Thermodynamics

Chapter 16 | 815EXAMPLE 16–11Composition of Different Phases of a MixtureIn absorption refrigeration systems, a two-phase equilibrium mixture of liquidammonia (NH 3 ) and water (H 2 O) is frequently used. Consider one such mixtureat 40°C, shown in Fig. 16–27. If the composition of the liquid phase is70 percent NH 3 and 30 percent H 2 O by mole numbers, determine the compositionof the vapor phase of this mixture.Solution A two-phase mixture of ammonia and water at a specified temperatureis considered. The composition of the liquid phase is given, and thecomposition of the vapor phase is to be determined.Assumptions The mixture is ideal and thus Raoult’s law is applicable.Properties The saturation pressures of H 2 O and NH 3 at 40°C are P H2 O,sat 7.3851 kPa and P NH3 ,sat 1554.33 kPa.Analysis The vapor pressures are determined fromP H2 O,gas side y H2 O,liquid side P H2 O,sat 1T2 0.30 17.3851 kPa2 2.22 kPaP NH3 ,gas side y NH3 ,liquid side P NH3 ,sat 1T2 0.70 11554.33 kPa2 1088.03 kPaVAPORLIQUIDH 2 O + NH 340°Cy g,H2 O = ?y g,NH3 = ?y f,H2 O = 0.30y f,NH3 = 0.70FIGURE 16–27Schematic for Example 16–11.The total pressure of the mixture isP total P H2 O P NH3 2.22 1088.03 1090.25 kPaThen the mole fractions in the gas phase arey H2 O,gas side P H 2 O,gas side 2.22 kPaP total 1090.25 kPa 0.0020y NH3 ,gas side P NH 3 ,gas sideP total1088.03 kPa1090.25 kPa 0.9980Discussion Note that the gas phase consists almost entirely of ammonia,making this mixture very suitable for absorption refrigeration.SUMMARYAn isolated system is said to be in chemical equilibrium if nochanges occur in the chemical composition of the system.The criterion for chemical equilibrium is based on the secondlaw of thermodynamics, and for a system at a specified temperatureand pressure it can be expressed asFor the reaction1dG2 T, P 0n A A n B B ∆ n C C n D Dwhere the n’s are the stoichiometric coefficients, the equilibriumcriterion can be expressed in terms of the Gibbs functionsasn C g C n D g D n A g A n B g B 0which is valid for any chemical reaction regardless of thephases involved.For reacting systems that consist of ideal gases only, theequilibrium constant K P can be expressed aswhere the standard-state Gibbs function change ∆G*(T) andthe equilibrium constant K P are defined asandK P e ¢G*1T 2>R uT¢G* 1T2 n C g * C1T2 n D g * D1T2 n A g * A1T2 n B g * B1T2K P P n CC P n DDP n AA P n BBHere, P i ’s are the partial pressures of the components in atm.The K P of ideal-gas mixtures can also be expressed in termsof the mole numbers of the components asK P N n CC N n DDN n AA N n BBaP bN total¢n