Thermodynamics

708 | ThermodynamicsSUMMARYA mixture of two or more gases of fixed chemical compositionis called a nonreacting gas mixture The composition of agas mixture is described by specifying either the mole fractionor the mass fraction of each component, defined aswhereThe apparent (or average) molar mass and gas constant of amixture are expressed asAlso,Dalton’s law of additive pressures states that the pressureof a gas mixture is equal to the sum of the pressures each gaswould exert if it existed alone at the mixture temperature andvolume. Amagat’s law of additive volumes states that the volumeof a gas mixture is equal to the sum of the volumes eachgas would occupy if it existed alone at the mixture temperatureand pressure. Dalton’s and Amagat’s laws hold exactlyfor ideal-gas mixtures, but only approximately for real-gasmixtures. They can be expressed asDalton’s law:Amagat’s law:mf i m im mandy i N iN mm m aki1M m m mN m akm i andN m aki1y i M i andR m R uM mmf i y M ii andMM m 1kmmf iaP m akV m akHere P i is called the component pressure and V i is calledthe component volume. Also, the ratio P i /P m is called thepressure fraction and the ratio V i /V m is called the volumefraction of component i. For ideal gases, P i and V i can berelated to y i byP i V i N i yP m V m N imThe quantity y i P m is called the partial pressure and the quantityy i V m is called the partial volume. The P-v-T behaviorof real-gas mixtures can be predicted by using generalizedi1i1N ii1i1 M iP i 1T m , V m 2V i 1T m , P m 2compressibility charts. The compressibility factor of the mixturecan be expressed in terms of the compressibility factorsof the individual gases aswhere Z i is determined either at T m and V m (Dalton’s law) or atT m and P m (Amagat’s law) for each individual gas. The P-v-Tbehavior of a gas mixture can also be predicted approximatelyby Kay’s rule, which involves treating a gas mixture as a puresubstance with pseudocritical properties determined fromThe extensive properties of a gas mixture, in general, canbe determined by summing the contributions of each componentof the mixture. The evaluation of intensive properties ofa gas mixture, however, involves averaging in terms of massor mole fractions:andP ¿ cr,m aki1U m aku m aki1h m aki1s m aki1c v,m aki1c p,m aki1i1H m aki1S m aki1kZ m a y i Z iU i akH i akS i aki1i1y i P cr,i andT ¿ cr,m aki1i1m i u i akm i s i akmf i u i andu m akmf i h i andh m akmf i s i ands m akmf i c v,i andc v,m akmf i c p,i andc p,m akThese relations are exact for ideal-gas mixtures and approximatefor real-gas mixtures. The properties or property changesof individual components can be determined by using idealgasor real-gas relations developed in earlier chapters.i1m i h i aki1i1i1i1i1N i u iN i h iN i s iy i u iy i h iy i s ii1i1i1y i T cr,iy i c v,iy i c p,i