Transfer activity coefficient defined

Some authors" express the transfer free energy in the form of an activity coefficient defined by Eq. (8-59). 

Note that the tGA are the standard molar Gibbs energies of solvation of the (combined ions of the) electrolyte [5]. Alternatively, a transfer activity coefficient can be defined as... 

When we consider the solvent effect on the reactivity of a chemical species, it is convenient to use the transfer activity coefficients9 instead of the Gibbs energies of transfer. The transfer activity coefficient, yt(i,R->S), is defined by... 

The transfer activity coefficient y for a solute S in H20-D20 mixture is defined in terms of the Gibbs free energy (J6rtranBfer) for the process... 

Here the pH is the value for acidity referred to the standard state defined from the limiting reference behavior for the hydrogen ions in the solvent in question, and PH is the pH value of the aqueous reference buffer corrected for liquid junction and transfer activity coefficient as follows ... 

The meaning to be attached to pH values obtained in different solvents and under different conditions needs interpretation. For example, solutions of pH 5 in the three solvents water, ethanol, and acetonitrile do not denote the same acidity (acidity defined as a measure of the tendency for protons to be donated to basic substances). In view of what is known about transfer activity coefficients (Section 4-1), an acetonitrile solution of pH 5 is far more acidic (higher absolute activity) than an ethanol solution of pH 5 and, in turn, one in ethanol is more acidic than one in water. The significant point is that a solution of, say, pH 5 in a given solvent has an acidity 10 times the acidity of another solution of pH 6 in that same solvent. A single universal scale of pH for all solvents does not exist instead there is a different scale for every solvent of differing composition. To denote pH values in nonaqueous solvents, the... 

An electron transfer reaction, Equation 6.6, is characterised thermodynamically by the standard potential, °, i.e. the value of the potential at which the activities of the oxidised form (O) and the reduced form (R) of the redox couple are equal. Thus, the second term in the Nernst equation, Equation 6.7, vanishes. Here and throughout this chapter n is the number of electrons (for organic compounds, typically, n = 1), II is the gas constant, T is the absolute temperature and F is the Faraday constant. Parentheses, ( ), are used for activities and brackets, [ ], for concentrations /Q and /R are the activity coefficients of O and R, respectively. However, what may be measured directly is the formal potential E° defined in Equation 6.8, and it follows that the relationship between E° and E° is given by Equation 6.9. Usually, it maybe assumed that the activity coefficients are unity in dilute solution and, therefore, that E° = E°. 

The inclusion of activity coefficients into the simple equations was briefly considered by Purlee (1959) but his discussion fails to draw attention to the distinction between the transfer effect and the activity coefficient (y) which expresses the non-ideal concentration-dependence of the activity of solute species (defined relative to a standard state having the properties of the infinitely dilute solution in a given solvent). This solvent isotope effect on activity coefficients y is a much less important problem than the transfer effect, at least for fairly dilute solutions. For example, we have already mentioned (Section IA) that the nearequality of the dielectric constants of H20 and D20 ensures that mean activity coefficients y of electrolytes are almost the same in the two solvents over the concentration range in which the Debye-Hiickel limiting law applies. For 0-05 m solutions of HC1 the difference is within 0-1% and thus entirely negligible in the present context. Of course, more sizeable differences appear if concentrations are based on the molality scale (Gary et ah, 1964a) (see Section IA). 

The parameter R is the gas constant, T is the temperature, F is the Faraday constant and n is the number of electrons consumed in the electron transfer step (Eq. 2). The standard potential, Eq of the redox couple O/R is defined as the reduction potential of O when the activity coefficients for both O and R are equal to one. Once Fq is known, the electrode potential can be used to measure concentrations in solutions or to calculate equilibrium constants, for redox equilibria (Eq. 3) involving two or more redox couples as shown in Eq. 4. 

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... 

Where and LH are the corresponding activation energy and enthalpy of phase transition and the coefficient defines the maximum probability that molecules will cross the interface between the liquid and SCF (vapor) phases. This simple relationship can explain the behavior of the mass transfer coefficient in Figure 15 when it is dominated by the interfacial resistance. Indeed, increases with temperature T according to Eq. (49) also, both parameters E and A// should decrease with increase of pressure, since the structure and composition of the liquid and vapor phases become very similar to each other around the mixture critical point. The decrease of A/f with pressure for the ethanol-C02 system has been confirmed by interferometric studies of jet mixing described in Section 3.2 and also by calorimetric measurements described by Cordray et al. (68). According to Eq. (43) the diffusion mass transfer coefficient may also increase in parallel with ki as a result of more intensive convection within the diffusion boundary layer. 

The interfacial area is another quantity that is impractical to measure. Therefore, capacity coefficients, defined as (kxO), (kyO), (Kyof and (KyO), are used instead of the mass transfer coefficients. The quantity a is the interfacial area per unit of active column volume. Since both a and the transfer coefficients must be determined in one way or another (usually experimentally), there is no benefit gained from determining them separately. They are, therefore, most commonly reported as groups. In terms of these coefficients. Equations 15.11 and 15.12 are rewritten as... 

Where H2O0 and H2OW represent water in the hydrophobic and hydrophilic phases respectively, Ki is the equilibrium constant for homogeneous esterification and K2 a constant for the transfer of water between phases. Neglecting activity coefficients, letting bracketed terms represent concentrations and K2 = [H2OWMH2O0], the overall apparent equilibrium constant, Kapp. can be defined as ... 

One way of probing the interactions between solvated ions is to study aqueous bulk electrolyte activity coefficients, y. For the most common choice of reference state, the mean activity coefficient is a measure of the excess free energy, fM = ksT In y, of transferring a solvated salt pair from an infinite dilution to a solution -with a finite salt concentration. In the present context, we are interested in the ion specijkity and therefore — for a fixed salt concentration — define a free energy of exchanging one counter ion -with another. For example,... 

The Gibbs energy of activation in Eq. (5.4) can be split into an enthalpy and an entropy term AGjx = AH x - T AS]x. Define two transfer coefficients... 

The transfer of an electron to (reduction) or from (oxidation) the substrate is an activated process, characterized by a rate constant kg, defined as the standard (or formal) potential E, and the transfer coefficient a. The three situations mentioned below can be distinguished ... 

Internal diffusion in porous catalysts, if dominant, also reduces the observed activity of the biocatalyst. The decisive coefficient for mass transfer is the effective diffusion coefficient De((, which is defined in Eq. (5.56), where D0is the diffusion coefficient in solution, e the porosity of the carrier, and t the tortuosity factor. 

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