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

These sets of problems are about the concentrations and dilution of solutions from one concentration to another concentration.

Concentration Problems

1.	What is the molarity of a 18.0 mL solution if it contains: (a) 5.34 g of Zn(NO3)2, (b) 7.58 g of CaC2O4.H2O, (c) 4.39 g of H3BO3? (mol. wt.: Zn(NO3)2=189.3898, CaC2O4.H2O=146.1148, H3BO3=61.8319)
	Answer: (a) 1.6 M, (b) 2.9 M, (c) 3.9 M
2.	Determine the weight in grams of the solute contained in a given volume and a given concentration of the following solutions: (a) 5.0 L of 5.76 M CuSO4 solution, (b) 12.0 mL of 0.83 M Mg(OH)2 solution, (c) 24.0 mL of 2.3 M CuSCN solution. (mol. wt.: CuSO4=159.6036, Mg(OH)2=58.3196, CuSCN=121.6237)
	Answer: (a) 4596.6 g, (b) 0.6 g, (c) 6.7 g
3.	Calculate the weight of the solute required in order to prepare the following solutions: (a) 12.0 mL of 3.36 M Zn(NO3)2.6H2O solution, (b) 1.0 L of 1.35 M NaIO3 solution, (c) 6.0 L of 2.78 M NaCl solution. (mol. wt.: Zn(NO3)2.6H2O=297.481, NaIO3=197.89247, NaCl=58.44277)
	Answer: (a) 12 g, (b) 267.2 g, (c) 974.8 g
4.	What is the molarity (M) of the following solutions: (a) 33% (w/w) sodium hydroxide solution with a density of 1.36 g/mL, (b) 40% (w/w) hydrobromic acid solution with a density of 1.38 g/mL. (mol. wt.: NaOH=39.99707, HBr=80.9119)
	Answer: (a) 11.22 M, (b) 6.82 M
5.	Determine the weight in grams of the solute contained in the following solutions: (a) 10.0 mL of 0.58 M K2S2O5 solution, (b) 2.0 L of 1.78 M CaF2 solution, (c) 5.0 L of 0.48 M NaOH solution. (mol. wt.: K2S2O5=222.3136, CaF2=78.0768, NaOH=39.99707)
	Answer: (a) 1.3 g, (b) 278 g, (c) 96 g
6.	Calculate the resulting molarity (M) of CH3COO-1 from the mixture of 18.00 mL of 4.79 M NaCH3COO solution and 21.00 mL of 3.11 M Ba(CH3COO)2 solution, assuming their volumes are additive.
	Answer: 5.56 M
7.	Determine the weight in grams of the solute contained in the following solutions: (a) 10.0 mL of 0.92 M KClO3 solution, (b) 2.0 L of 1.38 M KSCN solution, (c) 4.0 L of 0.32 M ZnBr2 solution. (mol. wt.: KClO3=122.5495, KSCN=97.176, ZnBr2=225.188)
	Answer: (a) 1.1 g, (b) 268.2 g, (c) 288.2 g
8.	Calculate the final molarity (M) of a mixed solution of 23.0 mL of 4.29 M CdC2O4.3H2O solution and 16.0 mL of 1.8 M CdC2O4.3H2O solution, assuming their volumes are additive.
	Answer: 3.3 M
9.	Determine the weight in grams of the solute contained in a given volume and a given concentration of the following solutions: (a) 5.0 L of 0.13 M Ca(NO3)2.4H2O solution, (b) 14.0 mL of 5.73 M Na2CO3.H2O solution, (c) 22.0 mL of 5.89 M Na4P2O7 solution. (mol. wt.: Ca(NO3)2.4H2O=236.1506, Na2CO3.H2O=124.00394, Na4P2O7=265.9024)
	Answer: (a) 153.5 g, (b) 9.9 g, (c) 34.5 g
10.	Calculate the resulting molarity (M) of C2O4-2 from the mixture of 6.00 mL of 1.9 M K2C2O4 solution and 9.00 mL of 4.78 M BaC2O4 solution, assuming their volumes are additive.
	Answer: 3.6 M

Dilution Problems

1.	What is the volume of the diluted solution of 25.0 mL of 4.77 M Mg(NO3)2.6H2O if its final concentration is 0.41 M Mg(NO3)2.6H2O?
	Answer: 290.9 mL
2.	What is the volume of the diluted solution of 17.0 mL of 3.91 M AgNO3 if its final concentration is 1.4 M AgNO3?
	Answer: 47.5 mL
3.	14 mL of an unknown concentration of Co(NO3)2.6H2O solution was diluted to 21.9 mL to make a concentration of 1.46 M Co(NO3)2.6H2O. Determine the initial concentration of the diluted solution.
	Answer: 2.28 M
4.	36.3 mL of 2.62 M K2CrO4 solution was prepared from an unknown volume of 4.32 M K2CrO4 solution. What was the initial volume of the solution?
	Answer: 22.0 mL
5.	What is the volume of the diluted solution of 18.0 mL of 1.56 M NaClO3 if its final concentration is 1.44 M NaClO3?
	Answer: 19.5 mL
6.	What is the volume of the diluted solution of 10.0 mL of 2.27 M KIO3 if its final concentration is 2.07 M KIO3?
	Answer: 11 mL
7.	If 7.0 mL of 3.5 M NaHCO3 solution is diluted to 35.0 mL, calculate the new molarity of the solution.
	Answer: 0.7 M
8.	18.9 mL of 2.34 M KI solution was prepared from an unknown volume of 4.03 M KI solution. What was the initial volume of the solution?
	Answer: 11.0 mL
9.	5 mL of an unknown concentration of K2SO4 solution was diluted to 19.4 mL to make a concentration of 0.7 M K2SO4. Determine the initial concentration of the diluted solution.
	Answer: 2.72 M
10.	327 mL of 0.1 M NaNO2 solution was prepared from an unknown volume of 5.45 M NaNO2 solution. What was the initial volume of the solution?
	Answer: 6.0 mL