Phase rule equation

Quadruple point is a point where four different phases meet. Thus P = 4, substituting the values in the phase rule equation... 

In a part of this system which has been studied by Hemley (11), four phases can exist at equilibrium aqueous solution, solid quartz, solid kaolinite (Al1 Si2Or)(OH)4), and potassium mica (KAl tSi 4Oio(OH)2). The variables are p, T, and the various concentrations [K+], [IF], [CT], [Al]a(J, [Si(OH)4].i(, etc. If we apply the phase rule (Equation 1) to equilibria of the four phases mentioned, we find F = 5 -f 2 — 4 = 3. The most practical choice of independent variables would seem to be p, T, and [CT]. These are easy to control, and CT is the one ion that must remain in the aqueous phase since there is no place for it in the solid phases. The phase rule now states that after the values for these... 

In water system, the three phases viz., ice (s), water (/) and vapours (g) remain in equilibrium at a fixed temperature (0.0075°C) and fixed pressure (4.58 mm). At no other temperature and pressure, all the three phases can coexist in equilibrium. From phase rule equation (F = C - P + 2), we can also show that value of F of the system is zero, i.e.,... 

Triple point is that point where all the three phases in a one component system exist in equilibrium. At this point, both the variables, e.g., temperature and pressure are fixed, i.e., they have definite values. Thus, triple point is a non-variant point, i.e., degree of freedom is zero. It is also clear from phase rule equation i.e.,... 

Problem 7 What is a two component system and how it is graphically represented Define reduced phase rule equation and condensed state. 

F=(C-P + 2)-l or F—C-P+1 This equation is known as condensed or reduced phase rule equation. 

In solid-liquid system, a negligible change in pressure produces no change in equilibrium as the vapour pressure of solid is negligible. Therefore, in such a system, the pressure variable may be taken as nearly constant. So, a system in which vapour phase is ignored is known as a condensed system. For such a system, we apply the condensed phase rule equation, F=C-P+ 1. 

Returning now to the beginning of this Frame we can see that using the Phase Rule (equation (30.21)) where three phases solid, liquid and gas co-exist (then p = 3) and the number of components (c = 1) because a pure material is being considered, then ... 

Enthalpy-concentration charts are particularly useful for two-component systems in which vapor and liquid phases are in equilibrium. The Gibbs phase rule (Equation 6.2-1) specifies that such a system has (2 -I- 2 - 2) = 2 degrees of freedom. If as before we fix the system pressure, then specifying only one more intensive variable—the system temperature, or the mass or mole fraction of either component in either phase—fixes the values of all other intensive variables in both phases. An H-x diagram for the ammonia-water system at 1 atm is shown in Figure 8.5-2. 

This difference is further reinforced by application of the phase mle to the equihbrium between two strictly defined polymorphs of a compound or the equihbrium between a compound and a corresponding solvate of that compound. In the former case, there is only one component (in the phase rule sense—the compound). There are two phases (the two polymorphs) and, therefore, there is only one degree of freedom for equihbrium between two polymorphs by application of the phase rule equation... 

But, first, we must mention a slight modification of the regular phase rule. Equation (11.1). As shown in Figure 17.9, the experiments we are discussing at a fixed pressure of 1 bar can be represented on a plane or section through P-T-X space. The general phase rule (11.1) applies to this P-T-X space. The fact that we confine ourselves to a fixed P plane within this space means that we have used one of our degrees of freedom - we have chosen P = 1 bar, and the same would be true for any other constant P section (or constant T section, for that matter). Therefore on our T-X plane the phase rule is... 

The tie lines are defined as the lines in the two-phase region (7 = 2) on which the system intensive parameters are constant. It follows from Elquation 8 that tie lines connect the binodal points corresponding to the coexisting phases. It should be noted that any tie line is unambiguously defined by 1/ intensive parameters, according to the phase rule (Equation 112). 

According to Gibbs phase rule (Equation 1.2-32), in a i/-component system with 7 phases, / parameters (such as temperature, pressure, component concentrations) may... 

Gibbs phase rule (Equation 1) for the system (polymolecular P)-fLMWL requires some modification. First, phase equilibria are considered under constant (atmospheric) pressure, i.e. pressure is fixed and no longer a variable. Second, the degrees of polymerization Pi with i = 1,2,..., s — 1 and concentrations of components become variables. The number of degrees of freedom for the m-multiple critical points is cancelled by (m - -1) conditions of its existence (see Equation 46, including n = — 1), so there remains... 

Since the minimum number of phases in any system is 1, it is dear from the phase rule equation... 

As we know, the vapour pressure of every liquid rises with the rise in temperatiu e, so from the figure it is clear that at the normal boiling point of water (100°C) the vapour pressure becomes equal to 760 mm of Hg. The two phases in equilibrimn edong OA are liquid water emd its vapour. Hence, the curve is univariant, as follows from the phase rule equation,... 

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