Solution standard state

Reference 170. The original values have been converted to a 1 molal ideal solution standard state (see reference 176)... 

It is normally a very good approximation to assume that the titration process under study occurs under a pressure of 0.1 MPa. Therefore, the pressure corrections involved in the conversion of AT/icp to the standard state are usually negligible, and in many cases, it is licit to make A77icp = A/T p. When appropriate, other corrections, such as those related to solution standard states, can be applied as described by Vanderzee [129,130]. 

If the fused salt does not exist at the temperature of interest, one normally uses the infinitely dilute solute standard state. While these equations can easily be converted to that basis, the results are not immediately useful for two reasons ... 

Debye-Huckel effects are significant in the dilute range and are not considered, and (2) the usual composition scale for the solute standard state is molality rather than mole fraction. Both of these problems have been overcome, and the more complex relationships are being presented elsewhere (17). However, for most purposes, the virial coefficient equations for electrolytes are more convenient and have been widely used. Hence our primary presentation will be in those terms. 

Solutions are usually classified as nonelectrolyte or electrolyte depending upon whether one or more of the components dissociates in the mixture. The two types of solutions are often treated differently. In electrolyte solutions properties like the activity coefficients and the osmotic coefficients are emphasized, with the dilute solution standard state chosen for the solute.c With nonelectrolyte solutions we often choose a Raoult s law standard state for both components, and we are more interested in the changes in the thermodynamic properties with mixing, AmjxZ. In this chapter, we will restrict our discussion to nonelectrolyte mixtures and use the change AmjxZ to help us understand the nature of the interactions that are occurring in the mixture. In the next chapter, we will describe the properties of electrolyte solutions. 

In equations (18.91) and (18.92), C° 2 and V are the partial molar heat capacity and partial molar volume of the surfactant in the infinitely dilute solution (standard state values). 

This equation relates the activity on the Henrian scale to the activity on the Raoultian scale. The Henrian standard state is sometimes called the infinitely dilute solution standard state because it is mostly used for dilute solutions. 

As the activities in aqueous electrolyte solutions are defined with respect to the 1 molality standard state ( or infinitely dilute solution standard state), the activity of an ionic species becomes equal to its molality as the concentration approaches zero (Henry s Law). 

Equation (31) implies that the properties of the solution change smoothly into those of pure component i as xt — 1. The pure components of an ideal solution must, therefore, have the same phase as the solution. Standard states of an ideal liquid solution are thus just the pure liquid components at the given T and P. Comparing Eq. (31) with the normal form of the chemical potential given in Eq. (47) of Chapter 6, p = p° + RTXna, we see that, for the ideal solution, the... 

The units used to express solubilities of gases, e.g. Henry s law coefficients, Ostwald coefficients and Bunsen coefficients, have to be converted to the relevant solution standard state (p. 213). Such solubilities (Battino and Clever, 1966 Wilhelm and Battino, 1973) are valuable in the analysis of kinetic data. For example, the solubility of a neutral solute in a range of aqueous mixtures can provide some indication of the variation of the chemical potential of a neutral reactant because, from eqn (11), 8m AGe = 8mnf. Where the pure solute is a liquid or solid, it is often convenient to chose the pure solute as a standard state, represented by the symbol, ° in eqn (12). Similar comments apply to the related thermodynamic quan-... 

In the solution standard state, apolar solutes are surrounded by a region of enhanced water-structure (p. 250). As x2 increases, the... 

Some workers, while retaining the one-molar ideal solution standard state for the solution phase, use a one-atmosphere standard state in the gas... 

A choice must be made for the reference state for the solute either the pure liquid (possibly supercooled), or the solute at infinite dilution in the solvent. The latter differs from the conventional solute standard state only in the use of the mole fraction scale rather than molality units. The activity coefficient of a symmetrical salt MX is either... 

The standard state for a pure liquid or solid is taken to be the substance in that state of aggregation at a pressure of 1 bar. This same standard state is also used for liquid mixtures of those components that exist as a liquid at the conditions of the mixture. Such substances are sometimes referred to as liquids that may act as a solvent. For substances that exist only as a solid or a gas in the pure component state at the temperature of the mixture, sometimes referred to as substances that can act only as a solute, the situation is more complicated, and standard states based on Henry s law may be used. In this case the pressure is again fixed at 1 bar, and thermal properties such as the standard-state enthalpy and heat capacity are based on the properties of the substance in the solvent at infinite dilution, but the standard-state Gibbs energy and entropy are based on a hypothetical state.of unit concentration (either unit molality or unit mole fraction, depending on the form of Henry s law used), with the standard-state fugacity at these conditions extrapolated from infinite-dilution behavior in the solvent, as shown in Fig. 9.1-3a and b. Therefore just as for a gas where the ideal gas state at 1 bar is a hypothetical state, the standard state of a substance that can only behave as a solute is a hypothetical state. However, one important characteristic of the solute standard state is that the properties depend strongly upon the solvent. used. Therefore, the standard-state properties are a function of the temperature, the solute, and the solvent. This can lead to difficulties when a mixed solvent is used. 

Although density measurements of varying degrees of accuracy have been reported for ethanolic solutions, standard state partial molal volumes in ethanol have been evaluated for only a few electrolytes. Vosburgh, Connell and Butler reported for LiCl in water and a series of alcohols, including ethanol. They observed that the salt had a much smaller value of F in the alcohols than in water, and that for all the systems studied it was smallest in ethanol. Sobkowski and Mine have reported for HCl in water and the three lower alcohols and also observe F to be smaller in the alcohols than in water, but it is smallest in methanol rather than ethanol. Lee and Hyne have reported F° at 50.25°C for the tetraalkylammonium chlorides in ethanol-water mixtures up to 0.4 mol fraction of ethanol. With the tetramethyl and tetraethyl salts, the volumes are all very positive in water but decrease rapidly with an increase in alcohol content and appear to be at a minimum around 0.3 to 0.4 mol fraction of ethanol. The higher tetraalkyl salts are not entirely consistent with this pattern. 

In 10.1 we present the basic thermodynamic relations that are used to start phase-equilibrium calculations we discuss vapor-liquid, liquid-liquid, and liquid-solid calculations. We have seen that the most interesting phase behavior occurs in nonideal solutions, but when we describe nonidealities using an ideal solution as a basis, we must select an appropriate standard state. Common options for standard states are discussed in 10.2 they include pure-component standard states and dilute-solution standard states. 

Solute-free dilute-solution standard state. In this case we do not have a value for /pure 1/ SO we cannot apply (10.2.61). But we are able to find or estimate a value for the solute-free Henry s constant at our solute-free mole fractions (10.2.59). The value is found to be H g = 2.547 bar. Then we obtain the fugacity from... 

This is the same value found in (10.2.63) using the Lewis-RandaU standard state and found in (10.2.66) using the solute-free dilute-solution standard state. 

In general we can say that the reference-solvent dilute-solution standard state is easier to use than the solute-free dilute-solution standard state (except, of course, when Y can be assumed to be unity). This is because is completely independent of composition, while depends on the solute-free mole fractions. But more generally, the lesson is that the three kinds of activity coefficients are simply proportional they are aU embedded with the same information, so they aU give the same value for a fugacity. We use the particular standard state that allows us to take advantage of available data and that simplifies calculations. 

For the infinite-dilution limit, we choose component i to be a solute, and use the solute-free, dilute-solution standard state, so f° = H . Then we have... 

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