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Lecture 7.pdf-Simple mixtures Chapter 5 Sections A
Lecture_7.pdf-Simple mixtures Chapter 5 Sections A
Lecture 7.pdf-Simple mixtures Chapt...
Lecture_7.pdf-Simple mixtures Chapter 5 Sections A
Page 12
Chemical potential (
μ
) wider
significance
Chemical potential does more than show how G varies with composition
Similarly, chemical potential shows how H and A may change
Page 13
Thermodynamics of mixing
Perfect gases
•
Gibbs energy of a mixture depends on its
composition :
–
G = n
A
μ
A
+ n
B
μ
B
(for 2 components)
•
At constant T & p, systems tend towards lower
Gibbs energy
•
Mixing : spontaneous change of composition
–
Example : 2 gases, introduced into the same
container, will spontaneously mix; this
Page 14
PHYSICAL CHEMISTRY: THERMODYNAMICS, STRUCTURE, AND CHANGE 10E | PETER ATKINS | JULIO DE PAULA
©2014
W. H. FREEMAN AND COMPANY
CHAPTER 5:
FIGURE 5A.6
Page 15
Thermodynamics of mixing
Perfect gases - 2
Two perfect gases (A & B) at same T & p
Initially (before mixing), they each have their “pure” values
of chemical potential:
μ
= G
m
=
μ
ϴ
+RT ln (p/p
ϴ
)
(where
μ
ϴ
is the standard chemical potential of the pure gas
at 1 bar)
Convention : replace p/p
ϴ
by p (since p
ϴ
is = 1 bar)
Then :
μ
=
μ
ϴ
+ RT ln p for each gas
Thus in the initial state (before mixing) , for the
system:
G
i
= n
A
μ
A
+ n
B
μ
B
=
Page 16
Thermodynamics of mixing
Perfect gases - 3
Before mixing , for the
system:
G
i
= n
A
(
μ
ϴ
A
+ RT ln p) + n
B
(
μ
ϴ
B
+RT ln p)
After mixing, the partial pressures of the gases are p
A
and p
B
, with p
A
+
p
B
= p
After mixing, for the system :
G
f
= n
A
(
μ
ϴ
A
+ RT ln p
A
) + n
B
(
μ
ϴ
B
+RT ln p
B
)
The difference G
f
–
G
i
=
∆
mix
G is given by :
∆
mix
G = n
A
RT ln (p
A
/p) + n
B
R
T ln (p
B
/p)
Which may be rewritten as :
∆
mix
G =
Recall :
Page 17
Thermodynamics of mixing
Perfect gases - 4
∆
mix
G = nRT(x
A
ln x
A
+ x
B
ln x
B
)
Because mole fractions are always < 1,
the ln values in the equation are
always negative.
Thus
∆
mix
G <0 for all compositions, i.e.
perfect gases mix spontaneously in all
proportions
Page 18
Thermodynamics of mixing
Perfect gases - 5
Entropy
Since
It follows that:
∆
mix
S= - nR(x
A
lnx
A
+ x
B
lnx
B
)
Page 19
Thermodynamics of mixing
Perfect gases - 6
Enthalpy
Since
∆
G =
∆
H -T
∆
S
⇨
∆
H =
∆
G + T
∆
S
And
∆
mix
G = nRT(x
A
ln x
A
+ x
B
ln x
B
)
∆
mix
S= - nR(x
A
lnx
A
+ x
B
lnx
B
)
∆
mix
H = nRT(x
A
ln x
A
+ x
B
ln x
B
) +T [- nR(x
A
lnx
A
+ x
B
lnx
B
)]
Page 20
Chemical potentials of liquids
•
To discuss the equilibrium properties
of liquid mixtures, we need to know
how
G varies with composition.
•
Recall : at equilibrium, the chemical
potential of a substance in the liquid
phase is equal to its chemical
potential in the gas phase.
Page 21
μ
of liquids : ideal solutions
•
Using superscript
*
for quantities related to pure substances :
μ
A
* (l) for example
•
Vapor pressure of a pure liquid is p
A
*
•
Recall, for a perfect gas
μ
=
μ
ϴ
+RT ln (p/p
ϴ
)
•
Since, at equilibrium,
μ
A
(l) =
μ
A
(g), we can write
If another substance (solute) is also present in the liquid, its
μ
A
*
is changed to
μ
A
and its vapour pressure is changed to pA. The
vapour and solvent are still in equilibrium, so :
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