Freezing Point Depression Problems

The freezing point depression is a colligative property of dilute solutions. It depends on the number of solute particles present in the solution. This relationship is expressed by the following equation: The structural formulas of the organic solvents and organic solutes used in this set of freezing point depression problems are given below along with their common names, derived names or IUPAC names.

1.	Calculate the weight of ethyl ether required to mix with 0.8 L of water to make an aqueous solution which has a freezing point of -1.5° C. Freezing point of water is 0° C. Kf = 1.86°C-kg/mol.
	Answer: 47.82 g
2.	Determine the freezing point depression of an aqueous solution which contains 168.64 g glycerin and 0.2 L of water. Freezing point of water is 0° C. Kf = 1.86°C-kg/mol.
	Answer: -17.03° C
3.	What is the freezing point of an aqueous solution containing 0.46 mol diethylene glycol and 170 g of water? (Given: waterTf = 0° C; Kf = 1.86°C-kg/mol.)
	Answer: -5.03° C

4.	Calculate the freezing point of a phenylethyl alcohol-benzene mixture which has 12 % phenylethyl alcohol by weight. (Given:  benzene has a freezing point of 5.45° C; Kf = 4.9°C-kg/mol.)
	Answer: -0.02° C
5.	If a solution of 38.23 g of an unknown compound in 0.12 kg benzene has a freezing point of -4.81° C, what is the molecular weight of the solute? (Given: benzeneTf = 5.45° C; Kf = 4.9°C-kg/mol.)
	Answer: 152.15 g
6.	What is the concentration in molality (m) of an aqueous solution of glycerin if the freezing point of the solution is -1.93° C. (Given: waterTf = 0° C; Kf of water is 1.86°C-kg/mol.)
	Answer: 1.04 m
7.	What is the concentration in molality (m) of a solution of bromobenzene in benzene if the freezing point of the solution is -2.36° C. (Given: benzeneTf = 5.45° C; Kf = 4.9°C-kg/mol.)
	Answer: 1.59 m

8.	Calculate the freezing point of a solution of 53.69 g methyl n-propyl ether in 0.09 kg water. Freezing point of water is 0° C. Kf = 1.86°C-kg/mol.
	Answer: -14.97° C
9.	What is the freezing point of a solution of 114.27 g glycol in 0.47 kg water? The observed melting point of a sample of pure water is 0° C. Kf for water is 1.86°C-kg/mol.
	Answer: -7.29° C
10.	Calculate the freezing point of a solution of 21.82 g ethyl ether in 0.08 kg water. Freezing point of water is 0° C. Kf = 1.86°C-kg/mol.
	Answer: -6.84° C
11.	If a solution of 60.08 g of an unknown compound in 0.39 kg toluene has a freezing point of -100.45° C, what is the molecular weight of the solute? (Given: tolueneTf = -95° C; Kf = 3.33°C-kg/mol.)
	Answer: 94.13 g
12.	If a solution of 106.33 g of an unknown compound in 0.27 kg water has a freezing point of -11.8° C, what is the molecular weight of the solute? (Given: waterTf = 0° C; Kf = 1.86°C-kg/mol.)
	Answer: 62.08 g
13.	An aqueous solution, which has a composition of 52.19 g of an organic compound and 0.16 kg water, freezes at -20.21° C. Calculate the molecular weight of the solute. (Given:  water has a freezing point of 0° C; Kf = 1.86°C-kg/mol.)
	Answer: 30.02 g

14.	Pure benzene has a freezing point of 5.45° C. When a sample of 0.15 kg of benzene was mixed with 102.94 g of an unidentified compound, the sample was observed to freeze at -11.18° C. Determine the molecular weight of the compound. (Given: Kf = 4.9°C-kg/mol.)
	Answer: 202.21 g
15.	Pure naphthalene has a freezing point of 80.22° C. When a sample of 0.59 kg of naphthalene was mixed with 315.35 g of an unidentified compound, the sample was observed to freeze at 59.68° C. Determine the molecular weight of the compound. (Given: Kf = 6.85°C-kg/mol.)
	Answer: 178.25 g
16.	If a solution of 235.48 g of an unknown compound in 5.43 kg naphthalene has a freezing point of 78.75° C, what is the molecular weight of the solute? (Given: naphthaleneTf = 80.22° C; Kf = 6.85°C-kg/mol.)
	Answer: 202.08 g
17.	Pure toluene has a freezing point of -95° C. When a sample of 0.35 kg of toluene was mixed with 237.85 g of an unidentified compound, the sample was observed to freeze at -106.19° C. Determine the molecular weight of the compound. (Given: Kf = 3.33°C-kg/mol.)
	Answer: 202.23 g

18.	What is the freezing point of an aqueous solution containing 0.95 mol glutaric acid and 180 g of water? (Given: waterTf = 0° C; Kf = 1.86°C-kg/mol.)
	Answer: -9.82° C
19.	What is the freezing point of a solution of 198.14 g xylene in 1.18 kg naphthalene? The observed melting point of a sample of pure naphthalene is 80.22° C. Kf for naphthalene is 6.85°C-kg/mol.
	Answer: 69.39° C
20.	Calculate the freezing point of a glutaric acid-water mixture which has 6 % glutaric acid by weight. (Given:  water has a freezing point of 0° C; Kf = 1.86°C-kg/mol.)
	Answer: -0.9° C