Question

At −12.5 ∘C, a common temperature for household freezers, what is the maximum mass of fructose (C6H12O6) you can add to 2.50 kg of pure water and still have the solution freeze? Assume that fructose is a molecular solid and does not ionize when it dissolves in water.

Answer 1

To determine the maximum mass of fructose that can be added without freezing, one must calculate the freezing point depression, determine molality, convert to moles of solute, and finally calculate the mass using the molar mass of fructose.

Step-by-step explanation:

To answer the question about the maximum mass of fructose (C6H12O6) that can be added to 2.50 kg of pure water at − 12.5 °C without freezing, we first need to understand the concept of freezing point depression. This is a colligative property where the freezing point of a solvent decreases when a non-volatile solute is added. The equation for freezing point depression is ΔT_f = i × K_f × m, where ΔT_f is the change in temperature, i is the van't Hoff factor (i = 1 for fructose as it does not ionize), K_f is the freezing point depression constant for water (-1.86 °C/m), and m is molality of the solution.

To find the mass of fructose, rearrange the equation to solve for molality, calculate the number of moles of fructose, and then use the molar mass of fructose (180.16 g/mol) to find the mass in grams. The steps are:

• Calculate the change in freezing point (ΔT_f).
• Determine the molality (m) using the equation ΔT_f = K_f × m.
• Convert molality to moles of solute, considering the mass of the solvent (water).
• Calculate the mass of fructose using its molar mass.