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8/19/2019 ChE 323 lecture 6_1 ed_02_12_14
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8/19/2019 ChE 323 lecture 6_1 ed_02_12_14
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Simple Mixtures hapter Outline
Introduction to Simple MixturesThermodynamic description of mixtures
6.1 Partial molar quantities
6.2 Thermodynamics of mixing
6.3 The chemical potential of liquidsThe properties of solutions
6.4 Ideal solutions, simple mixtures, and
non-ideal solutions
6.5 Colligative properties
6.6 Activities of regular solutions
6.9 The activities of ions in solution
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REVIEW OF BASIC CONCEPTS
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Mixtures
All matter
Substance
Compound
Element
Mixture
Homogeneous
Heterogeneous
A mixture of substances can vary in composition and properties from one sample
to another.
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What are Solutions?
•Solutions are homogeneous
mixtures of substances
composed of at least one
solute and one solvent.
•Solutions can be gases,
liquids, or solids.
Ideal and non-ideal solutions
Electrolytes and non-electrolytes
GENERAL TYPES
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How is a solution formed?
Steps that lead to the formation of a liquid solution
“Like dissolves like.”
1. Breaking up the solute into
individual components(expanding the solute).
2. Overcoming intermolecular
forces in the solvent to make
room for the solute
(expanding the solvent).3. Allowing the solute and
solvent to interact to form the
solution.
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Enthalpy (Heat) of Solution
The enthalpy change associated with the formation of asolution
soln 1 2 3 H H H H
Energy is absorbed!
Energy is released!
endothermic
exothermic
0 H ???
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Enthalpy (Heat) of Solution
(a) Process is exothermic if Step 3 releases more energy than that required in Step 1 & 2.
(b) Process is endothermic if Steps 1 & 2 require more energy than what is released in Step 3.
Pure
components
Separate solventmolecules ΔH1
Separate solute
molecules ΔH2
(Endothermic)
(Exothermic)
ΔHsoln = 0
ΔHsoln > 0
ΔHsoln
< 0
Allow solvent
and solute
molecules to mixΔH3
E n t h a l p y
. H
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Intermolecular forces in a solution
1
B
B2
3
(1) Solvent molecules, A-A
(3)Solvent and solutemolecules, A-B
(2)Solute molecules, B-B
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IMFs in Mixtures
Four possibilities for the relative strengths of IMFs:
1.IMFs are of the same type and of the same strength, solute and solvent
mix randomly ΔHsoln
= 0 : IDEAL SOLUTIONS.
2.IMFs between unlike molecules exceed
IMFs between like molecules, asolution forms, ΔH
soln
< 0 exothermic : NON-IDEAL SOLUTIONS
3.IMFs between solute and solvent molecules are somewhat weaker than
between molecules of the same kind, complete mixing may still occur,
ΔH
soln
> 0 endothermic : NON-IDEAL SOLUTIONS
4.IMFs between unlike molecules are much weaker than those between like
molecules, the components remain segregated in a heterogeneous mixture:
NO SOLUTION FORMS.
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Solubility of a Nonpolar Solute and a
Polar Solvent
H2 will be large & positive
because it takes considerable
energy to overcome thehydrogen bonding forces
among the water molecules to
expand.
Large amounts ofenergy would have to
be expended in order to
form an oil-water
solution!
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Solubility of an Ionic Solute and a
Polar Solvent
1 786 / NaCl s Na g Cl g H kJ mol
2 2 3
= 783 /
hyd H O l Na g Cl g Na aq Cl aq H H H
kJ mol
soln 3 / H kJ mol
Why is NaCl soluble in
water???
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Solubility of an Ionic Solute and a
Polar Solvent
(a)Orange & yellow spheres separated by apartition in a closed container. (b) The
spheres after the partition is removed and the
container has been shaken for some time.
(a) (b)Increase indegree of
disorder!
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Possible ases for Solution Formation
Processes that require large amounts of energy tend not to occur!!!
Solvent/solute
combination
H1 H2 H3 Hsol’n Outcome
Polar solvent,
polar solute
Large Large Large,
negative
Small Solution forms
Polar solvent,non polar solute
Small Large Small Large,positive
No solution forms
Nonpolar
solvent,
nonpolar solute
Small Small Small Small Solution forms
Nonpolar
solvent, polar
solute
Large Small Small Large,
positive
No solution forms
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Factors Affecting Solubility
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Try this….1. Predict whether or not a
solution will form in
each of the following
mixtures:
a Ethyl alcohol and water
b Octanol and water
c Hexane and octane
2. Benzoic acid is much more
soluble in aqueous NaOH
solution than it is in pure
water. Can you suggest a
reason for this?
