Standard state for the solvent

But that is not all. For dilute solutions, the solvent concentration is high (55 mol kg ) for pure water, and does not vary significantly unless the solute is fairly concentrated. It is therefore common practice and fully justified to use unit mole fraction as the standard state for the solvent. The standard state of a close up pure solid in an electrochemical reaction is similarly treated as unit mole fraction (sometimes referred to as the pure component) this includes metals, solid oxides etc. 

Thus, with a Henry s law standard state, H° is the enthalpy in an infinitely dilute solution. For mixtures, in which we choose a Raoult s law standard state for the solvent and a Henry s law standard state for the solute, we can... 

The case of liquid solutions is more complicated because the conventions vary. These are always stated in introductory chapters of the thermochemical databases and deserve a careful reading. In most tables and in the present book, it is agreed that the standard state for the solvent is the pure solvent under the pressure of 1 bar (which corresponds to unit activity). For the solute, the standard state may refer to the substance in a hypothetical ideal solution at unit molality (the amount of substance of solute per kilogram of solvent) or at mole fraction x = 1. 

Solvent We have defined the pure solvent at the same temperature as the solution and at its equilibrium vapor pressure as the standard state for the solvent. It follows that... 

It should be noted that it is at this point that the postulated standard state for the solvent is introduced. 

In a liquid mixture, when there is a fairly balanced composition in the compounds then the pure compounds can be kept as standard states using the molar ratios to define the ideal activities. Consequently, the activities are expressed as ji. x,. However, the solutions most commonly seen in electrochemistry involve a compound, called a solvent, which is found in much greater quantity than other compounds, called solutes. Here one often distinguishes between these two types of compounds by choosing a different standard state for the solvent and the solutes ... 

In solutions, particularly electrolyte solutions, the standard state for the solvent is always the pure phase (pure water), so that, for example, refers to the molar volume of pure component 1, that is, pure water. For the solute, the standard state for most properties is, as just mentioned, the state of infinite dilution, so we could use for tho partial molar volume of the solute in the standard state. However, this proves a bit confusing, so for clarity we introduce superscript °° to indicate the infinite dilution state (1 ), and we understand that this is also the standard state for most properties. This raises the question of what symbol to use for the solute in its pure state. The lUPAC recommends the use of for pure substances, but our examples involve only minerals so we will just use the mineral name. Thus we use for the molar volume of pure NaCl. 

It will be useful to have an expression for the Gibbs energy of mixing of real solutions. This is a bit more complicated for aqueous systems which are unsymmetrical, that is, which have different standard states for the solvent and solute, and a completely different method of expressing deviations from ideality - osmotic coefficients for the solvent, and Henryan activity coefficients for the solutes. This development follows Pitzer (1991). 

Standard State of a Solvent in a Mixture The usual choice of a standard state for a solvent in a solution is the pure solvent at a pressure of 1 bar, the same convention as for a pure solid or liquid. Thus,u... 

For solvents, 1, is equal to V because the standard state is the pure solvent, if we neglect the small effect of the difference between the vapor pressure of pure solvent and 1 bar. As the standard state for the solute is the hypothetical unit mole fraction state (Fig. 16.2) or the hypothetical 1-molal solution (Fig. 16.4), the chemical potential of the solute that follows Henry s law is given either by Equation (15.5) or Equation (15.11). In either case, because mole fraction and molality are not pressure dependent. 

The activity of the solvent often can be obtained by an experimental technique known as the isopiestic method [5]. With this method we compare solutions of two different nonvolatile solutes for one of which, the reference solution, the activity of the solvent has been determined previously with high precision. If both solutions are placed in an evacuated container, solvent will evaporate from the solution with higher vapor pressure and condense into the solution with lower vapor pressure until equilibrium is attained. The solute concentration for each solution then is determined by analysis. Once the molality of the reference solution is known, the activity of the solvent in the reference solution can be read from records of previous experiments with reference solutions. As the standard state of the solvent is the same for all solutes, the activity of the solvent is the same in both solutions at equUibrium. Once the activity of the solvent is known as a function of m2 for the new solution, the activity of the new solute can be calculated by the methods discussed previously in this section. 

From the standpoint of the operational definition of the standard state for the above free energy changes, we must remember that, while mole fractions are strongly recommended composition measures (61 Mil), in practice, both molalities, m, and concentrations, c, are widely used. For dilute aqueous solutions at moderate temperatures the numerical values of m and c are only slightly different. This no longer holds for other solvents. 

The activities of each solvent are shown in columns five and six of Tables I and II and are plotted in Figure 1 for 2-propanol. The standard state for the activities of each solvent was taken as the state for the pure component at the same temperature and pressure as that of the mixture. Assuming the vapor mixture obeys the ideal solution law, that is 0 2 = Wn + the activities were cal-... 

Thus, the standard state of the solvent is the pure solvent and is identical to the reference state for the solvent in all of its thermodynamic properties. 

When the infinitely dilute solution, with respect to all solutes, is used as the reference state of the solution at all temperatures and pressures, Ap c approaches zero as all cfs approach zero. Thus, the standard state of the solvent is the pure solvent at all temperature and pressures and is identical to the reference state of the solvent for all thermodynamic functions. 

