Solvent standard state

Conditions appropriate to the three conventions introduced for the standard state (solvent, solute, and gases) usually do not occur under biological situations. A solute is essentially never at a concentration of 1 m, neither is an important gas at a pressure of 1 atm, nor is a pure solvent present (except sometimes for water). Hence, care must be exercised when... 

For estimation of thermodynamic properties of dissolved species, one can use the Entropy Correspondence Principle ( ), where the entropy of an ion at a given temperature is regarded as a function of the charge, the dielectric constant, mass, radius, and other variables. The function depends mainly upon the choice of the standard state, solvent, and temperature. The temperature dependency of entropy was derived based on the above principles and experimental data. By conducting the a square regression on Criss-Cobble s data ( ), we obtained the following eqtiation for calculating the entropies of species in aqueous solution. 

In a binary liquid solution containing one noncondensable and one condensable component, it is customary to refer to the first as the solute and to the second as the solvent. Equation (13) is used for the normalization of the solvent s activity coefficient but Equation (14) is used for the solute. Since the normalizations for the two components are not the same, they are said to follow the unsymmetric convention. The standard-state fugacity of the solvent is the fugacity of the pure liquid. The standard-state fugacity of the solute is Henry s constant. 

The use of Henry s constant for a standard-state fugacity means that the standard-state fugacity for a noncondensable component depends not only on the temperature but also on the nature of the solvent. It is this feature of the unsymmetric convention which is its greatest disadvantage. As a result of this disadvantage special care must be exercised in the use of the unsymmetric convention for multicomponent solutions, as discussed in Chapter 4. 

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... 

Solvent variation can gready affect the acidity of hydantoins. Although two different standard states are employed for the piC scale and therefore care must be exercised when comparing absolute acidity constants measured in water and other solvents like dimethyl sulfoxide (DMSO), the huge difference in piC values, eg, 9.0 in water and 15.0 in DMSO (12) in the case of hydantoin itself, indicates that water provides a better stabilization for the hydantoin anion and hence an increased acidity when compared to DMSO. 

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. 

The difficulties engendered by a hypothetical liquid standard state can be eliminated by the use of unsymmetrically normalized activity coefficients. These have been used for many years in other areas of solution thermodynamics (e.g., for solutions of electrolytes or polymers in liquid solvents) but they have only recently been employed in high-pressure vapor-liquid equilibria (P7). 

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... 

The standard-state fugacity for y is H , Henry s constant for solute 2 in solvent 1 at pressure P. ... 

In defining the activity through equations (6.83) and (6.84), we have made no restrictions on the choice of a standard state except to note that specification of temperature is not a part of the standard state condition. We are free to choose standard states in whatever manner we desire.p However, choices are usually made that are convenient and simplify calculations involving activities. The usual choices differ for a gas, pure solid or liquid, and solvent or solute in solution. We will now summarize these choices of standard states and indicate the reasons. Before doing so, we note that activities for a substance with different choices of standard states are proportional to one another. This can be seen as follows With a particular choice of standard state... 

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... 

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... 

We have chosen the pure solvent as the lower limit of the integration. Under this condition a = 1 (Raoult s law standard state), and T = Tf, the melting temperature of the pure solvent. Integration of the left side of the equation gives... 

The isopiestic method is based upon the equality of the solvent chemical potentials and fugacities when solutions of different solutes, but the same solvent, are allowed to come to equilibrium together. A method in which a solute is allowed to establish an equilibrium distribution between two solvents has also been developed to determine activities of the solute, usually based on the Henry s law standard state. In this case, one brings together two immiscible solvents, A and B, adds a solute, and shakes the mixture to obtain two phases that are in equilibrium, a solution of the solute in A with composition. vA, and a solution of the solute in B with composition, a . 

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... 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

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... 

The activity is a measure of the tendency of a substance to react relative to its reacting tendency in the standard state. Here we relate activity to c/c for ideal solutions. For ideal gases and ideal solvents, the activity approaches P/P and X, respectively. Although c is taken to be 1.0 M, Equation (8) works best when c is much less than 1.0 M. 

In the freezing point depression method, one measures the temperature lowering AT/ required to render the activity of the solvent in the solution equal to that of the pure crystalline solvent (referred to the pure liquid as the standard state see above). Then... 

Since the pure solvent has been chosen as the standard state, ai = Pi/Pij to the approximation that the vapor may be regarded as an ideal gas. For the osmotic pressure itVi=—(mi—Mi) where Vi is the molar volume of the solvent. Thus, according to Eq. (26)... 

The free energy of mixing polymer segments with solvent in the volume element 5F, obtained from 5(AaSm ) in conjunction with a term kTxi niV representing the standard state free energy of mixing (see Eq. 20), is... 

The temperature at which this condition is satisfied may be referred to as the melting point Tm, which will depend, of course, on the composition of the liquid phase. If a diluent is present in the liquid phase, Tm may be regarded alternatively as the temperature at which the specified composition is that of a saturated solution. If the liquid polymer is pure, /Xn —mS where mS represents the chemical potential in the standard state, which, in accordance with custom in the treatment of solutions, we take to be the pure liquid at the same temperature and pressure. At the melting point T of the pure polymer, therefore, /x2 = /xt- To the extent that the polymer contains impurities (e.g., solvents, or copolymerized units), ixu will be less than juJ. Hence fXu after the addition of a diluent to the polymer at the temperature T will be less than and in order to re-establish the condition of equilibrium = a lower temperature Tm is required. 

A system s standard state is defined as the state in which p = p and hence = 1. We must bear in mind that the standard state does not coincide with the limiting state (at low concentrations) when the system becomes ideal. Hence, in the standard state the value of activity differs from the value of concentration (except for the solvent). 

According to Snyder [28], the solvent strength 8° is the standard free energy of adsorbed solvent molecules in a standard state, and it is given by Equation 4.11 ... 

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. 

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