Ideal solutions definition

Such a rough comparison of real mixtures with ideal solutions is definitely not perfect but it allows the authors of [230] to proceed using conventional theory. The general conclusion following this comparison is that the quantum. /-diffusion model just slightly differs from its... 

The activities of the various components 1,2,3. .. of an ideal solution are, according to the definition of an ideal solution, equal to their mole fractions Ni, N2,. . . . The activity, for present purposes, may be taken as the ratio of the partial pressure Pi of the constituent in the solution to the vapor pressure P of the pure constituent i in the liquid state at the same temperature. Although few solutions conform even approximately to ideal behavior at all concentrations, it may be shown that the activity of the solvent must converge to its mole fraction Ni as the concentration of the solute(s) is made sufficiently small. According to the most elementary considerations, at sufficiently high dilutions the activity 2 of the solute must become proportional to its mole fraction, provided merely that it does not dissociate in solution. In other words, the escaping tendency of the solute must be proportional to the number of solute particles present in the solution, if the solution is sufficiently dilute. This assertion is equally plausible for monomeric and polymeric solutes, although the... 

This is in accordance with the definition of an ideal solution given in Section 3.2. 

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 relative partial molar enthalpies of the species are obtained by using Eqs. (70) and (75) in Eq. (41). When the interaction coefficients linear functions of T as assumed here, these enthalpies can be written down directly from Eq. (70) since the partial derivatives defining them in Eq. (41) are all taken at constant values for the species mole fractions. Since the concept of excess quantities measures a quantity for a solution relative to its value in an ideal solution, all nonzero enthalpy quantities are excess. The total enthalpy of mixing is then the same as the excess enthalpy of mixing and a relative partial molar enthalpy is the same as the excess relative partial molar enthalpy. Therefore for brevity the adjective excess is not used here in connection with enthalpy quantities. By definition the relation between the relative partial molar entropy of species j, Sj, and the excess relative partial molar entropy sj is... 

The attentive student may be concerned that the concept of ideal solution as introduced in Chapter 6 is possibly inconsistent with the usage of that term as defined in (7.45a-c). However, Sidebar 7.8 demonstrates that these definitions of solution ideality are in fact consistent. We may therefore regard chemical potential-based definitions of binary solution ideality [cf. (6.57)],... 

In Equation 11.42, note that two definitions of ideal solution... 

The average cost based tariff covers all costs by definition so the budget constraint does not necessarily lead to cost effectiveness. Rather to the contrary, cost incentives are relatively ineffective, as costs very well can be passed on to shippers by increasing the tariffs. In addition, rationing efficiency is a less than ideal solution as the average cost and hence the tariff is inversely related to flow. If the pipeline is not allowed to make a profit,... 

The relation between Raoult s law and the definition of an ideal solution given by Equation (8.57) is obtained by a study of Equation (10.35) or (10.40). If a solution is ideal, then A/i must be zero and the right-hand side of both equations must be zero. If we write Pyt in both equations as Pt, the partial pressure of the component, and Pyj in Equation (10.40) as P[, then the logarithmic term becomes lnfP P ), which is zero when Raoult s law, given in the form Pl = P[xl, is obeyed. We then see that to define an ideal solution in terms of Raoult s law and still be consistent with Equation (10.57) requires that the experimental measurements be made at the same total pressure and that the vapor behaves as an ideal gas. 

Because thermodynamics describes macroscopic behaviors, we need a macroscopic definition of the ideal solution in addition to the microscopic description given above. We define an ideal solution as one that, for each of its components, at all T and P and over the entire range of concentrations,... 

These two kinds of energy are included in the definition of the chemical potential of ions. The difference W = p. — x° indicates the work gained (or consumed) during the transfer of one gram-ion from the state of an actual solution of a concentration c, to an ideal solution with the unity concentration ... 

Because of the complex functionality of the K-values, these calculations in general require iterative procedures suited only to computer solution. However, in the case of mixtures of light hydrocarbons, in which the molecular force fields are relatively weak and uncomplicated, we may assume as a reasonable approximation that both the liquid and the vapor phases are ideal solutions. By definition of the fugacity coefficient of a species in solution, =fffxtP. But by Eq. (11.61), f f = xj,. Therefore... 

For solutions comprised of species of equal molecular volume in which all molecular interactions are the same, one can show by the methods of statistical thermodynamics that the lowest possible value of the entropy is given by an equation analogous to Eq. (10.7). Thus we complete the definition of an ideal solution by specifying that its entropy be given by the equation ... 

Related Calculations. Many systems deviate from the ideal solution behavior in either or both phases, so the K values given by K = // jP are not adequate. The rigorous thermodynamic definition of K is... 

The activity coefficient is a measure of the deviation of liquid solutions from ideal behavior, and unity in ideal solutions. We have the definitions of excess properties of Gibbs energy, volume, and enthalpy, which are experimentally measurable... 

We may introduce the following approximations. First, for ideal solutions, the activity coefficients are unity (yk = 1), and concentrations are equal to mole fractions ak = xk. Second, using the definitions... 

As we mentioned earlier in this section, it was van t Hoff who saw an analogy between the properties of dilute solutions and the gas laws. Just as an equation of state can be written for an ideal gas, so can an equation of state be written for an ideal solution in terms of its osmotic pressure, as shown in Table 12-2. It is then a straightforward matter of remembering the definition of a mole (the weight of something divided by its molecu-... 

Activities of Electrolytes.—When the solute is an electrolyte, the standard states for the ions are chosen, in the manner previously indicated, as a hypothetical ideal solution of unit activity in this solution the thermodynamic properties of the solute, e.g., the partial molal heat content, heat capacity, volume, etc., will be those of a real solution at infinite dilution, i.e., when it behaves ideally. With this definition of the standard state the activity of an ion becomes equal to its concentration at infinite dilution. 

An appropriate definition of an ideal solution is one in which for each component... 

The ideal solution is introduced to provide a model of solution behavit which we may compare actual solution behavior. Such a model is arbitrary, as an idealization it should be simple, and at the same time it should confc to actual solution behavior over some limited range of conditions. The definit of Eq. (12.45) ensures that the ideal solution exhibits simple behavior. Moreol the two standard-state fugacities chosen, f1 LR) and/-(HL), ensure that models represent real-solution behavior at a limiting condition. 

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