Ideal solution temperature-composition

The variation of the entropy of formation of an ideal solution with composition is shown inFigure3.10. It is again a characteristic ofan ideal solution that the partial (ASA,ld, A. Sg1, ld) and the integral molar (ASM,ld) entropies of its formation are independent of temperature. 

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]. 

Raoult s Law. The molar composition of a liquid phase (ideal solution) in equilibrium with its vapor at any temperature T is given by... 

Ideal solution behavior over extended ranges in both composition and temperature requires that the following conditions be fulfilled (i) the entropy of mixing must be given by ... 

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. 

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. 

As shown in Figure 23, the value of TGaSb in the Al-Ga-Sb system is significantly different from unity as a result of nonidealities in the liquid solution. The value of rGaSb in this system is also nearly independent of both composition and temperature. Thus this system can be modeled as an ideal solution in both phases if the value of 0GaSb was suitably adjusted. 

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... 

When we consider the solubility of a solid component in a solvent, the emphasis is placed on obtaining the mole fraction or other composition variable as a function of the temperature. Thus, Equation (10.96) gives the solubility as a function of the temperature in this interpretation. The solubility in an ideal solution is given by... 

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... 

Knowledge of the variation of the value of y with temperature and composition is of prime importance in solution thermodynamics. Now a question arises as to how to express the extent of deviation of this value from ideal behaviour. As we have discussed in the preceding section, in ideal solutions attractive forces between the unlike molecules in solution are the same as those between the like molecules in the pure phase. Therefore the escaping tendency of the component / in an ideal solution is the same as that in its pure state. From the Raoult s law,... 

Although temperature-composition phase diagrams of many liquids are similar to the one for an ideal solution shown above, there are a number of important solutions which exhibit a marked deviation. 

When the ideal solution is used as the reference for real solutions, thermodynamic properties are designated by (RL) for Raoulfs law reference. This reference is often used in solutions in which all solutes are liquids at the temperature of interest, especially when the compositions of components are varied over a considerable range. In this case, for every component, we write Eq. (3) as... 

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... 

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 ... 

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