Chemistry Practice Problems Freezing Point Depression Practice Problems Solution: Radiator coolant is often a 50/50 % by volume mixt...

Solution: Radiator coolant is often a 50/50 % by volume mixture of ethylene glycol, HOCH2CH2OH (62.1 g/mol), and water. At 20°C, the density of ethylene glycol is 1.1088 g/mL and the density of water is 0.9982 g/mL. Assuming that the volumes are additive, what is the expected freezing point (°C) of a 50/50(v/v)% ethylene glycol/water solution? Kf = 1.86°C/m for water. Enter your answer as the nearest whole number with no units.a. 100.53°Cb. 101.23°Cc. 100.08°Cd. 103.91°Ce. 100.31°C

Problem

Radiator coolant is often a 50/50 % by volume mixture of ethylene glycol, HOCH2CH2OH (62.1 g/mol), and water. At 20°C, the density of ethylene glycol is 1.1088 g/mL and the density of water is 0.9982 g/mL. Assuming that the volumes are additive, what is the expected freezing point (°C) of a 50/50(v/v)% ethylene glycol/water solution? Kf = 1.86°C/m for water. Enter your answer as the nearest whole number with no units.

a. 100.53°C

b. 101.23°C

c. 100.08°C

d. 103.91°C

e. 100.31°C


Solution

We’re being asked to calculate for the freezing point of an aqueous solution containing 50% (v/v) ethylene glycol

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


ΔTf=ΔTf, solution-ΔTf, pure solvent



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


ΔTf=i Kf m


where: 

i = van’t Hoff factor

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

Kf = freezing point depression constant (in ˚C/m)



We need to convert the 50% (v/v) of ethylene glycol to molality. Recall that the molality of a solution is given by:


Molality (m)=moles of soluteKilograms of solvent


We will calculate the freezing point of the solution using the following steps:

Step 1. Determine the composition of the solution.
Step 2. Calculate the moles of the solute.
Step 3. Calculate the mass of the solvent (in kg).
Step 4. Calculate the molality of the solution.
Step 5. Calculate the freezing point of the solution


Step 1. Determine the composition of the solution.

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