Ideal behavior liquid

Assuming ideal liquid behavior, the total partial pressure of the organic phase is given by the sum of the partial pressures of its components according to Raoult s law. 

The solid compound in Fig. 9-11 is said to have a congruent melting point since it melts into a liquid of the same composition as the compound. A solid compound is said to have an incongruent melting point if it does not melt into a liquid phase of the same composition but decomposes. It is of interest that solid-compound formation can occur with ideal-liquid behavior. 

The theory of hydrodynamics similarly describes an ideal liquid behavior making use of the viscosity (see Sect 5.6). The viscosity is the property of a fluid (liquid or gas) by which it resists a change in shape. The word viscous derives from the Latin viscum, the term for the birdlime, the sticky substance made from mistletoe and used to catch birds. One calls the viscosity Newtonian, if the stress is directly proportional to the rate of strain and independent of the strain itself. The proportionality constant is the viscosity, q, as indicated in the center of Fig. 4.157. The definitions and units are listed, and a sketch for the viscous shear-effect between a stationary, lower and an upper, mobile plate is also reproduced in the figure. Schematically, the Newtonian viscosity is represented by the dashpot drawn in the upper left comer, to contrast the Hookean elastic spring in the upper right. 

The theory of hydrodynamics similarly describes an ideal liquid behavior making use of the viscosity. Newton s law suggests that in this case the stress is directly proportional to the rate of strain and independent of the strain. The... 

Liquid solutions are often most easily dealt with through properties that measure their deviations, not from ideal gas behavior, but from ideal solution behavior. Thus the mathematical formaUsm of excess properties is analogous to that of the residual properties. 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

The above method is commonly used for gases and infrequently for liquid mixtures. At atmospheric conditions when ideal gas behavior is realized, the total volume of the mixture equals the sum of the pure-component volumes ( V ). That is, V = V and... 

In our discussion of (vapor + liquid) phase equilibria to date, we have limited our description to near-ideal mixtures. As we saw in Chapter 6, positive and negative deviations from ideal solution behavior are common. Extreme deviations result in azeotropy, and sometimes to (liquid -I- liquid) phase equilibrium. A variety of critical loci can occur involving a combination of (vapor + liquid) and (liquid -I- liquid) phase equilibria, but we will limit further discussion in this chapter to an introduction to (liquid + liquid) phase equilibria and reserve more detailed discussion of what we designate as (fluid + fluid) equilibria to advanced texts. 

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

Solution Ideal gas behavior is a reasonable approximation for the feed stream. The inlet concentrations are 287mol/m of methane and 15mol/m of carbon dioxide. The column pressure drop is mainly due to the liquid head on the trays and will be negligible compared with 8 atm unless there are an enormous number of trays. Thus, the gas flow rate F will be approximately constant for the column as a whole. With fast reaction and a controlling gas-side resistance, c = 0. The gas-phase balance gives everything that is necessary to solve the problem ... 

Mixtures of isomers, such as o-, m- and / -xylene mixtures, and adjacent members of homologous series, such as n-hexane-n-heptane and benzene-toluene mixtures, give close to ideal liquid-phase behavior. For this case, yt = 1, and Equation 4.28 simplifies to ... 

Xi = mole fraction of Component i in the liquid phase Assuming ideal gas behavior (pi = y P),... 

Gases—pure component at one atmosphere, at which pressure ideal gas behavior is closely approximated Solid—pure solid component at unit pressure Liquid—pure liquid at its vapor pressure... 

Assuming ideal gas behavior, the equilibrium partial pressure, ph of a compound above a liquid solution or liquid mixture is a direct measure of the fugacity, fu, of that compound in the liquid phase (see Fig. 3.9 and Eq. 3-33). 

There are no ideal liquid solutions, just as there are no ideal gas mixtures. However, when liquids of similar chemical and physical characteristics are mixed, the behavior of the resulting solution is very much like the behavior of an ideal solution. Fortunately, most of the liquid mixtures encountered by petroleum engineers are mixtures of hydrocarbons with similar characteristics. Thus, ideal-solution principles can be applied to the calculation of the densities of these liquids. 

As in the case of ideal gases, ideal liquid solutions do not exist. Actually, the only solutions which approach ideal solution behavior are gas mixtures at low pressures. Liquid mixtures of components of the same homologous series approach ideal-solution behavior only at low pressures. However, studies of the phase behavior of ideal solutions help us understand the behavior of real solutions. 

EXAMPLE 12-1 Calculate the compositions and quantities of the gas and liquid when 1,0 lb mole of the following mixture is brought to equilibrium at 150°F and 200 psia. Assume ideal-solution behavior. 

Second, Raoult s equation is based on the assumption that the liquid behaves as an ideal solution. Ideal-solution behavior is approached only if the components of the liquid mixture are very similar chemically and physically. 

The heat of vaporization varies slowly with temperature and eventually becomes zero at the critical temperature. In addition, the assumptions which were used to approximate AV (ideal gas behavior and negligible volume of the condensed phase) are inaccurate at high pressures. However, the assumptions are adequate for data of moderate precision (about 1%) in the 1-760-torr range, and in these cases the heat of vaporization may be determined from the A parameter as indicated in Eq. (3). Of course, different A and B parameters have to be determined for each particular phase (e.g., for the liquid, and for each solid phase, if more than one exists). IfA and if are known for one phase and the heat of transition (fusion or solid-state transition) is known, the heat of vaporization and its equivalent, the A value for the second phase, maybe calculated. The new value of B is then found by taking advantage of the fact that the vapor pressures for the two phases are identical at the transition temperature. 

Neglecting liquid volume and assuming ideal gas behavior for the vapor, the Clapeyron equation for pure water and for sea salt solutions becomes... 

Ideal Liquid Solutions, Two limiting laws of solution thermodynamics that are widely employed are Henry s law and Raoult s law, which represent vapor—liquid partitioning behavior in the concentration extremes. These laws are used frequendy in equilibrium problems and apply to a variety of real systems (10). 

The thermodynamic quantity 0y is a reduced standard-state chemical potential difference and is a function only of T, P, and the choice of standard state. The principal temperature dependence of the liquidus and solidus surfaces is contained in 0 j. The term is the ratio of the deviation from ideal-solution behavior in the liquid phase to that in the solid phase. This term is consistent with the notion that only the difference between the values of the Gibbs energy for the solid and liquid phases determines which equilibrium phases are present. Expressions for the limits of the quaternary phase diagram are easily obtained (e.g., for a ternary AJB C system, y = 1 and xD = 0 for a pseudobinary section, y = 1, xD = 0, and xc = 1/2 and for a binary AC system, x = y = xAC = 1 and xB = xD = 0). 

It is unusual to find systems that follow the ideal solution prediction as well as does (benzene+ 1,4-dimethylbenzene). Significant deviations from ideal solution behavior are common. Solid-phase transitions, solid compound formation, and (liquid 4- liquid) equilibria often complicate the phase diagram. Solid solutions are also present in some systems, although limited solid phase solubility is not uncommon. Our intent is to look at more complicated examples. As we do so, we will see, once again, how useful the phase diagram is in summarizing a large amount of information. 

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