Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

PROBLEMS 414

12.11The solubility of gaseous O 2 at a partial pressure of1:01bar and a temperature of310:2K, ex-
pressed as a concentration, is1:07 10 ^3 mol dm^3 in pure water and4:68 10 ^4 mol dm^3
in a3:0M aqueous solution of KCl.^17 This solubility decrease is thesalting-out effect. Calcu-

late the activity coefficient (^) c;Bof O 2 in the KCl solution.
12.12At298:15K, the partial molar volume of CO 2 (aq) is 33 cm^3 mol^1. Use Eq.12.8.35to es-
timate the percent change in the value of the Henry’s law constantkH,Bfor aqueous CO 2 at
298:15K when the total pressure is changed from1:00bar to10:00bar.
12.13Rettich et al^18 made high-precision measurements of the solubility of gaseous oxygen (O 2 ) in
water. Each measurement was made by equilibrating water and oxygen in a closed vessel for
a period of up to two days, at a temperature controlled within0:003K. The oxygen was
extracted from samples of known volume of the equilibrated liquid and gas phases, and the
amount of O 2 in each sample was determined fromp-V-Tmeasurements taking gas nonideal-
ity into account. It was then possible to evaluate the mole fractionxBof O 2 in the liquid phase
and the ratio.ngB=Vg/for the O 2 in the gas phase.
Table 12.5 Data for Problem 12. 13 (A = H 2 O, B = O 2 )
TD298:152K Second virial coefficients:
xBD2:02142 10 ^5 BAAD 1152  10 ^6 m^3 mol^1
.ngB=Vg/D35:9957mol m^3 BBBD16:2 10 ^6 m^3 mol^1
pAD3167:13Pa BABD27:0 10 ^6 m^3 mol^1
VAD18:069 10 ^6 m^3 mol^1
VB^1 D31:10 10 ^6 m^3 mol^1
Table12.5gives values of physical quantities atTD298:152K needed for this problem. The
values ofxBand.ngB=Vg/were obtained by Rettich et al from samples of liquid and gas phases
equilibrated at temperatureT, as explained above.pAis the saturation vapor pressure of pure
liquid water at this temperature.
Your calculations will be similar to those used by Rettich et al to obtain values of the Henry’s
law constant of oxygen to six significant figures. Your own calculations should also be carried
out to six significant figures. For the gas constant, use the valueRD8:31447J K^1 mol^1.
The method you will use to evaluate the Henry’s law constantkH,BDfB=xBat the experimen-
tal temperature and pressure is as follows. The value ofxBis known, and you need to find the
fugacityfBof the O 2 in the gas phase.fBcan be calculated fromBandpB. These in turn
can be calculated from the pressurep, the mole fractionyBof O 2 in the gas phase, and known
values of second virial coefficients. You will calculatepandyBby an iterative procedure.
Assume the gas has the virial equation of state.Vg=ng/D.RT=p/CB(Eq.9.3.21) and use
relevant relations in Sec.9.3.4.
(a)For the equilibrated liquid-gas system, calculate initial approximate values ofpandyB
by assuming thatpAis equal topAandpBis equal to.ngB=Vg/RT.
(b)Use your approximate values ofpandyBfrom part (a) to calculateA, the fugacity
coefficient of A in the gas mixture.
(c)Evaluate the fugacityfAof the H 2 O in the gas phase. Assumep,yB, andAhave the
values you calculated in parts (a) and (b). Hint: start with the value of the saturation vapor
pressure of pure water.
(^17) Ref. [ 106 ]. (^18) Ref. [ 143 ].