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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentPhysical Interpretation of partial molar quantities:
It may appear that there is something ¬ 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.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 Physical chemistry, Thermodynamics, Mole, pH, Colligative properties, RHS, KF, Raoult, è Aø

Click to edit the document details