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Chapter 13. Properties of Mixtures: Solutions. Properties of Mixtures: Solutions. 13.1 Types of solutions: Intermolecular forces and predicting solubility. 13.2 Energy changes in the solution process. 13.3 Solubility as an equilibrium process.

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Chapter 13

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Properties of mixtures solutions

Chapter 13

Properties of Mixtures: Solutions


Properties of mixtures solutions

Properties of Mixtures: Solutions

13.1 Types of solutions: Intermolecular forces and predicting solubility

13.2 Energy changes in the solution process

13.3 Solubility as an equilibrium process

13.4 Quantitative ways of expressing concentration

13.5 Colligative properties of solutions


Properties of mixtures solutions

The major types of intermolecular forces in solutions

(from Chapter 12)

Figure 13.1

(energies in parenthesis)


Properties of mixtures solutions

“LIKE DISSOLVES LIKE”

Substances with similar types of intermolecular forces dissolve in each other.

When a solute dissolves in a solvent, solute-solute interactions and solvent-solvent interactions are partly replaced with solute-solvent interactions.

The new forces created between solute and solvent must be comparable in strength to the forces destroyed within the solute and the solvent.


Properties of mixtures solutions

A major factor that determines

whether a solution forms:

The relative strengths of the intermolecular forces within and

between solute and solvent molecules


Properties of mixtures solutions

Some Definitions

Solvent: the most abundant component of a given solution

Solute: component dissolved in the solvent

Solubility (S): the maximum amount of solute that dissolves in a

fixed quantity of solvent at a given temperature (in the presence

of excess solute)

Dilute and concentrated solutions: qualitative terms


Properties of mixtures solutions

Hydration shells around an aqueous ion

Formation of ion-dipole

forces when a salt dissolves

in water

Figure 13.2


Properties of mixtures solutions

Liquid Solutions

  • Liquid-Liquid

  • Gas-Liquid

Gas and Solid Solutions

  • Gas-Gas

  • Gas-Solid

  • Solid-Solid


Properties of mixtures solutions

hexane =

CH3(CH2)4CH3

Competition

between

H-bonding

and dispersion

forces


Properties of mixtures solutions

Molecular Basis for the Solubility of CH3OH in H2O

H-bonding: CH3OH can serve as a donor and acceptor

(maximum number of three H-bonds / molecule)

Figure 13.3


Properties of mixtures solutions

PROBLEM:

Predict which solvent will dissolve more of the given solute:

PLAN:

Consider the intermolecular forces that exist between solute molecules and consider whether the new solvent-solute interactions can substitute for them.

(a) NaCl is ionic and forms ion-dipoles with the OH groups of bothmethanol and propanol. However, propanol is subject to greaterdispersion forces (more CH bonds than methanol).

(b) Hexane has no dipoles to interact with the OH groups of ethylene glycol. Water can H-bond to ethylene glycol.

(c) Diethyl ether can interact through dipole and dispersion forces. Ethanolcan provide both while water can only H-bond.

SAMPLE PROBLEM 13.1

Predicting relative solubilities of substances

(a) Sodium chloride in methanol (CH3OH) or in propanol (CH3CH2CH2OH)

(b) Ethylene glycol (HOCH2CH2OH) in hexane (CH3CH2CH2CH2CH2CH3)

or in water.

(c) Diethyl ether (CH3CH2OCH2CH3) in water or in ethanol (CH3CH2OH)

SOLUTION:


Properties of mixtures solutions

Structure-Function Correlations: A Soap

Soap: the salt form of a long-chain fatty acid; is amphipathic

in character (has polar and non-polar components)

Figure B13.1


Properties of mixtures solutions

The mode of action of the antibiotic, Gramicidin A

Destroys the Na+/K+ ion

concentration gradients

in the cell

Figure B13.2


Properties of mixtures solutions

Gas-Liquid Solutions

Non-polar gas solubility in

water is directly related to

the boiling point of the gas.

important to

aquatic life


Properties of mixtures solutions

Gas-gas solutions: All gases are infinitely soluble in one another.

