Asucrose solution is made using 144 g of sucrose (C12H22O11) and diluting to a total volume of 1.00 L. Calculate the freezing point and boiling point of the solution. (Assume a density of 1.06 g/mL for the final solution.)
Here, we are going to calculate the boiling point and freezing point of the solution .
Step 1: Calculation of the amount of sucrose in mol
Molar mass of sucrose =342.296 g/mol
Mass of sucrose = 144 g
Amount of glucose in mol = 144g/342.296 g/mol = 0.4207 mol
Step 2: Calculation of molality of the solution.
Density = Mass/volume = 1.06 g/mL
Volume = 1L= 1000 mL
Mass of solution = Density x volume = 1.06 g/mL x 1000 mL = 1060 g
Volume of solution = 1060g = 1.06 kg
Molality (m) of the solution = 0.4207 mol/1.06 kg =0.3968 m
Step 3: Calculation of freezing point of the solution.
The freezing point of depression of a solution is calculated by the equation:
Tf= m x Kf
Where m is the molality of the solution and Kf is the freezing point of depression constant for the solvent.
Tf= m x Kf , where kf = 1.86 oC/m
= 0.3968 m x 1.86 oC/m= 0.7382 oC
The freezing-point depression can be calculated as
where T∘f - the freezing point of the pure solvent (water) = 0 oC
Tf - the freezing point of the solution.
Tf = T∘f - ΔTf = 0 - 0.7382 oC = -0.7382 oC
Therefore , the freezing point of the solution is -0.7382 oC or -0.74 oC