Infinitely dilute solution reference

This gives us the relation between the equilibrium constant relative to the pure-substance reference (I) and that relative to the infinitely-dilute solution reference (II) ... 

Convention (11) (called the infinitely dilute solution reference) distinguishes amongst the components of a solution, those in the largest proportion(s), which are called the solvent(s) and those in the lowest proportions, which are called the solutes. The reference state is different for both categories of components ... 

So in a sufficiently diluted solution, the coefficients of activity, in the conventions infinitely dilute solution reference (11) and molar solution reference (111), are identical for both the solvent as well as the solutes. 

In convention (II), for the solvent, in the infinitely-dilute solution reference (which is to say, pure solvent), the relation is identical to the previous one ... 

Thus, the constant linking the activity coefficients expressed in the two conventions the pure-substance reference and the infinitely-dilute solution reference do not depend on the composition of the solution, but instead depends on the temperature by means of (amongst others) the chemical potentials of the reference states. The value is called Henry s... 

We can show that the activity coefficient of a component in a perfect solution in the infinitely-dilute solution reference is also 1 at all temperatures and in all compositions. 

When considering solutions, it is often more convenient to take the pure solvent and an infinitely dilute solute reference since the corresponding activity coefficient Yb is defined by ... 

For those dilute mixtures where the solute and the solvent are chemically very different, the activity coefficient of the solute soon becomes a function of solute mole fraction even when that mole fraction is small. That is, if solute and solvent are strongly dissimilar, the relations valid for an infinitely dilute solution rapidly become poor approximations as the concentration of solute rises. In such cases, it is necessary to relax the assumption (made by Krichevsky and Kasarnovsky) that at constant temperature the activity coefficient of the solute is a function of pressure but not of solute mole fraction. For those moderately dilute mixtures where the solute-solute interactions are very much different from the solute-solvent interactions, we can write the constant-pressure activity coefficients as Margules expansions in the mole fractions for the solvent (component 1), we write at constant temperature and at reference pressure Pr ... 

The value obtained by Hamm et alm directly by the immersion method is strikingly different and much more positive than others reported. It is in the right direction with respect to a polycrystalline surface, even though it is an extrapolated value that does not correspond to an existing surface state. In other words, the pzc corresponds to the state of a bare surface in the double-layer region, whereas in reality at that potential the actual surface is oxidized. Thus, such a pzc realizes to some extent the concept of ideal reference state, as in the case of ions in infinitely dilute solution. 

For a solution of a non-volatile substance (e.g. a solid) in a liquid the vapour pressure of the solute can be neglected. The reference state for such a substance is usually its very dilute solution—in the limiting case an infinitely dilute solution—which has identical properties with an ideal solution and is thus useful, especially for introducing activity coefficients (see Sections 1.1.4 and 1.3). The standard chemical potential of such a solute is defined as... 

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 coefficients are defined for infinitely dilute solution of solute in the solvent L. However, they are assumed to be valid even for concentrations of solute of 5 to 10 mol.%. The relationships are available for pure solvent, and could be used for mixture of solvents composed of molecules of close size and shape. They all refer to the solvent viscosity which can be estimated or measured. Pressure has a negligible influence on liquid viscosity, which decreases with temperature. As a consequence, pressure has a weak influence on liquid diffusion coefficient conversely, diffusivity increases significantly with temperature (Table 45.4). For mixtures of liquids, an averaged value for the viscosity should be employed. 

For this reason, the infinitely dilute solution frequently is called the reference state for the partial molar enthalpy of both solvent and solute. 

Absolute values of partial molar enthalpies cannot be determined, just as absolute values of enthalpies cannot be determined. Thus, it is necessary to choose some state as a reference and to express the partial molar enthalpy relative to that reference state. The most convenient choice for the reference state usually is the infinitely dilute solution. Without committing ourselves to this choice exclusively, we will nevertheless use it in most of our problems. 

All species are aqueous unless otherwise indicated. The reference state for amalgams is an infinitely dilute solution of the element in Hg. The temperature coefficient, dE°/dT, allows us to calculate the standard potential, E°(T), at temperature T E°(T) — Ec + (dE°/dT)AT. where A T is T — 298.15 K. Note the units mVIK for dE°ldT. Once you know E° for a net cell reaction at temperature T, you can find the equilibrium constant, K, for the reaction from the formula K — lOnFE°,RTln w, where n is the number of electrons in each half-reaction, F is the Faraday constant, and R is the gas constant. 