Gas-solid solutions: The gas molecules occupy the spaces

between the closely packed particles of the solid.

Solid-solid solutions: alloys (substitutional or interstitial)


Properties of mixtures solutions

The arrangement of atoms in two types of alloys

Figure 13.4


Properties of mixtures solutions

solute (aggregated) + heat solute (separated) DHsolute > 0

solvent (aggregated) + heat solvent (separated) DHsolvent > 0

solute (separated) + solvent (separated) solution + heatDHmix < 0

Heats of solution and solution cycles

Dissolution of a solid: breaking down the process into three steps

1. Solute particles separate from each other - endothermic

2. Solvent particles separate from each other - endothermic

3. Separate solute and solvent particles mix - exothermic


Properties of mixtures solutions

Calculating the heat of solution, DHsoln

The total enthalpy change that occurs when a solution forms by

dissolving a solute into a solvent.

DHsoln=DHsolute+DHsolvent+DHmix

A thermochemical solution cycle


Properties of mixtures solutions

Solution cycles and the enthalpy components of the heat of solution

Figure 13.5


Properties of mixtures solutions

H2O

M+ (g) [or X- (g)] M+ (aq) [or X- (aq)] DHhydr of the ion < 0

M+ (g) + X- (g) MX(s) DHlattice is always (-)

Heats of Hydration

The solvation of ions by water is always exothermic.

(for 1 mole of gaseous ions)

DHhydr is related to the charge density of the ion, that is, both coulombic charge and ion size are important.

Lattice energy is the DH involved in the formation of an ionic solid from its gaseous ions.

Thus, DHsoln = -DHlattice + DHhydr


Properties of mixtures solutions

Heats of Hydration and Ionic Character

  • For a given size, greater charge leads to a more (-) DHhydr

  • For a given charge, smaller size leads to a more (-) DHhydr


Properties of mixtures solutions

Table 13.4Trends in Ionic Heats of Hydration

ion

ionic radius (pm)

DHhydr (kJ/mol)

Group 1A

Li+

76

-510

Na+

102

-410

K+

138

-336

Rb+

152

-315

Cs+

167

-282

Group 2A

Mg2+

72

-1903

Ca2+

100

-1591

Sr2+

118

-1424

Ba2+

135

-1317

Group 7A

F-

133

-431

Cl-

181

-313

Br-

196

-284

I-

220

-247


Properties of mixtures solutions

Enthalpy Diagrams for Dissolving Three Different Ionic Compounds in Water

NaCl

NH4NO3

Figure 13.6

NaOH


Properties of mixtures solutions

Entropy Considerations

The natural tendency of most systems is to become more

disordered; entropy increases.

Entropy always favors the formation of solutions.

Dissolution: involves a change in enthalpy and a change in

entropy.


Properties of mixtures solutions

Enthalpy diagrams for dissolving NaCl and octane in hexane

NaCl in insoluble in hexane!

In this case, dissolution is

entropy-driven!

Figure 13.7


Properties of mixtures solutions

More Definitions

When excess undissolved solute is in equilibrium with

the dissolved solute: a saturated solution

An unsaturated solution: more solute can be dissolved,

ultimately producing a saturated solution

A supersaturated solution: a solution that contains more

than the equilibrium amount of dissolved solute


Properties of mixtures solutions

solute (undissolved) solute (dissolved)

Equilibrium in a saturated solution

Figure 13.8


Properties of mixtures solutions

Sodium acetate crystallizing from a supersaturated solution

nucleation

a saturated solution

results

Figure 13.9


Properties of mixtures solutions

Solubility and Temperature

Most solids are more soluble at higher temperatures.

The sign of the heat of solution, however, does not predict reliably the effect

of temperature on solubility; e.g., NaOH and NH4NO3 have

DHsoln of opposite signs, yet their solubility in H2O increases

with temperature.


