Liquid chemical equation, specifying state

We have considered volume changes resulting from density changes in liquid and gaseous systems. These volume changes were thermodynamically determined using an equation of state for the fluid that specifies volume or density as a function of composition, pressure, temperature, and any other state variable that may be important. This is the usual case in chemical engineering problems. In Example 2.10, the density depended only on the composition. In Example 2.11, the density depended on composition and pressure, but the pressure was specified. 

The recipe for brownies will specify whether each ingredient should be used in a solid or liquid form. The recipe also may state that the batter should bake at 400°F for 20 min. Additional instructions tell what to do if you are baking at high elevation. Chemical equations are similar. Equations for chemical reactions often list the physical state of each reactant and the conditions under which the reaction takes place. 

What is the minimum number of variables to specify fully a stream A stream can be defined as the flow of material between two units in a flowsheet. The variables normally associated with a stream are its temperature, pressure, total flow, overall mole fractions, phase fractions and phase mole fractions, total enthalpy, phase enthalpies, entropy, etc. Assuming phase and chemical equilibrium, how many of those variables must be specified to completely fix the stream Without further considerations, for this case, intuition gives us the correct answer. We know without writing equations that if we specify temperature, pressure, and individual component flows, the stream is fully specified. Of course, a priori we cannot know the final state of the stream (i.e., multiphase or single phase liquid, vapor, solid, or a mixture of them). If we are interested in a stream with some specific conditions like saturated liquid, we cannot specify simultaneously pressure and temperature but pressure (or temperature) and phase fraction. A convention in process simulators is that when vapor (liquid) phase fraction is specified to zero or one, saturated conditions are assumed (bubble point or dew point). However, when vapor or liquid phase fractions are calculated, a value of one (zero) does not mean saturated conditions but that the stream is in vapor (liquid) phase. 

The reader might have noticed that the isotherms obtained from an equation of state, such as the van der Waals equation, do not coincide with the isotherms shown in Fig 7.2 at the part of the curve that is flat, i.e. where the liquid and vapor states coexist. The flat part of the curve represents what is physically realized when a gas is compressed at a temperature below the critical temperature. Using the condition that the chemical potential of the liquid and the vapor phases must be equal at equilibrium. Maxwell was able to specify where the flat part of the curve would occur. 

The equation for the second component is the same with change of subscripts. The problem is to determine values of xt and zl at specified temperatures by the use of the two equations. We define the quantity A [T, P] as equal to both sides of Equation (10.198). This quantity is the change of the chemical potential on mixing for the liquid phase that has been defined previously however, for the solid phase the standard state is now the pure liquid component. A similar definition is made for Ap%[T, P], The conditions of equilibrium then become... 

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