Ideal solution Henry s law

Fugadties Based on the Solute-Free, Henry s Law, Ideal Solution... 

Henry s constants are intensive, measurable properties having dimensions of pressure (10.2.20) indicates that the solute-free Henry s constant depends on temperature, pressure, and the solute-free mole fractions, but it does not depend on the solute mole fractions. With (10.2.20), the fugacity of a solute i in a Henry s law ideal solution is, as required, linear in the mole fraction of i,... 

For binary mixtures we can use a simple plot, as in Figure 10.5, to compare the Henry s law ideal solution to the Lewis-Randall ideality. The plot shows the real fugacity for component 1, as well as the Lewis-Randall and Heruy s law straight lines. The Lewis-Randall fugacity coincides with the real value at Xj = 0 and at Xj = 1, but the Henry s law fugacity coincides only at Xj = 0. Also, since x lies on [0,1], the intercept of the Henry s law curve at Xj = 1 is the Heruy s constant at the given T and P. 

Otherwise we usually have y < 1, as suggested by Figure 10.5 in contrast, in the Lewis-Randall standard state we usually have y, > 1, also suggested by Figure 10.5. This means that deviations from Lewis-Randall ideal-solution behaviors differ qualitatively from deviations from Henry s law ideal-solution behaviors. 

To measure deviations from a reference-solvent, Henry s law ideal solution, we introduce another activity coefficient defined by... 

Figure 12.9 For the fugacity of a supercritical solute(l) in a liquid solvent(2), the Poynting factor (PF) in FFF 5 (12.2.2) tends to compensate for the effects of the activity coefficient. This plot shows contributions to fugacities of hydrogen(l) in methanol(2) at 294.15 K. Points are the experimental data of Krichevskii et al. [3]. Horizontal line is for a Henry s law ideal solution. Upper line includes only the Poynting factor, while the lower line includes only the activity coefficient. Adapted from a figure in Campanella et al. [4].

If we take the standard state as the hypothetical 1 molar Henry s law solution (sometimes shortened to hypothetical ideal 1 molar solution, where the ideality referred to is Henry s law ideality in molarity units, that is, the proportionality of partial pressure and molarity, not Raoult s law ideality) we get... 

Eq. (4) is known as Henry s law, and solute is the Henry s law constant, which is less than Psoiute- Therefore, Henry s law applies to the solute in dilute solutions, and Raoult s law applies to solvent in dilute non-ideal solutions. Note the similarities between Eqs. (1) and (2) and between Eqs. (3) and (4) for the non-ideal dilute solution case. When the solution is ideal, Henry s law becomes identical to Raoult s law, and fsoiute becomes identical to f oiute- When the partial pressures of the solute and the solvent are directly proportional to their molefractions over the entire range, the solution is ideal. In a non-ideal solution, Raoult s law will apply to the solvent over the entire concentration range, whereas Henry s law will apply to the solute in a limited concentration range in which it is in a sufficiently diluted form. 

Solvent activity coefficients are defined (Parker, 1966) such that °y< reflects the change in the standard chemical potential fi of a solute, i (hypothetically ideal, in respect to Henry s Law, unimolar solution), on transfer from an arbitrarily chosen reference solvent (i.e. the standard... 

The standard state of an electrolyte is the hypothetical ideally dilute solution (Henry s law) at a molarity of 1 mol kg (Actually, as will be seen, electrolyte data are conventionally reported as for the fonnation of mdividual ions.) Standard states for non-electrolytes in dilute solution are rarely invoked. 

Substances at high dilution, e.g. a gas at low pressure or a solute in dilute solution, show simple behaviour. The ideal-gas law and Henry s law for dilute solutions antedate the development of the fonualism of classical themiodynamics. Earlier sections in this article have shown how these experimental laws lead to simple dieniiodynamic equations, but these results are added to therniodynaniics they are not part of the fonualism. Simple molecular theories, even if they are not always recognized as statistical mechanics, e.g. the kinetic theory of gases , make the experimental results seem trivially obvious. 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

The ideal solution law, Henry s Law, also enters into the establishment of performance of ideal and non-ideal solutions. 

Equilibrium data correlations can be extremely complex, especially when related to non-ideal multicomponent mixtures, and in order to handle such real life complex simulations, a commercial dynamic simulator with access to a physical property data-base often becomes essential. The approach in this text, is based, however, on the basic concepts of ideal behaviour, as expressed by Henry s law for gas absorption, the use of constant relative volatility values for distillation and constant distribution coeficients for solvent extraction. These have the advantage that they normally enable an explicit method of solution and avoid the more cumbersome iterative types of procedure, which would otherwise be required. Simulation examples in which more complex forms of equilibria are employed are STEAM and BUBBLE. 

In a general case of a mixture, no component takes preference and the standard state is that of the pure component. In solutions, however, one component, termed the solvent, is treated differently from the others, called solutes. Dilute solutions occupy a special position, as the solvent is present in a large excess. The quantities pertaining to the solvent are denoted by the subscript 0 and those of the solute by the subscript 1. For >0 and x0-+ 1, Po = Po and P — kxxx. Equation (1.1.5) is again valid for the chemical potentials of both components. The standard chemical potential of the solvent is defined in the same way as the standard chemical potential of the component of an ideal mixture, the standard state being that of the pure solvent. The standard chemical potential of the dissolved component jU is the chemical potential of that pure component in the physically unattainable state corresponding to linear extrapolation of the behaviour of this component according to Henry s law up to point xx = 1 at the temperature of the mixture T and at pressure p = kx, which is the proportionality constant of Henry s law. 