Properties of mixtures solutions

The relation between solubility and temperature for several ionic compounds

Figure 13.10


Properties of mixtures solutions

Gas Solubility in Water: Temperature Effects

For all gases, DHsolute = 0, DHhydr < 0; thus, DHsoln < 0

solute(g) + water(l) saturated solution(aq) + heat

Implications: gas solubility in water decreases with

increasing temperature


Properties of mixtures solutions

Thermal Pollution

Leads to O2

deprivation in aquatic

systems

Figure 13.11


Properties of mixtures solutions

Pressure Effects on Solubility

Essentially zero for solids and liquids, but substantial for gases!

gas + solvent saturated solution


Properties of mixtures solutions

The effect of pressure on gas solubility

gas volume is reduced;

pressure (concentration!)

increases; more collisions

occur with liquid surface

Figure 13.12


Properties of mixtures solutions

Henry’s Law

A quantitative relationship

between gas solubility and

pressure

Sgas = kHx Pgas

The solubility of a gas (Sgas) is directly proportional to the partial pressure of the gas (Pgas) above the solution.

Implications for scuba diving!

kH = Henry’s law constant

for a gas; units of mol/L.atm


Properties of mixtures solutions

PROBLEM:

The partial pressure of carbon dioxide gas inside a bottle of cola is 4 atm at 25 oC. What is the solubility of CO2? The Henry’s law constant for CO2 dissolved in water is 3.3 x 10-2 mol/L.atm at 25 oC.

S = (3.3 x 10-2 mol/L.atm)(4 atm) =

CO2

SAMPLE PROBLEM 13.2

Using Henry’s Law to calculate gas solubility

PLAN:

Knowing kH and Pgas, we can substitute into the Henry’s Law equation.

SOLUTION:

0.1 mol / L


Properties of mixtures solutions

amount (mol) of solute

molarity (M)

volume (L) of solution

amount (mol) of solute

molality (m)

mass (kg) of solvent

mass of solute

parts by mass

mass of solution

volume of solute

parts by volume

volume of solution

amount (mol) of solute

mole fraction 

amount (mol) of solute + amount (mol) of solvent

Table 13.5Concentration Definitions

concentration term

ratio


Properties of mixtures solutions

PROBLEM:

What is the molality of a solution prepared by dissolving 32.0 g of CaCl2 in 271 g of water?

mole CaCl2

32.0 g CaCl2

x

110.98 g CaCl2

0.288 mole CaCl2

kg

x

271 g H2O

103 g

SAMPLE PROBLEM 13.3

Calculating molality

PLAN:

Convert grams of CaCl2 into moles and grams of water to kg. Then substitute into the equation for molality.

SOLUTION:

= 0.288 mole CaCl2

= 1.06 m CaCl2

molality =


Properties of mixtures solutions

The Sex Attractant of the Gypsy Moth Potent at Extremely Low Concentrations!

100-300 molecules/mL air

100 parts per quadrillion by volume!

Practical Implications: a strategy used to target and

trap specific insects (Japanese beetles)

Figure 13.13


Properties of mixtures solutions

Other Expressions of Concentration

mass percent (% w/w) = mass solute / mass of solution x 100

(related to parts per million (ppm) or parts per billion (ppb))

volume percent (% (v/v) = volume solute / volume of solution x 100

% (w/v) = solute mass / solution volume x 100

mole percent (mol%) = mole fraction x 100


Properties of mixtures solutions

SAMPLE PROBLEM 13.4

Expressing concentration in parts by mass, parts by volume, and mole fraction

PROBLEM:

(a) Find the concentration of calcium (in ppm) in a 3.50 g pill thatcontains 40.5 mg of Ca.

(b) The label on a 0.750 liter bottle of Italian chianti indicates“11.5% alcohol by volume”. How many liters of alcoholdoes the wine contain?

