Phase rule components

The mass-balance restrictions are the C balances written for the C components present in the system. (Since we will only deal with non-reactive mixtures, each chemical compound present is a phase-rule component.) An alternative is to write (C — 1) component balances and one overall mass balance. 

The Phase Rule Components, Phases, and Degrees of Freedom 409... 

THE PHASE RULE COMPONENTS, PHASES, AND DEGREES OF FREEDOM... 

No other reactions occur. The entire system is in the gas phase. How many phase rule components C are in this system ... 

While the phase rule requires tliree components for an unsymmetrical tricritical point, theory can reduce this requirement to two components with a continuous variation of the interaction parameters. Lindli et al (1984) calculated a phase diagram from the van der Waals equation for binary mixtures and found (in accord with figure A2.5.13 that a tricritical point occurred at sufficiently large values of the parameter (a measure of the difference between the two components). 

At this point the system has throe phases (CUSO4 CuS04,Hj0 HjO vapour) and the number of components is two (anhydrous salt water). Hence by the phase rule, F + F = C + 2, t.e., 3+F = 2 + 2, or F=l. The system is consequently univariant, in other words, only one variable, e.g., temperature, need be fixed to define the system completely the pressure of water vapour in equilibrium with CUSO4 and CuS04,Hj0 should be constant at constant temperature. 

The problem presented to the designer of a gas-absorption unit usually specifies the following quantities (1) gas flow rate (2) gas composition, at least with respect to the component or components to be sorbed (3) operating pressure and allowable pressure drop across the absorber (4) minimum degree of recoverv of one or more solutes and, possibly, (5) the solvent to be employed. Items 3, 4, and 5 may be subject to economic considerations and therefore are sometimes left up to the designer. For determining the number of variables that must be specified in order to fix a unique solution for the design of an absorber one can use the same phase-rule approach described in Sec. 13 for distillation systems. 

Mols of component, i, at start of distillation Total mols of liquid in bottoms of still at time, Tj Total mols liquid (not including any steam) in bottom of still at start time Tq (batch charge) y intercept of operating line or constant at fixed pressure for Winn s relative volatility Mols of component, i, in bottoms No. components present, phase rule or no. components, or constant... 

Step 2. Determine the vapor pressure in the evaporator. According to the phase rule, for a mixture of two components (propane and butane) it is necessary to establish two variables of the liquid-vapor system in the evaporator to completely define the system and fix the value of all other variables. The assumed liquid mol fraction and a temperature of 0°F is known. The... 

This is a consequence of the phase rule there are two components in three phases, hence the number of degrees of freedom is 2, so that when the temperature and pressure are fixed, the composition of each layer is also defined. 

A surface of separation between two phases is called a specific surface of separation, and in considering the statesof such systems it is evident that every specific surface constitutes a new independent variable. If there are n components in r phases with x specific surfaces, the Phase Rule will therefore read ... 

Having phases together in equilibrium restricts the number of thermodynamic variables that can be varied independently and still maintain equilibrium. An expression known as the Gibbs phase rule relates the number of independent components C and number of phases P to the number of variables that can be changed independently. This number, known as the degrees of freedom f is equal to the number of independent variables present in the system minus the number of equations of constraint between the variables. 

While the Gibbs phase rule provides for a qualitative explanation, we can apply the Clapeyron equation, derived earlier [equation (5.71)], in conjunction with studying the temperature and pressure dependences of the chemical potential, to explain quantitatively some of the features of the one-component phase diagram. 

The framework for constructing such multi-component equilibrium models is the Gibbs phase rule. This rule is valid for a system that has reached equilibrium and it states that... 

The system, therefore, is at equilibrium at a given temperature when the partial pressure of carbon dioxide present has the required fixed value. This result is confirmed by experiment which shows that there is a certain fixed dissociation pressure of carbon dioxide for each temperature. The same conclusion can be deduced from the application of phase rule. In this case, there are two components occurring in three phases hence F=2-3 + 2 = l, or the system has one degree of freedom. It may thus legitimately be concluded that the assumption made in applying the law of mass action to a heterogeneous system is justified, and hence that in such systems the active mass of a solid is constant. 

The phase rule as has been pointed out in the preceding paragraph deals with the behavior of heterogeneous systems at equilibria. It essentially includes three special terms. These are (i) number of phases in the system (P) (ii) the number of components for the system (C) and (iii) the number of degrees of freedom available to the system (F). A system for the present purpose could be any substance or combination of substances, which is set apart from its surroundings or other substances, such that its equilibrium state may be studied. The simplest way to express the rule in the form of an equation combining the three terms is as follows ... 

In the case of a unary or one-component system, only temperature and pressure may be varied, so the coordinates of unary phase diagrams are pressure and temperature. In a typical unary diagram, as shown in Figure 3.11, the temperature is chosen as the horizontal axis by convention, although in binary diagrams temperature is chosen as the vertical axis. However, for a one-component system, the phase rule becomes F=l-P+2 = 3-P. This means that the maximum number of phases in equilibrium is three when F equals zero. This is illustrated in Figure 3.11 which has three areas, i.e., solid, liquid, and vapour In any... 

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