5.5. Partial Molar Quantities
Partial Molar quantities are required to deal with open
systems
, i.e., systems that
permit mass transfer between themselves and surroundings.
Consider an open
system with
n
1
moles of component 1,
n
2
moles of component 2,
n
3
moles of component 3, etc..
We would write the free energy change
dG
for
such a system as
dG
=
æ
è
¹
G
¹
P
ö
ø
T
,
n
1
,
n
2,...
dP
+
æ
è
¹
G
¹
T
ö
ø
P
,
n
1
,
n
2,...
dT
+
æ
è
ç
¹
G
¹
n
1
ö
ø
÷
P
,
T
,,
n
2,...
dn
1
+
...
=
VdP
−
SdT
+
G
1
dn
1
+
G
2
dn
2
+
...
In the second equality, the quantities
G
1
,
G
2
, etc.. are called
partial molar free
energies
.
Similarly, we may define partial molar volumes, partial molar
enthalpies, internal energies, and entropies:
V
1
=
æ
è
ç
¹
V
¹
n
1
ö
ø
÷
P
,
T
,,
n
2,...
;
H
1
=
æ
è
ç
¹
H
¹
n
1
ö
ø
÷
P
,
T
,,
n
2,...
; etc
Because of their great importance in the thermodynamics of solutions, we discuss
partial molar volumes and partial molar free energies further.
Partial Molar Volume:
The total volume of a solution of, say, two miscible liquids is given by
(5.33)
V
=
n
1
V
1
+
n
2
V
2
.
The units of partial molar volumes are the same as molar volumes.
The
relationship between the two, i.e., partial molar volume and the molar volume is a
subtle but important one.
In the case of ideal solutions, the partial molar volume of each component will
be identical to the molar volume of the pure substance in the absence of the
other component.
However, in the case of nonideal solutions, the presence of the second
component has a measurable influence on the molar volume of the first
component and vice versa.
Therefore, in general,
V
1
!
V
1
±
and
V
2
!
V
2
±
.
The standard state for defining partial molar quantities is a 1
molal
solution, i.e., a
solution that contains 1 mol of the substance in 1.0 kg of solvent.
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Physical Interpretation of partial molar quantities:
It may appear that there is something °not quite right± about the following two
equations:
V
=
n
1
V
1
+
n
2
V
2
, where
V
1
=
æ
è
ç
¹
V
¹
n
1
ö
ø
÷
P
,
T
,
n
2
,and
V
2
=
æ
è
ç
¹
V
¹
n
2
ö
ø
÷
P
,
T
,
n
1
.
Based on what we have seen so far, the first equation should be
which is simply another application of the chain rule in partial
dV
=
V
1
dn
1
+
V
2
dn
2
,
differentiation.
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 Fall '09
 Physical chemistry, Thermodynamics, Mole, pH, Colligative properties, RHS, KF, Raoult, è Aø

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