(c) A sample of rubbing alcohol contains 142 g of isopropylalcohol (C3H7OH) and 58.0 g of water. What are themole fractions of alcohol and water?

PLAN:

(a) Convert mg to g of Ca, find the ratio of g Ca to g pill, and multiplyby 106.

(b) Knowing the % alcohol and the total volume, the volume ofalcohol can be calculated.

(c) Convert g of solute and solvent to moles, and find the ratios ofeach part to the total.


Properties of mixtures solutions

40.5 mg Ca

x

g

x

106

103 mg

x

0.750 L chianti

11.5 L alcohol

100. L chianti

mole

mole

18.02 g

60.09 g

= 0.577

= 0.423

H2O

C3H7OH

SAMPLE PROBLEM 13.4

(continued)

SOLUTION:

(a)

= 1.16 x 104 ppm Ca

3.5 g

(b)

= 0.0862 L alcohol

(c)

moles isopropyl alcohol =

142 g

x

= 2.36 mol C3H7OH

x

moles water =

58.0 g

= 3.22 mol H2O

2.36 mol C3H7OH

3.22 mol H2O

2.36 mol C3H7OH + 3.22 mol H2O

2.36 mol C3H7OH + 3.22 mol H2O


Properties of mixtures solutions

PROBLEM:

Hydrogen peroxide is a powerful oxidizing agent used in concentrated solution in rocket fuels and in dilute solution as a hair bleach. An aqueous solution of H2O2 is 30.0% by mass and has a density of 1.11 g/mL. Calculate its:

SAMPLE PROBLEM 13.5

Converting concentration units

(a)molality

(b)mole fraction

(c)molarity

PLAN:

(a) To find the mass of solvent, assume the % is per 100 g of solution. Take the difference in the mass of the solute and solution to determine the mass of solvent.

(b) Convert g of solute and solvent to moles before finding c.

(c) Use the density to find the volume of the solution.

SOLUTION:

(a)

g of H2O = 100. g solution - 30.0 g H2O2 =

70.0 g H2O

mol H2O2

30.0 g H2O2

x

34.02 g H2O2

molality =

= 12.6 m H2O2

kg H2O

x

70.0 g H2O

103 g


Properties of mixtures solutions

mol H2O

18.02 g H2O

mL

1.11 g

L

103 mL

SAMPLE PROBLEM 13.5

(continued)

(b)

70.0 g H2O

x

= 3.88 mol H2O

0.882 mol H2O2

= 0.185 = c of H2O2

0.882 mol H2O2 + 3.88 mol H2O

(c)

= 90.1 mL solution

100.0 g solution

x

0.882 mol H2O2

= 9.79 M H2O2

90.1 mL solution

x


Properties of mixtures solutions

Colligative Properties

Physical properties of solutions dictated by the number of

solute particles present. Their chemical structures are

not factors in determining these properties!

  • vapor pressure lowering

  • boiling point elevation

  • freezing point depression

  • osmotic pressure


Properties of mixtures solutions

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

strong

non-electrolyte

weak

Three types of electrolytes

Figure 13.14


Properties of mixtures solutions

Vapor Pressure Lowering

The vapor pressure of a solution of a nonvolatile nonelectrolyte

is always lower than the vapor pressure of the pure solvent.

An entropy argument!

Figure 13.15


Properties of mixtures solutions

Quantitative Treatment of VP Lowering

Raoult’s Law (vapor pressure of a solvent above a solution, Psolvent)

Psolvent = csolvent x Posolvent

where Posolvent = vapor pressure of the pure solvent

How does the amount of solute affect the magnitude of the VP lowering?

( substitute 1- csolute forcsolventin the above equation and rearrange)

Posolvent - Psolvent = DP = csolutex Posolvent

(change in VP is proportional to the mole fraction of solute)


Properties of mixtures solutions

PROBLEM:

Calculate the vapor pressure lowering, DP, when 10.0 mL of glycerol (C3H8O3) is added to 500. mL of water at 50. oC. At this temperature, the vapor pressure of pure water is 92.5 torr and its density is 0.988 g/mL. The density of glycerol is 1.26 g/mL.

