Page 340 - Physical Chemistry

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Values of standard-state conventional thermodynamic properties of some ions in Section 10.10
water at 25°C are listed in the Appendix. Nonideal Gas Mixtures
The thermodynamic properties (10.91) to (10.93) for an electrolyte as a whole in
aqueous solution are indicated by the state designation ai (standing for aqueous, ion-
ized) in the NBS tables (Sec. 5.9). Thermodynamic properties for ion pairs, complex
ions, and simple ions in aqueous solution are indicated by ao (aqueous, undissoci-
ated). Thus, the NBS tables give at 298 K G°[ZnSO (ai)] 891.6 kJ/mol for the
f
4
ionized electrolyte ZnSO [Eq. (10.91)] and G°[ZnSO (ao)] 904.9 kJ/mol for
4
f
4
the ZnSO (aq) ion pair (Sec. 10.8).
4
Because of the strong ordering produced by hydration of ions, S° for dissolving
a salt in water is sometimes negative, even though a highly ordered low-entropy crys-
tal is destroyed and a mixture produced from two pure substances.
10.10 NONIDEAL GAS MIXTURES
Nonideal Gas Mixtures
The standard state of component i of a nonideal gas mixture is taken as pure gas i at
the temperature T of the mixture, at 1 bar pressure, and such that i exhibits ideal-gas
behavior. This is the same choice of standard state as that made in Sec. 5.1 for a pure
nonideal gas and in Sec. 6.1 for a component of an ideal gas mixture. Thermodynamic
properties of this fictitious standard state can be calculated once the behavior of the
real gas is known.
The activity a of a component of a nonideal gas mixture is defined as in (10.3):
i
a exp31m m°2>RT4 (10.94)
i
i
i
where m is the chemical potential of gas i in the mixture and m° is the chemical
i
i
potential of i in its standard state. Taking logs, we have, similar to (10.4),
m m°1T2 RT ln a i (10.95)
i
i
The choice of standard state (with P 1 bar) makes m° depend only on T for a com-
i
ponent of a nonideal gas mixture.
The fugacity f of a component of any gas mixture is defined as f a
1 bar:
i
i
i
f >P° a where P° 1 bar (10.96)
i
i
Since a is dimensionless, f has units of pressure. Since m in (10.94) is an intensive
i
i
i
property that depends on T, P, and the mixture’s mole fractions, f is a function of these
i
variables: f f (T, P, x , x , . . . ). Equation (10.95) becomes
1
2
i
i
m m°1T2 RT ln 1 f >P°2 (10.97)*
i
i
i
For an ideal gas mixture, (6.4) reads
id
m m° RT ln 1P >P°2
i
i
i
Comparison with (10.97) shows that the fugacity f plays the same role in a nonideal
i
gas mixture as the partial pressure P in an ideal gas mixture. Statistical mechanics
i
id
shows that, in the limit of zero pressure, m approaches m . Moreover, m° in (10.97) is
i
i
i
the same as m° in an ideal gas mixture. Therefore f in (10.97) must approach P in the
i
i
i
limit as the mixture’s pressure P goes to zero and the gas becomes ideal:
f S P as P S 0 or lim 1 f >P 2 1 (10.98)
i
i
i
i
PS0
The partial pressure P of gas i in a nonideal (or ideal) gas mixture is defined as
i
P x P [Eq. (1.23)]. The deviation of the fugacity f of i from the partial pressure P i
i
i
i