Vapor-liquid equilibrium Gibbs phase rule

So we expect that setting values for T and P would allow us to determine the compositions of vapor and liquid phases. However, near an azeotrope, the saturation curves pass through extrema, causing some tie lines to separate into two branches one on either side of the azeotrope with both branches having the same T and P. Therefore, the phase-equilibrium equations have two solutions for the compositions of both vapor and liquid. The Gibbs phase rule cannot account for nonmonotonicity of properties. To distinguish between the two pairs of roots, we need to set an additional property typically, the overall composition z. That is, we need an T" specification to uniquely identify states near azeotropes. 

Cooling the system is continued until the temperature of Point 2, where the hydrate phase (vertical area that begins at Point 7) forms from the vapor (Point 8) and liquid (Point 6). At Point 2 three phases (Lw-H-V) coexist for two components, so Gibbs Phase Rule (F = 2 — 3+2) indicates that only the isobaric pressure of the entire diagram is necessary to obtain the temperature and the concentrations of the three phases (Fw, H, and V) in equilibrium. 

S. A system composed of ethane hydrate, water, and ethane is classed aa a two-component system when Gibbs phase rule is applied since it could be formed from water and ethane. What is the variance of this system when a solid, a liquid, and a vapor phase coexist in equilibrium If the temperature of this three-phase system is specified, would it be possible to alter the pressure without the disappaaranoe of a phase ... 

If you apply the Gibbs phase rule to a multicomponent gas-liquid system at equilibrium, you will discover that the compositions of the two phases at a given temperature and pressure are not independent. Once the composition of one of the phases is specified (in terms of mole fractions. mass fractions, concentrations, or. for the vapor phase, partial pressures), the composition of the other phase is fixed and, in principle, can be determined from physical properties of the system components. 

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. 

If zinc produced by the reaction is in the liquid phase (and has a significant vapor pressure), at equilibrium how many degrees of freedom exist for the system In the decomposition of CaCOs in a sealed container from which the air was initially pumped out, you generate CO2 and CaO. If not all of the CaCOa decomposes at equilibrium, how many degrees of freedom exist for the system according to the Gibbs phase rule ... 

Assuming that each stage is an equilibrium stage, we know that the liquid and vapor leaving the stage are in equilibrium For a binary system, the Gibbs phase rule becomes... 

The Gibbs phase rule [46] states that at a certain temperature the phase equilibrium between the liquid phase and the vapor phase for a pure substance is reached at one corresponding pressure - the saturated vapor pressure. Using a cubic equation of state, the saturated vapor pressure is calculated as follows. 

Consider a liquid mixture of two components, A and B, in equilibrium with their vapors. This system contains two phases and two components. The Gibbs phase rule tells us that such a system has two degrees of freedom. We may take these degrees of freedom to be the pressure and the mole fraction, xa, of component A. Thus, if we consider a system subjected to a constant pressure, for each value of the mole fraction xa there is a corresponding temperature at which the two phases are in equilibrium. For example, if the applied pressure is 0.5 bar, for the liquid to be in equilibrium with its vapor the temperature must be set at an appropriate value T. 

We start by extending the Gibbs phase rule to multiple-component systems, in its most general form. We will confine our development of multiple-component systems to relatively simple ones, having two or three components at most. However, the ideas we will develop are generally applicable, so there will be little need to consider more complicated systems here. One example of a simple two-component system is a mixture of two liquids. We will consider that, as well as the characteristics of the vapor phase in equilibrium with the liquid. This will lead into a more detailed study of solutions, where different phases (solid, liquid, and gas) will act as either the solute or solvent. 

Could all three phases of water coexist over some finite range of temperatures Could the vapor-liquid equilibrium exist over a range of pressures at one temperature, instead of at just one pressure for any given temperature We have all been told, in previous courses, that the answer is no. But how would you prove that The answer is that we would use the phase rule, often called Gibbs phase rule after Josiah Willard Gibbs (1790-1861). 

One should keep in mind that for phase equilibria, such as the equilibrium between liquid and vapor, there are additional relationships between pressure and temperature. The number of degrees of freedom for the states decreases, owing to the additional relationships between temperature and pressure (phase rule of Gibbs). 

Bolhuis and Frenkel have studied the phase behavior of a mixture of hard spheres and hard rods. In particular, Bolhuis and Frenkel used Gibbs-ensemble simulations to determine the vapor-liquid coexistence curve. In a Gibbs-ensemble simulation one simulates two boxes that are kept in equilibrium with each other via Monte Carlo rules. In this case the gas box has as a low density of hard spheres and the liquid box has a high density of spheres. Similarly to the phase equilibrium calculation of linear alkanes, the exchange step, in which particles are exchanged between the two boxes, is the bottleneck of the simulation. For example, the insertion of a sphere into the gas phase would almost always fail because of overlaps with some of the rods. Bolhuis and Frenkel have used the following scheme to make this exchange possible ... 

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