Ideal solution pressure-composition

An ideal gas obeys Dalton s law that is, the total pressure is the sum of the partial pressures of the components. An ideal solution obeys Raoult s law that is, the partial pressure of the ith component in a solution is equal to the mole fraction of that component in the solution times the vapor pressure of pure component i. Use these relationships to relate the mole fraction of component 1 in the equilibrium vapor to its mole fraction in a two-component solution and relate the result to the ideal case of the copolymer composition equation. 

This equation, known as the Lewis-RandaH rule, appHes to each species in an ideal solution at all conditions of temperature, pressure, and composition. It shows that the fugacity of each species in an ideal solution is proportional to its mole fraction the proportionaUty constant is the fugacity of pure species i in the same physical state as the solution and at the same T and P. Ideal solution behavior is often approximated by solutions comprised of molecules similar in size and of the same chemical nature. 

If M represents the molar value of any extensive thermodynamic property, an excess property is defined as the difference between the actual property value of a solution and the value it would have as an ideal solution at the same temperature, pressure, and composition. Thus,... 

Activity coefficients are equal to 1.0 for an ideal solution when the mole fraction is equal to the activity. The activity (a) of a component, i, at a specific temperature, pressure and composition is defined as the ratio of the fugacity of i at these conditions to the fugacity of i at the standard state [54]. 

Figure 1. Ideal pressure-composition isotherms showing the hydrogen solid-solution phase, a, and the hydride phase, j3. The plateau marks the region of coexistence of the a and fl phases. As the temperature is increased the plateau narrows and eventually disappears at some consolule temperature...

H (MPa) (Eq. (13)) and HA (MPa m3 mor1) (Eq. (14)) are often referred to as Henry s constant , but they are in fact definitions which can be used for any composition of the phases. They reduce to Henry s law for an ideal gas phase (low pressure) and for infinitely dilute solution, and are Henry s constant as they are the limit when C qL (or xA) goes to zero. When both phases behave ideally, H depends on temperature only for a dilute dissolving gas, H depends also on pressure when the gas phase deviates from a perfect gas finally, for a non-ideal solution (gas or liquid), H depends on the composition. This clearly shows that H is not a classical thermodynamic constant and it should be called Henry s coefficient . 

The papers of Wagner and Schottky contained the first statistical treatment of defect-containing crystals. The point defects were assumed to form an ideal solution in the sense that they are supposed not to interact with each other. The equilibrium number of intrinsic point defects was found by minimizing the Gibbs free energy with respect to the numbers of defects at constant pressure, temperature, and chemical composition. The equilibrium between the crystal of a binary compound and its components was recognized to be a statistical one instead of being uniquely fixed. 

Let us now consider two special cases. In the first case, we assume that the compound of interest forms an ideal solution or mixture with the solvent or the liquid mixture, respectively. In assuming this, we are asserting that the chemical enjoys the same set of intermolecular interactions and freedoms that it has when it was dissolved in a liquid of itself (reference state). This means that Yu is equal to 1, and, therefore, for any solution or mixture composition, the fugacity (or the partial pressure of the compound i above the liquid) is simply given by ... 

Three pounds of 2,2-dimethyIbutane and 2 lb of 2,2,4-trimethyl-pentane are mixed in a sealed container. The temperature and pressure are adjusted to 5 psia and 100°F. Calculate the compositions and weights of the gas and liquid at equilibrium. Assume that the mixture acts like an ideal solution. 

Since the logarithmic term is zero in Eq. (11) under tins limiting condition, i is the chemical potential of pure component A at the temperature and pressure under consideration. For ideal solutions the activity coefficients of both components will be unity over the whole range of composition. 

The change of enthalpy on mixing, AHM[T, P, x], at constant temperature and pressure is seen to be zero for an ideal solution. The change of the heat capacity on mixing at constant temperature and pressure is also zero for an ideal solution, as are all higher derivatives of AHM with respect to both the temperature and pressure at constant composition. Differentiation of Equations (8.57), (8.59), and (8.60) with respect to the pressure yields... 

Ethylene bromide, C2H4Br2, and 1,2-dibromopropane, C H Bit. form ideal solutions over the entire range of composition. At 85°C the vapor pressures of the pure liquids are 173 torr and 127 ton, respectively, (a) Calculate the partial pressure of each component and the total pressure of the solution at 85°C if 10.0 g of ethylene bromide are dissolved in 80.0 g of 1,2-dibromopropane. (b) Calculate the mole fraction of ethylene bromide in the vapor in equilibrium with the above solution, (c) What would be the mole fraction of ethylene bromide in a solution at 85°C of a 50 50 mole mixture in the vapor ... 

