Enthalpy Balances Involving Phase Change

Multi-stage separation calculations require heat balances involving transition between the phases. The enthalpy balance equations must, therefore, include heats of vaporization and condensation. Usually these heats are not calculated separately but are implied by using appropriate methods for calculating liquid enthalpies and vapor enthalpies. Consider, for instance, a system where a vapor stream and a liquid stream enter with enthalpies and // respectively, and leave as a mixed phase stream with vapor enthalpy and liquid enthalpy h2. These are total stream enthalpy rates with units such as kJ/h. If no heat is added to or removed from the system, an energy balance is written as 

Any heat of condensation or vaporization that accompanies this step is included in this energy balance. 

It is possible to cause phase transition without the addition or removal of heat and without any pressure change by bringing together streams with distinct compositions. The process of mixing and attaining equilibrium may involve the transition of certain components from one phase to the other. As this takes place, temperature changes are expected due to heat of condensation or vaporization. Example 1.16 illustrates these effects. 

Normal butane and normal hexane are two chemically similar components, and a mixture of them at low pressures is expected to have characteristics approaching those of an ideal solution. Thus, for instance, the enthalpy of a liquid mixture of these two components may be approximated by the summation of the products of each pure component enthalpy at mixture conditions times its mole fraction. The excess enthalpy could be neglected. 

The following are enthalpy data for a vapor stream 1 and a liquid stream 2 that mix, reach equilibrium adiabatically at the same pressure, and separate into a vapor stream 3 and a liquid stream 4. The calculations are based on the Soave equation of state. 

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A large number of chemical reactions carried out in industry do not involve phase change. Consequently, we shall further refine our energy balance to apply to single-phase chemical reaclions. Under these conditions the enthalpy of species i at temperature T is related to the enthalpy of formation at the reference temperature Tg by... 

Enthalpy-concentration diagrams greatly facilitate the calculation of energy balances involving concentration and phase changes this is illustrated in Example 3.6. 

Calculations of the relations between the input and output amounts and compositions and the number of extraction stages are based on material balances and equilibrium relations. Knowledge of efficiencies and capacities of the equipment then is applied to find its actual size and configuration. Since extraction processes usually are performed under adiabatic and isothermal conditions, in this respect the design problem is simpler than for thermal separations where enthalpy balances also are involved. On the other hand, the design is complicated by the fact that extraction is feasible only of nonideal liquid mixtures. Consequently, the activity coefficient behaviors of two liquid phases must be taken into account or direct equilibrium data must be available. In countercurrent extraction, critical physical properties such as interfacial tension and viscosities can change dramatically through the extraction system. The variation in physical properties must be evaluated carefully. 

Using an automated film balance the behavior of mixed monomolecular films exhibiting deviations from ideality was studied. Particular attention was paid to condensation effects obtained when cholesterol is mixed with a more expanded component. The deviations at various film pressures are discussed in terms of the partial molecular areas of the film components. Slope changes in these plots are caused by phase transitions of the expanded monolayer component and do not indicate the formation of surface complexes. In addition, the excess free energies, entropies, and enthalpies of mixing were evaluated, but these parameters could be interpreted only for systems involving pure expanded components, for which it is clear that the observed condensation effects must involve molecular interactions. 

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