Activity coefficients energy

Null (1970) discusses some alternate models for the excess Gibbs energy which appear to be well suited for systems whose activity coefficients show extrema. 

The quantitative relationship between the degree of adsorption at a solution iaterface (7), G—L or L—L, and the lowering of the free-surface energy can be deduced by usiag an approximate form of the Gibbs adsorption isotherm (eq. 9), which is appHcable to dilute biaary solutions where the activity coefficient is unity and the radius of curvature of the surface is not too great ... 

The difference on the left is the partial excess Gibbs energy G y the dimensionless mXio J on the right is called the activity coefficient of species i in solution, y. Thus, by definition. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

A.ctivity Coefficients. Activity coefficients in Hquid mixtures are directiy related to the molar excess Gibbs energy of mixing, AG, which is defined as the difference in the molar Gibbs energy of mixing between the real and ideal mixtures. It is typically an assumed function. Various functional forms of AG give rise to many of the different activity coefficient models found in the Hterature (1—3,18). Typically, the Hquid-phase activity coefficient is a function of temperature and composition expHcit pressure dependence is rarely included. 

Gamma/Phi Approach For many XT E systems of interest the pressure is low enough that a relatively simple equation of state, such as the two-term virial equation, is satisfactoiy for the vapor phase. Liquid-phase behavior, on the other hand, may be conveniently described by an equation for the excess Gibbs energy, from which activity coefficients are derived. The fugacity of species i in the liquid phase is then given by Eq. (4-102), written... 

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

By combining these ions with other counterions, single ion transfer activity coefficients are calculated. By these techniques transfer free energies or activity coefficients have been determined for many ions and nonelectrolytes in a wide variety of solvents.Parker has discussed the extrathermodynamic assumptions that lead to single ion quantities. 

Usually SmGo is a small difference between two large numbers, so it is more accurate to measure 8mG directly by the techniques discussed above than to estimate it indirectly. Solvation is then usually considered in terms of transfer free energies or activity coefficients. 

Table 8-8 gives some nonelectrolyte transfer free energies, and Table 8-9 lists single ion transfer activity coefficients. Note especially the remarkable values for anions in dipolar aprotic solvents, indicating extensive desolvation in these solvents relative to methanol. This is consistent with the enhanced nucleophilic reactivity of anions in dipolar aprotic solvents. Parker and Blandamer have considered transfer activity coefficients for binary aqueous mixtures. 

In agreement with (98), the left-hand side is just the standard free energy of solution AF°. Here y, as defined by (106), is the usual activity coefficient on the molality scale. In particular, when the solid is in contact with its saturated solution, there is no change in the free energy when additional ions are taken into solution. In this case, if in (108) we write m, t and y,at, the values of m and y in the saturated solution, we may set AF equal to zero. This will be discussed in Sec. 100. 

The saturated solution of potassium iodate in water at 25°C has a molality equal to 0.43. Taking the activity coefficient y in this saturated solution to be 0.52, find the conventional free energy of solution at 25°C, and calculate in electron-volts per ion pair the value of L for the removal of tho ions K+ and (IOs) into water at 25°C. 

The activity coefficient y,fpr) is determined by differentiation of gE, the molar excess Gibbs energy at reference pressure Pr,... 

The Debye-Hiickel formula for the activity coefficient of an ion was developed by a consideration of ion atmosphere effects.10 It starts with an electrostatic expression for the free energy of interaction for one ion with one mole of others ... 

The activity coefficients in the above equation may be determined by obtaining experimental data for D/ m, and relating Ka to the free energy change for the reaction using the equation AGf = -RT In K. 

FIGURE 3.10. (a) Showing the relationship between the activation free energy Ag and the reaction free energy AG0 for the X + CH3Y- XCH3 + Y system. (6) The dependence of the "linear correlation coefficient 8 = d bg /d AG0 on AG0. 

When repulsion forces exist between the particles, the chemical potential of the corresponding species will increase (an additional energy j > 0 must be expended to place a particle into a given volume), and hence, the activity coefficient will be larger than unity. When attraction forces are present, the activity coefficient will be smaller than unity. 

Therefore, the activity coefficients in solutions are determined primarily by the energy of electrostatic interaction w j between the ions. It is only in concentrated solutions when solvation conditions may change, that changes in (but not the existence of) solvation energy must be included, and that nonelectrostatic interactions between ions must be accounted for. 

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