Page 315 - Physical Chemistry

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Chapter 10 Convention I standard state of each solution component i is taken as pure liquid i at
Nonideal Solutions the temperature and pressure of the solution:

m° m *1T, P2 for all components (10.7)*
I,i
i
where the subscript I indicates the Convention I choice of standard states, the degree
indicates the standard state, and the star indicates a pure substance. Convention I is the
same convention as that used for ideal solutions (Sec. 9.6).
The value of the chemical potential m 10G>0n 2 is clearly independent of
i
i T,P,n j i
the choice of standard state. However, the value of m° depends on the choice of stan-
i
dard state. Therefore, a exp[(m m°)/RT] [Eq. (10.3)] depends on this choice;
i
i
i
hence g a /x also depends on the choice of standard state. We use the subscript I
i
i
i
to denote Convention I activities, activity coefficients, and standard-state chemical
potentials, writing them as a , g , and m° . An alternative notation for g is f (which
I,i
i
I,i
I,i
I,i
can be confused with the quantity fugacity, defined in Sec. 10.10).
Since the Convention I standard state is the same as the ideal-solution standard
id
state, m° in the ideal-solution equation m m° RT ln x is the same as m° in the
i
i
i
i
I,i
Convention I nonideal equation m m° RT ln g x . It follows that for an ideal
i
I,i i
I,i
solution g 1. For a nonideal solution, the deviations of the g ’s from 1 measure
I,i
I,i
the deviation of the solution’s behavior from ideal-solution behavior.
Equations (10.6) and (10.7) give m m* RT ln g x .As x goes to 1 at constant
i
i
I,i i
i
T and P, the chemical potential m goes to m*, since the solution becomes pure i. Hence
i
i
the x → 1 limit of this last equation is m* m* RT ln g or ln g 0 and g 1:
i
I,i
I,i
i
i
I,i
g S 1 as x S 1 for each i (10.8)*
i
I,i
The Convention I activity coefficient of species i goes to 1 as the solution composition
approaches pure i (see Fig. 10.3a).
Since the Convention I standard state of each solution component is the pure sub-
stance, the Convention I standard-state thermodynamic properties of i equal the cor-
responding properties of pure i. Convention I puts all the components on the same
footing and does not single out one component as the solvent. Therefore, Convention
I is often called the symmetrical convention.
Convention II Convention II (also called the unsymmetrical convention) is
used when one wants to treat one solution component (the solvent A) differently from
the other components (the solutes i). Common cases are solutions of solids or gases in
a liquid solvent.
The Convention II standard state of the solvent A is pure liquid A at the T and P
of the solution. With m° m*(T, P), Eq. (10.6) becomes m m* RT ln g II,A A
x .
A
II,A
A
A
Taking the limit of this equation as x → 1, we find [as in (10.8)] that g II,A → 1 as
A
x → 1. Thus
A
m° II,A m*1T, P2, g II,A S 1 as x S 1 (10.9)*
A
A
For each solute i A, Convention II chooses the standard state so that g II,i goes
to 1 in the limit of infinite dilution:
g II,i S 1 as x S 1 for each i A (10.10)*
A
Note that the limit in (10.10) is taken as the solvent mole fraction x goes to 1 (and
A
hence x → 0), which is quite different from (10.8), where the limit is taken as x → 1.
i
i
We choose a Convention II standard state that is consistent with (10.10) as follows.
x must equal 1 in the
Setting m in (10.6) equal to m°, we get 0 RT ln g x , so g II,i i
i
i
i i
standard state. When x is near 1 and the solute mole fractions are small, then by
A
(10.10) the activity coefficient g II,i is close to 1. We choose the standard state of each
solute i as the fictitious state obtained as follows. We pretend that the behavior of m i