Calculations Involving Calculations Involving Colligative PropertiesColligative Properties

Prentice-Hall Chapter 16.4Prentice-Hall Chapter 16.4Dr. YagerDr. Yager

ObjectivesObjectives

SolveSolve problems related to molality and problems related to molality and mole fraction of a solutionmole fraction of a solution

DescribeDescribe how freezing-point depression how freezing-point depression and boiling point elevation are related to and boiling point elevation are related to molalitymolality

CalculateCalculate magnitudes of freezing-point magnitudes of freezing-point depression and boiling point elevation depression and boiling point elevation

The DifferenceThe Difference

solution of liters

solute of moles (M) Molarity

solvent of kilograms

solute of moles (m) Molality

molality (m)- new term

Molarity (M) - term from 16.2

Key PointKey Point

MolalityMolality and and mole fractionsmole fractions are two additional are two additional ways in which chemists express the concentration ways in which chemists express the concentration of a solution.of a solution.

The molality (m) is the number of moles of solute dissolved in 1 kilogram (1000 g) of solvent. Molality is also known as molal concentration.

To make a 0.500m solution of NaCl, use a balance to measure 1.000 kg of water and add 0.500 mol (29.3 g) of NaCl.

How many grams of sodium fluoride are needed to prepare a 0.400m NaF solution that contains 750 g of water?

solvent of kilograms

solute of moles molality

g 13.g 12.6 solute of gramsmol

g42.0 x mol 0.30 solute of grams

mol 0.30 solute of moles

kg .75

solute of moles m 0.400

In a solution containing nA mol of solute A and nB mol of solvent B, the mole fraction of solute A (XA) and the mole fraction of solvent B (XB) can be expressed as follows:

Mole Fraction can be of Mole Fraction can be of Solute or SolventSolute or Solvent

solvent of moles solute of moles

solvent of moles solvent of mf

solvent of moles solute of moles

solute of moles solute of mf

Adding Ethlylene Glycol (EG) to water as antifreeze.

A solution contains 50.0g of carbon tetrachloride (CCl4) and 50.0g 0f chloroform (CHCl3). Calculate the mole fraction of each component in the solution.

mol 0.419

molg

119.3

g 50.0CHCl of moles

mol 0.325

molg

153.8

g 50.0CCl of moles

3

4

0.563 0.419mo 0.325mol

mol 0.419CHCl of fraction mole

0.437 0.419mol 0.325mol

mol 0.325CCl of fraction mole

3

4

The magnitudes of the freezing-point depression and the boiling-point elevation of a solution are directly proportional to the molal concentration (m), when the solute is molecular, not ionic.

Freezing-Point Depression and Freezing-Point Depression and Boiling-Point ElevationBoiling-Point Elevation

The constant, Kf, is the molal freezing-point depression constant, which is equal to the change in freezing point for a 1-molal solution of a nonvolatile molecular solute.

The constant, Kb, is the molal boiling-point elevation constant, which is equal to the change in boiling point for a 1-molal solution of a nonvolatile molecular solute.

What is the freezing point depression of an aqueous solution of 10.0 g of glucose (C6H12O6) in 50.0 g H2O?

C2.071.11m x m

C1.86m x KT

1.11mkg .0500

mol .0555glucose of molality

mol 0.0555

molg

180.

10.0g glucose of moles

oo

ff

What mass of NaCl would have to be dissolved in 1.000 kg of water to raise the boiling point by 2.00oC?

g 114 mol

g58.5 x mol 1.96 NaCl of grams

NaCl mol 1.96 NaCl mol 1 x particles mol 2

particles mol 3.91 NaCl mol

NaCl mol 1

particles mol 2x

1.000kg

NaCl mol

1.000kg

particles 3.91mol 3.91m

3.91m

mC

.512

C2.00particles of molality

C2.00salt water of molality x m

C0.512m x KT

0

0

00

bb

1. What is the mole fraction of He in a 1. What is the mole fraction of He in a gaseous solution containing 4.0 g of gaseous solution containing 4.0 g of He, 6.5 g of Ar, and 10.0 g of Ne?He, 6.5 g of Ar, and 10.0 g of Ne?

a.a. 0.600.60

b.b. 1.51.5

c.c. 0.200.20

d.d. 0.110.11

1. What is the mole fraction of He in a 1. What is the mole fraction of He in a gaseous solution containing 4.0 g of gaseous solution containing 4.0 g of He, 6.5 g of Ar, and 10.0 g of Ne?He, 6.5 g of Ar, and 10.0 g of Ne?

a.a. 0.600.60

b.b. 1.51.5

c.c. 0.200.20

d.d. 0.110.11

2. The freezing point depression caused 2. The freezing point depression caused by a given concentration of a by a given concentration of a nonvolatile molecular solute nonvolatile molecular solute

a.a. depends on the solute.depends on the solute.

b.b. depends on the solvent.depends on the solvent.

c.c. is always the same.is always the same.

d.d. cannot be determined.cannot be determined.

2. The freezing point depression caused 2. The freezing point depression caused by a given concentration of a by a given concentration of a nonvolatile molecular solute nonvolatile molecular solute

a.a. depends on the solute.depends on the solute.

b.b. depends on the solvent.depends on the solvent.

c.c. is always the same.is always the same.

d.d. cannot be determined.cannot be determined.

3. What are the freezing and boiling 3. What are the freezing and boiling points of a 0.1points of a 0.1mm solution of CaCl solution of CaCl22 in in

water? water?

a.a. -0.2°C, 100.1°C-0.2°C, 100.1°C

b.b. -0.6°C, 100.1°C-0.6°C, 100.1°C

c.c. -0.6°C, 100.2°C-0.6°C, 100.2°C

d.d. -0.6°C, 99.8°C -0.6°C, 99.8°C

3. What are the freezing and boiling 3. What are the freezing and boiling points of a 0.1points of a 0.1mm solution of CaCl solution of CaCl22 in in

water? water?

a.a. -0.2°C, 100.1°C-0.2°C, 100.1°C

b.b. -0.6°C, 100.1°C-0.6°C, 100.1°C

c.c. -0.6°C, 100.2°C-0.6°C, 100.2°C

d.d. -0.6°C, 99.8°C -0.6°C, 99.8°C

4. Compared to the freezing point 4. Compared to the freezing point depression by ethylene glycol (Cdepression by ethylene glycol (C22HH66OO22,) ,)

for a given solvent, the freezing point for a given solvent, the freezing point depression caused by the same molal depression caused by the same molal concentration of CaClconcentration of CaCl22 would be would be

• exactly the same.exactly the same.

• twice as large.twice as large.

• three times as large.three times as large.

• four times as largefour times as large

4. Compared to the freezing point 4. Compared to the freezing point depression by ethylene glycol (Cdepression by ethylene glycol (C22HH66OO22,) ,)

for a given solvent, the freezing point for a given solvent, the freezing point depression caused by the same molal depression caused by the same molal concentration of CaClconcentration of CaCl22 would be would be

• exactly the same.exactly the same.

• twice as large.twice as large.

• three times as large.three times as large.

• four times as largefour times as large