In our quantum mechanical solvation modeling,12 27 we take the standard state of the vapor to be a 1 molar ideal gas at 298° K and the standard state of the solute to be a hypothetical 1 molar Henry s law solute at the same... 

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 . 

To determine the amount of substance and the concentration of carbon monoxide in solution, we have to relate these quantities to the CO pressure. That can be done as described by using Henry s law. The only (important) difference is that now the CO pressure is too high to justify use of the ideal gas model. Hence, for the present case, equation 14.15 becomes [316]... 

The thermodynamic development above has been strictly limited to the case of ideal gases and mixtures of ideal gases. As pressure increases, corrections for vapor nonideality become increasingly important. They cannot be neglected at elevated pressures (particularly in the critical region). Similar corrections are necessary in the condensed phase for solutions which show marked departures from Raoult s or Henry s laws which are the common ideal reference solutions of choice. For nonideal solutions, in both gas and condensed phases, there is no longer any direct... 

Table 5.3 Solute and solvent solubility isotope effects for (benzene-water) solutions at 306.2 K obtained from IE s on Henry s Law coefficients, Ki and Kn- [Isotope effects on free energies of transfer, ideal gas to solution in the limit of infinite dilution] (Dutta-Choudhury, M., Miljevic, N.

At temperatures well below UCST, solubilities of hydrocarbons in water or water in hydrocarbons drop to very low values. The solutions are very nearly ideal in the Henry s law sense, and the isotope effects on solubility can be directly interpreted as the isotope effect on the standard state partial molar free energy of transfer from the Raoult s law standard state to the Henry s law standard state. Good examples include the aqueous solutions of benzene, cyclohexane, toluene,... 

According to Henry s law, the vapour pressure of a gas above its solution is directly proportional to the concentration c, or the mole fraction Xg of this gas in solution. It applies if the solutions are sufficiently ideal. 

For solutions obeying Henry s law, as for ideal solutions, and for solutions of ideal gases, the chemical potential is a linear function of the logarithm of the composition variable, and the standard chemical potential depends on the choice of composition variable. The chemical potential is, of course, independent of our choice of standard state and composition measure. 

Equation (15.13) can describe either an ideal solution [see Equation (14.7)] or a solution sufficiently dilute that Henry s law is followed [see Equation (15.5)]. In either case, it follows that... 

In the preceding chapters we considered Raoult s law and Henry s law, which are laws that describe the thermodynamic behavior of dilute solutions of nonelectrolytes these laws are strictly valid only in the limit of infinite dilution. They led to a simple linear dependence of the chemical potential on the logarithm of the mole fraction of solvent and solute, as in Equations (14.6) (Raoult s law) and (15.5) (Heiuy s law) or on the logarithm of the molality of the solute, as in Equation (15.11) (Hemy s law). These equations are of the same form as the equation derived for the dependence of the chemical potential of an ideal gas on the pressure [Equation (10.15)]. 

Fig. 2.4 The vapor pressure diagram of a dilute solution of the solute B in the solvent A. The region of ideal dilute solutions, where Raoult s and Henry s laws are obeyed by the solvent and solute, respectively, is indicated. Deviations from the ideal at higher concentrations of the solute are shown. (From Ref. 3.)...

Given a nonionic solute that has a relatively low solubility in each of the two liquids, and given equations that permit estimates of its solubility in each liquid to be made, the distribution ratio would be approximately the ratio of these solubilities. The approximation arises from several sources. One is that, in the ternary (solvent extraction) system, the two liquid phases are not the pure liquid solvents where the solubilities have been measured or estimated, but rather, their mutually saturated solutions. The lower the mutual solubility of the two solvents, the better can the approximation be made. Even at low concentrations, however, the solute may not obey Henry s law in one or both of the solvents (i.e., not form a dilute ideal solution with it). It may, for instance, dimerize or form a regular solution with an appreciable value of b(J) (see section 2.2). Such complications become negligible at very low concentrations, but not necessarily in the saturated solutions. 

Figure 10,1 (A) Activity-molar concentration plot. Trace element concentration range is shown as a zone of constant slope where Henry s law is obeyed. Dashed lines and question marks at high dilution in some circumstances Henry s law has a limit also toward inhnite dilution. The intercept of Henry s law slope with ordinate axis defines Henry s law standard state chemical potential. (B) Deviations from Nernst s law behavior in a logarithmic plot of normalized trace/carrier distribution between solid phase s and ideal aqueous solution aq. Reproduced with modifications from liyama (1974), Bullettin de la Societee Francaise de Mineralogie et Cristallographie, 97, 143-151, by permission from Masson S.A., Paris, France. A in part A and log A in part B have the same significance, because both represent the result of deviations from Henry s law behavior in solid.

An ideal solution therefore satisfies both Raoult s and Henry s laws at all concentrations, i.e.,... 

As defined by (7.49a, b), a Henry s law solution is a more general and useful approximation than an ideal solution as defined by (7.45) or (7.47), but each of these approximations is often inadequate for real solutions at concentrations of chemical interest. 

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