PLAN:

Find the mol fraction, c, of glycerol in solution and multiply by the vapor pressure of water.

0.988 g H2O

1.26 g C3H8O3

mol H2O

mol C3H8O3

mL C3H8O3

mL H2O

18.02 g H2O

92.09 g C3H8O3

c = 0.00498

SAMPLE PROBLEM 13.6

Using Raoult’s Law to find the vapor pressure lowering

SOLUTION:

10.0 mL C3H8O3

= 0.137 mol C3H8O3

x

x

x

= 27.4 mol H2O

500.0 mL H2O

x

0.137 mol C3H8O3

DP =

x

92.5 torr

= 0.461 torr

0.137 mol C3H8O3 + 27.4 mol H2O


Properties of mixtures solutions

Boiling Point Elevation

A solution boils at a higher temperature than the pure solvent.

This effect is explained by differences between the VP of

the solution and VP of the pure solvent at a given temperature.


Properties of mixtures solutions

Superimposed phase diagrams of solvent and solution

aqueous solution:

dashed lines

pure water:

solid lines

Figure 13.16


Properties of mixtures solutions

Quantitative Treatment of BP Elevation

The magnitude of the effect is proportional to solute concentration.

DTb = Kbm

(m = solution molality, Kb = molal BP elevation constant, DTb= BP elevation)

DTb = Tb (solution) - Tb (solvent)


Properties of mixtures solutions

Quantitative Treatment of FP Depression

The magnitude of the effect is proportional to solute concentration.

DTf = Kfm

(m = solution molality, Kf = molal FP depression constant, DTf= FP depression)

DTf = Tf (solvent) - Tf (solution)


Properties of mixtures solutions

Table 13.6Molal Boiling Point Elevation and Freezing Point Depression Constants of Several Solvents

melting

point (oC)

boiling

point (oC)*

solvent

Kb(oC/m)

Kf (oC/m)

acetic acid

117.9

3.07

16.6

3.90

benzene

80.1

2.53

5.5

4.90

carbon disulfide

46.2

2.34

-111.5

3.83

carbon tetrachloride

76.5

5.03

-23

30.

chloroform

61.7

3.63

-63.5

4.70

diethyl ether

34.5

2.02

-116.2

1.79

ethanol

78.5

1.22

-117.3

1.99

water

100.0

0.512

0.0

1.86

*at 1 atm.


Properties of mixtures solutions

PROBLEM:

You add 1.00 kg of ethylene glycol antifreeze (C2H6O2) to your car radiator, which contains 4450 g of water. What are the boiling and freezing points of the resulting solution?

PLAN:

Find the number of mols of ethylene glycol and m of the solution; multiply by the boiling or freezing point constant; add or subtract, respectively, the changes from the boiling point and freezing point of water.

mol C2H6O2

62.07 g C2H6O2

SAMPLE PROBLEM 13.7

Determining the boiling point elevation and freezing point depression of a solution

SOLUTION:

x

1.00 x 103 g C2H6O2

= 16.1 mol C2H6O2

16.1 mol C2H6O2

= 3.62 m C2H6O2

4.450 kg H2O

DTb =

0.512 oC/m

x

3.62 m

= 1.85 oC

DTf =

1.86 oC/m

x

3.62 m

BP = 101.85 oC

FP = -6.73 oC


Properties of mixtures solutions

Osmotic Pressure

  • Applies only to aqueous solutions!

  • Two solutions of different concentrations are separated by a semi-permeable membrane (allows water but notsolute to pass through)


Properties of mixtures solutions

The development of osmotic pressure

osmotic

pressure

applied pressure needed to prevent volume increase; equal to the osmotic pressure

pure solvent

solution

semipermeable

membrane

Figure 13.17


Properties of mixtures solutions

Quantitative Treatment of Osmotic Pressure (P)

OP is proportional to the number of solute particles in a given

volume of solution (to M).

