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In a nonideal gas mixture, the fugacities f and fugacity coefficients f are defined Problems
i i
so that the chemical potentials have the form m m° RT ln ( f /P°) m°
i i i i
RT ln (f P /P°), where P x P and the standard state of each component is the
i i i i
hypothetical pure ideal gas at 1 bar and the temperature of the mixture. Fugacity
coefficients in a mixture can be found from P-V-T data for the mixture or can be
estimated from an equation of state for the mixture.
Important kinds of calculations discussed in this chapter include:
l
• Calculation of activity coefficients from vapor-pressure data using P g x P*
i I,i i i
l
l
or P K g x and P g x P*.
i i II,i i A II,A A A
• Calculation of activity coefficients of a nonvolatile solute from solvent vapor-
pressure data and the Gibbs–Duhem equation.
• Calculation of electrolyte activity coefficients from the Debye–Hückel equation
or the Davies equation.
• Calculation of fugacity coefficients from P-V-T data or an equation of state.
FURTHER READING AND DATA SOURCES
Denbigh, chaps. 7, 9, 10; McGlashan, chaps. 16, 18, 20; Prigogine and Defay, chaps.
20, 21, 27; Eyring, Henderson, and Jost, vol. I, pp. 320–352; Lewis and Randall,
chaps. 20, 21, 22; Robinson and Stokes, chaps. 1, 2, 12 to 15; Bockris and Reddy, chap.
3; Davies.
Excess quantities: M. L. McGlashan (ed.), Specialist Periodical Reports,
Chemical Thermodynamics, vol. 2, Chemical Society, 1978, pp. 247–538.
Electrolyte-solution activity coefficients and osmotic coefficients: Robinson and
Stokes, appendices; R. Parsons, Handbook of Electrochemical Constants, Academic
Press, 1959.
Fugacities of gases: Landolt-Börnstein, vol. II, part 1, pp. 310–327; TRC
Thermodynamic Tables (see Sec. 5.9 for the full reference).
PROBLEMS
Section 10.1 Section 10.2
10.1 True or false? (a) When a solution component is in its 10.5 (a) Take
/
n of G E G G id to show that
i
id
standard state, its activity is 1. (b) If m increases in an isother- E m i m i . (b) Use the result of (a) to show
i 10G >0n i 2 T,P,n j i
mal, isobaric process, then a must increase. (c) a and g are in- that
i i i
tensive properties. (d) The Convention I standard states are E (10.106)
the same as those for an ideal solution and the Convention II RT ln g i 10G >0n i 2 T,P,n j i
E
Hence g can be found from G data. (c) For a solution of the
standard states are the same as for an ideally dilute solution. i
E
E
E
liquids B and C, the mean molar G is G G /(n n ).
(e) All activity coefficients g go to 1 in the limit x → 1. m B C
i i E E
Differentiate G (n n )G with respect to n at constant
C
B
m
B
10.2 For each of the following quantities, state whether its n and use
G /
n (
G /
x )(
x /
n ) to show that
E
E
value depends on the choice of standard state for i: (a) m ; C B B B B n C
i E E
(b) m°; (c) g ; (d) a . RT ln g I,B G m x C 10G m >0x B 2 T,P
i i i
10.3 Prove that 0 a 1. [Hint: Use (4.90).]
I,i Section 10.3
10.4 Justify the validity of the following equations for 10.6 True or false? (a) For the solvent in a solution, g
standard-state Convention II solute partial molar properties: g . (b) For the solvent in a solution, a a . II,A
I,A II,A I,A
V° ,i V i , H° ,i H ,i , S° ,i 1S i R ln x i 2 q
q
q
10.7 At 35°C, the vapor pressure of chloroform is 295.1 torr,
where the infinity superscript denotes infinite dilution. and that of ethanol (eth) is 102.8 torr. A chloroform–ethanol