For this problem, we use the freezing point depression formula:
Tf,solvent - Tf,solution = Kf×m
Where
Tf,solvent is freezing pt of the solvent
Tf,solution is freezing pt of solution
Kf is the molal freezing point depression constant of the solvent
m is the molality equal to mol solute/kg solvent
For water as solvent, Tf,solvent = 0°C; Kf = 1.86 °C/m:
0°C - ⁻10.5 °C = (1.86 °C/m)(m)
Solving for m,
m = 5.645 mol solute/kg solvent
5.645 = mol solute/1 kg water
mol solute = 5.645 mol fructose
Since the molar massof fructose is 180.16 g/mol,
Mass of Fructose = 5.645 mol * 180.16 g/mol
Mass of Fructose = 1,017.03 g fructose or 1.017 kg fructose