P a nsolute/Vsoln or P aM

The constant of proportionality = RT, so P = M x R x T

T is the Kelvin temperature


Properties of mixtures solutions

Underlying Principle of Colligative Properties

Each property stems from an inability of solute particles to

cross between two phases.


Properties of mixtures solutions

Determination of Solute Molar Mass by Exploiting Colligative Properties

In principle, any colligative property can be used, but OP gives the

most accurate results (better dynamic range).


Properties of mixtures solutions

PROBLEM:

Biochemists have discovered more than 400 mutant varieties of hemoglobin (Hb), the blood protein that carries oxygen throughout the body. A physician studying a form of Hb associated with a fatal disease first finds its molar mass (M). She dissolves 21.5 mg of the protein in water at 5.0 oC to make 1.50 mL of solution and measures an osmotic pressure of 3.61 torr. What is the molar mass of this Hb mutant?

PLAN:

We know P as well as R and T. Convert P to atm and T to Kelvin. Use the P equation to find the molarity M and then the amount and volume of the sample to calculate M.

atm

P

760 torr

RT

L

2.08 x 10-4 mol

L

103 mL

g

1

103 mg

3.12 x 10-7 mol

SAMPLE PROBLEM 13.8

Determining molar mass from osmotic pressure

SOLUTION:

3.61 torr

x

M =

=

= 2.08 x 10-4M

(0.0821 L . atm/mol . K)(278.15 K)

= 3.12 x 10-7 mol

x

1.50 mL

x

# mol = g/M

21.5 mg

x

x

= 6.89 x 104 g/mol


Properties of mixtures solutions

Fractional Distillation of Volatile

Nonelectrolytes

The presence of each volatile component

lowers the vapor pressure of the other.

partial pressure = mole fraction x vapor pressure of pure gas

For vapor: mole fraction = partial pressure / total pressure

(thus, the vapor has a higher mole fraction of the more volatile

solution component)


Properties of mixtures solutions

Gasoline vapors

Condenser

Gas

Gasoline 38 oC

Kerosene 150 oC

Heating oil 260 oC

Lubricating oil 315 oC - 370 oC

Crude oil vapors from heater

Steam

Residue (asphalt, tar)

The process of fractional distillation

Figure 13.18


Properties of mixtures solutions

Colligative Properties of Electrolyte Solutions

Must consider the full dissociation into ions!

van’t Hoff factor (i) = measured value for electrolyte solution

expected value for nonelectrolyte solution

This factor is multiplied into the appropriate equations; for example,

P = i (MRT).

For ideal behavior, i = mol particles in solution / mol dissolved solute

But solutions are not ideal; for example, for BP elevation of NaCl

solutions, i = 1.9, not 2!

Data suggest that the ions are not behaving

as independent particles!


Properties of mixtures solutions

Non-ideal behavior of electrolyte solutions

Observed values of i are less

than the predicted (expected)

values.

Figure 13.19


Properties of mixtures solutions

An ionic atmosphere model for non-ideal behavior of electrolyte solutions

ionic atmospheres

Concept of effective

concentration

Figure 13.20


Properties of mixtures solutions

Some Practical Applications

  • ion-exchange (water softeners)

  • water purification


Properties of mixtures solutions

Ion exchange for removal of hard-water cations

Use of ion-exchange

resins

Figure B13.4


Properties of mixtures solutions

Reverse osmosis for the removal of ions

Desalination Process

Figure B13.5


Properties of mixtures solutions

End of Assigned Material


Properties of mixtures solutions

Photo by C.A.Bailey, CalPoly SLO (Myanmar)

Light scattering and the Tyndall effect

Figure 13.21


Properties of mixtures solutions

A Cottrell precipitator for removing particulates from

industrial smokestack gases

Figure 13.22


Properties of mixtures solutions

The steps in a typical municipal water treatment plant

Figure B13.3


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