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Partial Molar Quantities
The Thermodynamics of Mixing
The Chemical Potentials of Liquids
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Partial Molar Properties
Partial pressure
Partial molar volumePartial molar Gibbs energy (Chemicalpotential )
The thermodynamic contribution of a substance (per
mole) to an overall property of a mixture
Partial olar Quantities
NOTE: Partial molar properties are intensive properties!
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The Partial Molar Volume
The contribution (per mole) of substance, J, to the overall volume, V J , of a solution at constant temperature, pressure, and amount of solution
components (Silbey & Alberty, 2001)
FINITION
1000 mL H2O 1 mol H2O 1018 mL H2O
1014 mL EtOH-H2O sol’n1000 mL EtOH 1 mol H2O
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The Partial Molar Volume
The partial molar volume can also
be regarded as the change in
volume per mole of A added to a
large volume of the mixture.
, , '(the amount of all other substances present are constant)
J
J p T n
V V
n
a b Amount of A, n A
V o l u m
e ,
V
V(a)
V(b)
The partial molar volume of a substance is
the slope of the variation of the total volume
of the sample plotted against the
composition.
A A B BV n V n V NOTE:
The partial molar volume is a function of
composition!
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The Partial Molar Volume
• The partial molar volume varies
with composition since the
environment of each type of molecule changes with each
change in composition.
The partial molar volumes of water
and ethanol at 25oC.
1014 mL EtOH-H2O sol’n1000 mL EtOH 1 mol H2O
Does the partial molar volume always have a positive value
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Partial Molar Gibbs Energy Chemical Potential
• For a substance in a mixture, the chemical potential is defined
as being the partial molar Gibbs energy
, , '(the amount of all other substances present are constant)
J
J p T n
G
n
• The slope of a plot of Gibbs energy
against the amount of the component
J , with the pressure and temperature
(and the amounts of other substances)held constant
A A B BG n n
Total Gibbs energy of the binary mixture @ constant T & p
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Partial Molar Gibbs Energy Chemical Potential
• When composition, T , & p vary
... A A B BdG Vdp SdT dn dn
Fundamental equation of chemical thermodynamics
At constant pressure and temperature,
... A A B BdG dn dn
,maxedG dw
Non-expansion work takes place due to the changing composition of the
systems!
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The Chemical Potential:On A Wider Scope
• The chemical potential also shows how the internal
energy varies with composition.
Recall,
TS pV U G GTS pV U
So,
An infinitesimal change in U f or a system of variable composition
dGSdT TdS Vdp pdV dU ... B B A A nnTdS pdV dU
At constant volume and entropy
...
B B A A
nndU
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The Chemical Potential:On A Wider Scope
• The chemical potential also shows how the extensive
thermodynamic properties – H, U, A, and G – vary
with composition.
',, n pS J
J n
H
',, nV S J
J n
U
',, nT V J
J n
A
',, nT p J
J n
G
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The Gibbs-Duhem Equation
i
j
i
i
j
i
ii dnd ndG11
i
j
i
idnSdT VdpdG1
SdT Vdpd n j
i
ii
1
At constant p and T
01
j
i
iid n
For a binary system
A
B
A B d
n
nd The partial molar property of another substance can
be determined from the property of the other.
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To ponder on…
1 Distinguish ideal solutions
from non-ideal solutions with
respect to chemical
potential?
2 Interpret
Raoult’s and
Henry’s laws using the
underlying principle ofchemical potential?
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Remember,
The Gibbs energy of the mixture depends on itscomposition.
At constant T and p systems tend towards lower
Gibbs energy.
Spontaneous mixing results inspontaneous change in
composition!
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Other Thermodynamic Mixing Functions
Entropy of mixing
) xln x xln x( nRT
GS
B B A An ,n , p
mix
mix B A
Enthalpy of mixing
S T H G
0 H mix At constant T and pThere are nointeractions between
the molecules
forming the gaseous
mixture!The driving force for mixing is the increasing
entropy of the system as the molecules mingle.
The entropy of the surroundings remain
unchanged.
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Thermodynamic Functions of Perfect Gases
Perfect gases mix spontaneously in all proportions since entropy increases
for all compositions and temperatures.
There is no heat transfer to the surroundings when perfect gases mix thus
the entropy of the surroundings remain unchanged.