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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
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