Properties of Mixtures: Solutions

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Chapter 13
Properties of Mixtures Solutions
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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
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The major types of intermolecular forces in
solutions
(from Chapter 12)
Figure 13.1
(energies in parenthesis)
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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.
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A major factor that determines whether a
solution forms
The relative strengths of the intermolecular
forces within and between solute and solvent
molecules
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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
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Hydration shells around an aqueous ion
Formation of ion-dipole forces when a salt
dissolves in water
Figure 13.2
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Liquid Solutions

• Liquid-Liquid
• Gas-Liquid

Gas and Solid Solutions

• Gas-Gas
• Gas-Solid
• Solid-Solid

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hexane CH3(CH2)4CH3
Competition between H-bonding and dispersion
forces
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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
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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
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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
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The mode of action of the antibiotic, Gramicidin A
Destroys the Na/K ion concentration
gradients in the cell
Figure B13.2
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Gas-Liquid Solutions
Non-polar gas solubility in water is directly
related to the boiling point of the gas.
important to aquatic life
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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)
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The arrangement of atoms in two types of alloys
Figure 13.4
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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
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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
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Solution cycles and the enthalpy components of
the heat of solution
Figure 13.5
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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
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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

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Table 13.4 Trends 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
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Enthalpy Diagrams for Dissolving Three Different
Ionic Compounds in Water
NH4NO3
NaCl
Figure 13.6
NaOH
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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.
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Enthalpy diagrams for dissolving NaCl and octane
in hexane
NaCl in insoluble in hexane!
In this case, dissolution is entropy-driven!
Figure 13.7
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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
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Equilibrium in a saturated solution
Figure 13.8
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Sodium acetate crystallizing from a
supersaturated solution
nucleation
a saturated solution results
Figure 13.9
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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.
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The relation between solubility and temperature
for several ionic compounds
Figure 13.10
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Gas Solubility in Water Temperature Effects
For all gases, DHsolute 0, DHhydr lt 0 thus,
DHsoln lt 0
solute(g) water(l) saturated
solution(aq) heat
Implications gas solubility in water decreases
with increasing temperature
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Thermal Pollution
Leads to O2 deprivation in aquatic systems
Figure 13.11
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Pressure Effects on Solubility
Essentially zero for solids and liquids, but
substantial for gases!
gas solvent saturated solution
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The effect of pressure on gas solubility
gas volume is reduced pressure
(concentration!) increases more collisions occur
with liquid surface
Figure 13.12
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Henrys Law
A quantitative relationship between gas
solubility and pressure
Sgas kH x 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 Henrys law constant for a gas units of
mol/L.atm
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SAMPLE PROBLEM 13.2
Using Henrys Law to calculate gas solubility
PLAN
Knowing kH and Pgas, we can substitute into the
Henrys Law equation.
SOLUTION
0.1 mol / L
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Table 13.5 Concentration Definitions
concentration term
ratio
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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
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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
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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

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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 that contains 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 alcohol does the wine contain?
(c) A sample of rubbing alcohol contains 142 g
of isopropyl alcohol (C3H7OH) and 58.0 g of
water. What are the mole fractions of alcohol
and water?
PLAN
(a) Convert mg to g of Ca, find the ratio of g
Ca to g pill, and multiply by 106.
(b) Knowing the alcohol and the total volume,
the volume of alcohol can be calculated.
(c) Convert g of solute and solvent to moles,
and find the ratios of each part to the total.
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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
2.36 mol C3H7OH
x
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
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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
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SAMPLE PROBLEM 13.5
(continued)
(b)
70.0 g H2O
3.88 mol H2O
x
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
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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

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Three types of electrolytes
Figure 13.14
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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
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Quantitative Treatment of VP Lowering
Raoults 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 for csolvent in the above equation and
rearrange)
Posolvent - Psolvent DP csolute x
Posolvent
(change in VP is proportional to the mole
fraction of solute)
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SAMPLE PROBLEM 13.6
Using Raoults 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
92.5 torr
x
0.461 torr
0.137 mol C3H8O3 27.4 mol H2O
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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.
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Superimposed phase diagrams of solvent and
solution
aqueous solution dashed lines pure water solid
lines
Figure 13.16
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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)
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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)
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Table 13.6 Molal Boiling Point Elevation and
Freezing Point Depression Constants
of Several Solvents
boiling point (oC)
melting 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.
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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
3.62 m
x
1.85 oC
DTf
1.86 oC/m
3.62 m
x
BP 101.85 oC
FP -6.73 oC
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Osmotic Pressure

• Applies only to aqueous solutions!
• Two solutions of different concentrations are
  separated by a semi-permeable membrane (allows
  water but not solute to pass through)

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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
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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 a M
The constant of proportionality RT, so P M
x R x T
T is the Kelvin temperature
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Underlying Principle of Colligative Properties
Each property stems from an inability of solute
particles to cross between two phases.
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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).
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SAMPLE PROBLEM 13.8
Determining molar mass from osmotic pressure
SOLUTION
3.61 torr
x
M

2.08 x 10-4 M
(0.0821 L . atm/mol . K)(278.15 K)
3.12 x 10-7 mol
1.50 mL
x
x
mol g/M
21.5 mg
6.89 x 104 g/mol
x
x
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Fractional Distillation of Volatile Nonelectrolyte
s
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)
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The process of fractional distillation
Figure 13.18
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Colligative Properties of Electrolyte Solutions
Must consider the full dissociation into ions!
vant 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!
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Non-ideal behavior of electrolyte solutions
Observed values of i are less than the predicted
(expected) values.
Figure 13.19
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An ionic atmosphere model for non-ideal behavior
of electrolyte solutions
ionic atmospheres
Concept of effective concentration
Figure 13.20
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Some Practical Applications

• ion-exchange (water softeners)
• water purification

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Ion exchange for removal of hard-water cations
Use of ion-exchange resins
Figure B13.4
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Reverse osmosis for the removal of ions
Desalination Process
Figure B13.5
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End of Assigned Material
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Light scattering and the Tyndall effect
Figure 13.21
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A Cottrell precipitator for removing particulates
from industrial smokestack gases
Figure 13.22
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The steps in a typical municipal water treatment
plant
Figure B13.3