Comparison with the standard form for the chemical potential, p = p° + RT In a [Eq. 47 of Chapter 6], shows that in the ideally dilute solution activities are equal to mole fractions for both solvent and solute. In order to find the standard state of the solvent in the ideally dilute solution, we note that at xA = 1 (infinite dilution, within the range of applicability of the model), we have p = p. The standard state of the solvent in the ideally dilute solution is pure solvent, just like the standard states of all components in an ideal solution. The solvent in the ideally dilute solution behaves just like a component of the ideal solution. Although it is also true that p° becomes p at x, = 1, this is clearly outside the realm of applicability of Eq. (43). In order to avoid this difficulty, in determining p° we make measurements at very low values ofx, and extrapolate to x, = 1 using p = p, — RT In x as if the high dilution behavior held to x, = 1. In other words, our standard state for a solute in the ideally dilute solution is the hypothetical state of pure solute with the behavior of the solute in the infinitely dilute solution. 

If we chose our standard state for the activity coefficient to be the pure liquid solvent at pressure P and temperature T, then the above equation becomes the expression for the standard state fugacity. The fugacity coefficient at the saturation pressure can be calculated from the second virial coefficient... 

In Equation (4-1), y is a measure of the effects of interionic or interparticle interactions, and y, a measure of the effect of changing the solvent. As the concentration of solute approaches zero, y approaches unity and y, approaches y a constant for each solute-solvent pair at a given temperature. The value of y, is related to the difference between the free energies of the solute in the usual standard states in the solvent and the reference solvent ... 

For water as solvent, pure liquid water is used as a standard state for the reference condition infinite dilution the activity of water is then defined as the mole fraction of pure water Xhjo-... 

As a standard state for the solid salt, the state of pure, solid salt is used. For solid-liquid equilibrium calculations in mixed solvent systems, it is important to choose the proper standard states for the ions. ... 

In order to be able to express the activity of a particular component numerically, it is necessary to define a reference state in which the activity is arbitrarily unity. The activity of a particular component is then the ratio of its value in a given solution to that in the reference state. For the solvent, the reference state is invariably taken to be the pure liquid and, if this is at a pressure of 1 atmosphere and at a definite temperature, it is also the standard state. Since the mole fraction as well as the activity is unity y =l. 

For dilute solutions the best choice of standard state for the solute is different from that adopted here (see 37b, III), but for the solvent in dilute solutions and for all constituents of solutions of completely miscible, or almost completely miscible, liquids, the standard state of unit activity is usually selected as that of the pure liquid at the same temperature and 1 atm, pressure. The activity scale is chosen, therefore, so as to make the activity of any constituent of a mixture equal to unity for that substance in the pure liquid state at 1 atm. pressure. According to the postulated standard state, the value of m for a given liquid depends only on the temperature and is independent of the pressure. 

As in the case of heats and heat capacities, ionic entropies have been examined more extensively in methanol and methanol-water mixtures than in other solvents. The earliest study was that of Latimer and Slansky who report entropies for NaCl, KCI, KBr, and HCl in water-methanol mixture from 0 to 100% methanol. Jakuszewski and Taniewska-Osinska " have determined the entropies of numerous halide salts and HCl at 25 C, and more recently Franks and Reid, using data from the literature, have calculated standard ionic entropies for several species in water-methanol mixtures covering the whole concentration range. It should be observed that these authors chose the mol fraction standard state for the solute in solution and ideal ionic gas as the standard state for the pure solute instead of the conventional hypothetical one molal solution and pure solid at OK. The former standard states are convenient when comparing entropies of solvation for the various species. Ionic entropies in methanol are considerably more negative than in water. 

Convention II is sometimes referred to as the application of the solute standard state to the solutes and the application of the solvent standard state to the solvent. Convention I is called the application of the solvent standard state to every component. The reason for having two conventions is that we would like to have activity coefficients nearly equal to unity as often as possible. In convention I we describe the deviation of each substance from Raoult s law. If Raoult s law is approximately obeyed by all substances, the use of convention I gives an activity coefficient approximately equal to unity for each substance. In convention II we describe the deviation of the solvent from Raoult s law and the deviation of a solute from Henry s law. If Henry s law is approximately obeyed by a solute, the use of convention II gives an activity coefficient approximately equal to unity for that solute, as well as an activity coefficient approximately equal to unity for the solvent, which would approximately obey Raoult s law. 

We need to define the standard state for the liquid in the electrolyte. By convention, we characterize the liquid composition in terms of concentration instead of mole fraction, where the concentration of species i, Ci, has units of molality, m (moles i per 1 kg of solvent). Moreover, we must specify a Henry s law standard state for the ions in solution they do not exist as pure species, so we cannot use the Lewis/RandaU reference state. Our standard state is chosen to be a 1-m ideal solution, in the Henry s law sense. If species i is not ideal at this concentration, we go to a low enough concentration that it obeys Henry s law, then extrapolate back to a hypothetical ideal liquid with 1-m concentration. The 1-m standard state for the electrolyte solution is analogous to that of 1 bar for vapors. Thus, all concentrations used should be in units ofm. 

Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std. state or ss). In this state... 

For the solvent (component 1),/° is the fugacity of pure saturated liquid 1 at the system temperature. However, the standard-state fugacity for the solute (component 2) is given by... 

A Raoult s law standard state is chosen for the solvent so that n] = /if. Substituting this equality and equation (6.155) into equation (6.156) and rearranging gives... 

Note that the first term in the rate law could be written ArisflH2o but if water is the solvent, as we shall assume, its activity is unity. Were one to write the term as ki,[H20], this would be tantamount to adopting a nonconventional standard state for water, which is usually not advisable. With [OH- ] [(CH3)2CHBr], the reaction follows first-order kinetics with... 

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