Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

PROBLEMS 415

(d)Use your most recently calculated values ofp,A, andfAto calculate an improved value

ofyB.

(e)Use your current values ofpandyBto evaluate the compression factorZof the gas

mixture, taking nonideality into account.

(f)Derive a general expression forpas a function of.ngB=Vg/,T,yB, andZ. Use this

expression to calculate an improved value ofp.

(g)Finally, use the improved values ofpandyBto evaluate the Henry’s law constantkH,Bat

the experimentalTandp.

12.14The method described in Prob. 12. 13 has been used to obtain high-precision values of the
Henry’s law constant,kH,B, for gaseous methane dissolved in water.^19 Table12.6lists values

Table 12.6 Data for Prob. 12. 14

1=.T=K/ ln.kH,B=p/ 1=.T=K/ ln.kH,B=p/

0:00363029 10:0569 0:00329870 10:6738

0:00359531 10:1361 0:00319326 10:8141

0:00352175 10:2895 0:00314307 10:8673

0:00347041 10:3883 0:00309444 10:9142

0:00341111 10:4951 0:00304739 10:9564

0:00335390 10:5906

of ln.kH,B=p/at eleven temperatures in the range 275 K– 328 K and at pressures close to 1 bar.

Use these data to evaluateÅsol,BHandÅsol,BCpatTD298:15K. This can be done by a

graphical method. Better precision will be obtained by making a least-squares fit of the data to

the three-term polynomial

ln.kH,B=p/DaCb.1=T /Cc.1=T /^2

and using the values of the coefficientsa,b, andcfor the evaluations.

12.15Liquid water and liquid benzene have very small mutual solubilities. Equilibria in the binary
water–benzene system were investigated by Tucker, Lane, and Christian^20 as follows. A known
amount of distilled water was admitted to an evacuated, thermostatted vessel. Part of the water
vaporized to form a vapor phase. Small, precisely measured volumes of liquid benzene were
then added incrementally from the sample loop of a liquid-chromatography valve. The benzene
distributed itself between the liquid and gaseous phases in the vessel. After each addition, the
pressure was read with a precision pressure gauge. From the known amounts of water and
benzene and the total pressure, the liquid composition and the partial pressure of the benzene
were calculated. The fugacity of the benzene in the vapor phase was calculated from its partial
pressure and the second virial coefficient.
At a fixed temperature, for mole fractionsxBof benzene in the liquid phase up to about
3  10 ^4 (less than the solubility of benzene in water), the fugacity of the benzene in the
equilibrated gas phase was found to have the following dependence onxB:
fB
xB
DkH,BAxB

HerekH,Bis the Henry’s law constant andAis a constant related to deviations from Henry’s

law. At 30 C, the measured values werekH,BD385:5bar andAD2:24 104 bar.

(^19) Ref. [ 144 ]. (^20) Ref. [ 159 ].