264
6 The Thermodynamics of Solutions
By convention II:
a
(II)
2
P 2
k 2
12.45 torr
160 torr
0.0778
γ
(II)
2
a 2
x 2
0.0778
0.100
0.778
The activity coefficient γ
(II)
2 is closer to unity than is γ
(I)
2 . The activity coefficient of the
solvent is the same in both conventions.
Exercise 6.15
Since diethyl ether is designated as the solvent in the previous example its activity and activity
coefficient are the same in convention II as in convention I. Find the activity and the activity
coefficient of diethyl ether in the previous example. The partial vapor pressure of diethyl ether at
this composition and pressure is equal to 408.6 torr and the vapor pressure of pure diethyl ether
at this temperature is equal to 442.6 torr.
The Molality Description
Activities and activity coefficients of solutes are also defined for the molality description.
The molality of solute number i is given by
m i
n i
w 1
n i
n 1 M 1
x i
x 1 M 1
(6.3-35)
where M 1 is the molar mass of the solvent and w 1 is the mass of the solvent in kilograms.
Once again, we want to have a version of Eq. (6.3-6). Using the relation of Eq. (6.3-35)
in Eq. (6.3-34), we write
µ i µ
◦(II)
i
+ RT ln(M 1 m
◦ ) + RT ln
γ
(II)
i x 1 m i
m ◦
(6.3-36)
where m ◦ is defined to equal 1 mol kg −1 (exactly). This equation is in the form of
Eq. (6.3-6) if
a
(m)
i
γ
(II)
i x 1 m i
m ◦
(6.3-37)
and
µ
◦(m)
i
µ
◦(II)
i
+ RT ln(M 1 m
◦ )
(6.3-38)
The standard state is the same as for the molality description of a dilute solute that
obeys Henry’s law: the hypothetical solution with molality equal to 1 mol kg −1 and
obeying the molality version of Henry’s law, Eq. (6.2-11).
We define the molality activity coefficient
γ
(m)
i
γ
(II)
i x 1
(6.3-39)
6 The Thermodynamics of Solutions
By convention II:
a
(II)
2
P 2
k 2
12.45 torr
160 torr
0.0778
γ
(II)
2
a 2
x 2
0.0778
0.100
0.778
The activity coefficient γ
(II)
2 is closer to unity than is γ
(I)
2 . The activity coefficient of the
solvent is the same in both conventions.
Exercise 6.15
Since diethyl ether is designated as the solvent in the previous example its activity and activity
coefficient are the same in convention II as in convention I. Find the activity and the activity
coefficient of diethyl ether in the previous example. The partial vapor pressure of diethyl ether at
this composition and pressure is equal to 408.6 torr and the vapor pressure of pure diethyl ether
at this temperature is equal to 442.6 torr.
The Molality Description
Activities and activity coefficients of solutes are also defined for the molality description.
The molality of solute number i is given by
m i
n i
w 1
n i
n 1 M 1
x i
x 1 M 1
(6.3-35)
where M 1 is the molar mass of the solvent and w 1 is the mass of the solvent in kilograms.
Once again, we want to have a version of Eq. (6.3-6). Using the relation of Eq. (6.3-35)
in Eq. (6.3-34), we write
µ i µ
◦(II)
i
+ RT ln(M 1 m
◦ ) + RT ln
γ
(II)
i x 1 m i
m ◦
(6.3-36)
where m ◦ is defined to equal 1 mol kg −1 (exactly). This equation is in the form of
Eq. (6.3-6) if
a
(m)
i
γ
(II)
i x 1 m i
m ◦
(6.3-37)
and
µ
◦(m)
i
µ
◦(II)
i
+ RT ln(M 1 m
◦ )
(6.3-38)
The standard state is the same as for the molality description of a dilute solute that
obeys Henry’s law: the hypothetical solution with molality equal to 1 mol kg −1 and
obeying the molality version of Henry’s law, Eq. (6.2-11).
We define the molality activity coefficient
γ
(m)
i
γ
(II)
i x 1
(6.3-39)