Solutions that obey these equations throughout the composition range are called ideal solutions. Recall that h a is the chemical potential of pure A at the temperature of interest, but at an arbitrary pressure, and hence is different from which is the chemical potential of pure A at the pressure of latm. However, the effect of pressure on the chemical potential is so small that... 

Assume that benzene and naphthalene form an ideal solution and that the solids are pure components (no solid solutions are formed) with melting points at 1.0 atm pressure of 5.5°C and 80.5°C. Estimate the composition and melting point of the benzene-naphthalene eutectic using Eq. (77). 

A solution in which the activity of each component is equal to its mole fraction under all conditions of temperature, pressure and composition, is said to be an ideal solution. 

The fugacity in Equation 2-39 is that of the component in the equilibrium mixture. However, fugacity of only the pure component is usually known. It is also necessary to know something about how the fugacity depends on the composition in order to relate the two, therefore, assumptions about the behavior of the reaction mixture must be made. The most common assumption is that the mixture behaves as an ideal solution. In this case, it is possible to relate the fugacity, f, at equilibrium to the fugacity of the pure component, f, at the same pressure and temperature by... 

What is the vapor pressure of a 60 40 w/w mixture of propane (MW = 44.1) and isobutane (MW = 58.1) Assume an ideal solution. The vapor pressures of propane and isobutane are 110 and 30.4 psig at 70°F, respectively. If the vessel is large enough, what is the vapor pressure and composition of the liquid mixture when the last drop of the liquid mixture vaporizes ... 

Figure 3.10 shows the vapor pressure/composition curve at a given temperature for an ideal solution. The three dotted straight lines represent the partial pressures of each constituent volatile liquid and the total vapor pressure. This linear relationship is derived from the mixture of two similar liquids (e.g., propane and isobutane). However, a dissimilar binary mixture will deviate from ideal behavior because the vaporization of the molecules A from the mixture is highly dependent on the interaction between the molecules A with the molecules B. If the attraction between the molecules A and B is much less than the attraction among the molecules A with each other, the A molecules will readily escape from the mixture of A and B. This results in a higher partial vapor pressure of A than expected from Raoult s law, and such a system is known to exhibit positive deviation from ideal behavior, as shown in Figure 3.10. When one constituent (i.e., A) of a binary mixture shows positive deviation from the ideal law, the other constituent must exhibit the same behavior and the whole system exhibits positive deviation from Raoult s law. If the two components of a binary mixture are extremely different [i.e., A is a polar compound (ethanol) and B is a nonpolar compound (n-hexane)], the positive deviations from ideal behavior are great. On the other hand, if the two liquids are both nonpolar (carbon tetrachloride/n-hexane), a smaller positive deviation is expected.

For the predominant component of a solution, i. e. the solvent, the 3tate of the pure liquid at the temperature of the systom and the pressure of 1 atm. is chosen as the standard state.. In so far as sufficiently diluted solutions are concerned (i. e. such solutions the composition of which differs but slightly from the pure solvent) the solvent can be considered to follow approximately Raoult s law valid for ideal solutions, according to which the fugacity / of the solvent in a solution can be expressed as the product of its molar fraction N-, ) and of the fugacity of the pure liquid substance f at the same temperature, thus ... 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

The application of Eq. (10.3) to specific phase-equilibrium problems requires use of models of solution behavior, which provide expressions for G or for the Hi as functions of temperature, pressure, and composition. The simplest of such expressions are for mixtures of ideal gases and for mixtures that form ideal solutions. These expressions, developed in this chapter, lead directly to Raoult s law, the simplest realistic relation between the compositions of phases coexisting in vapor/liquid equilibrium. Models of more general validity are treated in Chaps. 11 and 12. 

Then the pressure versus composition (PX) diagram for an ideal solution is shown in Fig. 4.5, while the temperature versus composition (TX) phase diagram is shown in Fig. 4.6. 

An excess property is the difference between the actual property value of a solution and the ideal solution value at the same composition, temperature, and pressure. Therefore, excess properties represent the nonideal behavior of liquid mixtures. The major thermodynamic properties for ideal mixtures are... 

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