molality of the solution (in m or mol/kg)

K_f = freezing point depression constant (in ˚C/m) of the solvent

We go through the following steps to solve the problem: 

Step 1. Calculate the molality of the solution

Step 2. Calculate the moles of the solute

Step 3. Calculate the mass of the solute