In Raoult s law at infinite dilution, the reference state is the pure liquid state. The activity coefficient at infinite dilution accounts for deviation from pure solute-solute interactions in solution. When positive deviations from Raoult s law occur, the partial pressure of the substance above the solution is greater than it is in an ideal solution,y 1, and the chromatographic retention time is decreased. 

The usual choice of a reference state other than the pure components is the infinitely dilute solution for which the mole fractions of all solutes are infinitesimally small and the mole fraction of the solvent approaches unity that is, the values of the thermodynamic properties of the system in the reference state are the limiting values as the mole fractions of all the solutes approach zero. However, this is not the only choice, and care must be taken in defining a reference state for multicomponent systems other than binary systems. We use a ternary system for purposes of illustration (Fig. 8.1). If we choose the component A to be the solvent, we may define the reference state to be the infinitely dilute solution of both B and C in A. Such a reference state would be useful for all possible compositions of the ternary systems. In other cases it may be advantageous to take a solution of A and B of fixed... 

When the infinitely dilute solution with respect to all solutes is chosen as the reference state for the solvent, the first two terms on the right-hand side of Equation (8.102) become zero at the reference state and... 

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. 

The definition is completed by assigning a value to m and (f>c in some reference state. To conform with the definitions made in Sections 8.9 and 8.10, the infinitely dilute solution with respect to all molalities or molarities is usually used as the reference state at all temperatures and pressures, and both m and c are made to approach unity as the sum of the molalities or molarities of the solutes approaches zero. The standard state of the solvent is again the pure solvent, and is identical to its reference state in all of its thermodynamic functions. 

B) As a second example, suppose that the original reference state of the /cth component, considered as a solute, is the pure substance and that mole fractions are used as the composition variable. It is then desired to make the infinitely dilute solution the reference state and to use the molality for the composition variable. Here, again, we express the chemical potential of the fcth component in the two equivalent ways ... 

C) In this example let the original reference state of the kth component, considered as a solute, be the infinitely dilute solution, and let the molalities be used to express the composition. Let the new reference state of the fcth component, again considered as a solute, be the infinitely dilute solution, but with the molarities being used as the composition variable. Then we have... 

The problems of the reference and standard states are slightly different when we use the infinitely dilute solution-of all solutes as the reference states. When we take the reference state of both the component and the species as the infinitely dilute solution, Equation (8.168) becomes... 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

These equations are used whenever we need an expression for the chemical potential of a strong electrolyte in solution. We have based the development only on a binary system. The equations are exactly the same when several strong electrolytes are present as solutes. In such cases the chemical potential of a given solute is a function of the molalities of all solutes through the mean activity coefficients. In general the reference state is defined as the solution in which the molality of all solutes is infinitesimally small. In special cases a mixed solvent consisting of the pure solvent and one or more solutes at a fixed molality may be used. The reference state in such cases is the infinitely dilute solution of all solutes except those whose concentrations are kept constant. Again, when two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be made and clearly stated. 

If we define the reference state for both y2 and y as the infinitely dilute solution, we have... 

We define the reference state as the infinitely dilute solution of the component in the solvent, so that yM2A, 7m 7ma-> and 7m 7a2- a l 8° t0 unity as m2 goes to zero. This definition fixes the values of the quantities m2a + Mma- )>... 

Special consideration must be given to systems involving liquid solutions of at least one solid component, for which the choice of either the pure solid or pure supercooled liquid as the standard state is not convenient. This case is encountered for all solutions in which the pure solute is not chosen as the reference state. As an example, we consider an aqueous solution of a solid B and choose the reference state to be the infinitely dilute solution. Then a general change of state for the formation of the solution from the components is written as... 

When the reference state is the infinitely dilute solution, the standard state for the enthalpy is also the infinitely dilute solution. We then change the standard state of component B from the pure solid to the infinitely dilute solution by adding to and subtracting from Equation (9.30) the quantity n2H2, where H2 is the partial molar enthalpy of the component in the... 

In many systems the pure liquid phase of a component is not attainable under the experimental conditions and thus cannot be used as the reference state for the component. It is then necessary to choose some other state, usually the infinitely dilute solution of the component in the liquid, as a reference state. We choose to illustrate the development under such circumstances by the use of Equations (10.28)—(10.30) under the appropriate experimental conditions. The combination of these equations yields... 

We define the reference state of the component to be the infinitely dilute solution of the component in the second component, so that Aapproaches... 

This definition involves indirectly the change of the reference state from the pure liquid to the infinitely dilute solution. 

The use of the infinitely dilute solution as the reference state of a volatile component is not convenient for the experimental study of isopiestic vapor-liquid equilibria. Equation (10.79) may be written as... 

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