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Potential of Dilute Solutions

Since the volume fraction of the solute 4 2 is very small in dilute macromolecular solutions, the expression ln(l - 2) can be expanded in a series [Pg.219]

Equation (6-45) contains the excess chemical potential instead of the chemical potential itself because the ideal term X X 2 has been omitted. This omission was necessary because the considerations have to be restricted to a small volume of solution where the segment distribution is uniform enough so that the lattice theory can be applied. Although in this equation the quantity (xo 0 ) is derived from the enthalpy of mixing and the factor 0.5 from the entropy of mixing, it is convenient to replace this combination of terms by another with a new enthalpy parameter k and a new entropy parameter [Pg.219]

The chemical potential gives the partial molar Gibbs energy of dilution. The partial molar dilution enthalpy and the partial molar dilution entropy are given by [Pg.219]

The combination of Equations (6-34), (6-46), and (6-48) thus gives an expression for the temperature dependence of the Flory-Huggins interaction parameter  [Pg.219]

The expression (xo — o) takes on the value of 0.5 for X2IX 0 in the theta state. It is smaller than 0.5 in good solvents, since then T 0. [Pg.219]


Ballantyne, B. and Swanston, D.W. The Irritant potential of dilute solutions of o-chlorobenzylldene malononltrlle (CS) on the eye and tongue. Acta Pharmacol. Toxicol. 32 266-277,... [Pg.167]

However, although viscosity is the most important parameter influencing the condire-tance equations of this type are doubtful. The mean-force potentials of dilute solutions are based on approximations which cannot really be corrected for by viscosity functions. A noteworthy extension is given in Ref. [Pg.61]

The chemical potentials of dilute solutions may be expressed in terms of molality (moles of solute per kilogram of solvent) or molarities Ck (moles of solute per liter of solution) instead of mole fractions X/t. In electrochemistry it is more common to use molality ntk. For dilute solutions, since Xk = (A jfc/A soivent)> we have the following conversion formulas for the different units... [Pg.214]

G. D. J. Phillies, /. Chem. Phys., 60, 2721 (1974). Excess Chemical Potential of Dilute Solutions of Spherical Polyelectrolytes. [Pg.349]

As seen from Eq. (130) an activity coefficient may deviate significantly from unity at higher salt concentrations. The activity coefficient can therefore also be used as a measure of the deviation of the salt solution from a thermodynamically ideal solution. If the chemical potential of a solute in a (pressure-dependent) standard state of infinite dilution is /x°, we find the standard partial molar volume from... [Pg.132]

We can show that if the solute obeys Henry s law in very dilute solutions, the solvent follows Raoult s law in the same solutions. Let us start from the Gibbs-Duhem Equation (9.34), which relates changes in the chemical potential of the solute to changes in the chemical potential of the solvent that is, for a two-component system... [Pg.341]

In the preceding chapters we considered Raoult s law and Henry s law, which are laws that describe the thermodynamic behavior of dilute solutions of nonelectrolytes these laws are strictly valid only in the limit of infinite dilution. They led to a simple linear dependence of the chemical potential on the logarithm of the mole fraction of solvent and solute, as in Equations (14.6) (Raoult s law) and (15.5) (Heiuy s law) or on the logarithm of the molality of the solute, as in Equation (15.11) (Hemy s law). These equations are of the same form as the equation derived for the dependence of the chemical potential of an ideal gas on the pressure [Equation (10.15)]. [Pg.357]

Although Pb tends to - °o as Xb tends to 0 (and In Xb also tends to - °o), the difference on the right-hand side of Eq. (2.18) tends to the finite quantity pi, the standard chemical potential of B. At infinite dilution (practically, at high dilution) of B in the solvent A, particles (molecules, ions) of B have in their surroundings only molecules of A, but not other particles of B, with which to interact. Their surroundings are thus a constant environment of A, independent of the actual concentration of B or of the eventual presence of other solutes, C, D, all at high dilution. The standard chemical potential of the solute in an ideal dilute solution thus describes the solute-solvent interactions exclusively. [Pg.56]

Consider now two practically immiscible solvents that form two phases, designated by and ". Let the solute B form a dilute ideal solution in each, so that Eq. (2.19) applies in each phase. When these two hquid phases are brought into contact, the concentrations (mole fractions) of the solute adjust by mass transfer between the phases until equilibrium is established and the chemical potential of the solute is the same in the two phases ... [Pg.58]

So far, we have used the pure liquid compound as reference state for describing the thermodynamics of transfer processes between different media (Chapter 3). When treating reactions of several different chemical species in one medium (e.g., water) it is, however, much more convenient to use the infinite dilution state in that medium as the reference state for the solutes. Hence, for acid-base reactions in aqueous solutions, in analogy to Eq. 3-34, we may express the chemical potential of the solute i as ... [Pg.246]

Defect thermodynamics, as outlined in this chapter, is to a large extent thermodynamics of dilute solutions. In this situation, the theoretical calculation of individual defect energies and defect entropies can be helpful. Numerical methods for their calculation are available, see [A. R. Allnatt, A. B. Lidiard (1993)]. If point defects interact, idealized models are necessary in order to find the relations between defect concentrations and thermodynamic variables, in particular the component potentials. We have briefly discussed the ideal pair (cluster) approach and its phenomenological extension by a series expansion formalism, which corresponds to the virial coefficient expansion for gases. [Pg.41]

Thus, u.°A for the solute in Eq. (II) is the chemical potential of the solute in a hypothetical standard state in which the solute at unit concentration has the properties which it has at infinite dilution. [Pg.30]

The molar Gibbs energy of micelle formation is the Gibbs energy difference between a mole of monomers in micelles and the standard chemical potential in dilute solution ... [Pg.253]

Although I did not know about the concept of the combinatorial contribution, I recognized the need for such a correction even in the initial version of COSMO-RS [C9]. Since at that time I only had in mind the calculation of infinite-dilution partition coefficients and of vapor pressures, I only cared about a solvent-size correction in pure solvents. I thought of two different solvent-size effects influencing the chemical potential of a solute X in a solvent S. The first is quite obvious—in 1 mol of a homogeneous liquid S,... [Pg.239]

Walkley s research interests over the years have focused on the thermodynamics and statistical mechanics of dilute solutions,248 intermolecular potential calculations, and Monte Carlo calculations. [Pg.270]

When the concentration of a multicomponent system is expressed in terms of the molalities of the solutes, the expression for the chemical potential of the individual solutes and for the solvent are somewhat different. For dilute solutions the molality of a solute is approximately proportional to its mole fraction. (The molality, m, is the number of moles of solute per kilogram of solvent. When two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be clearly stated.) In conformity with Equation (8.68), we then express the chemical potential of a solute in a solution at a given temperature and pressure as... [Pg.182]

When the excess chemical potential of the solute in the liquid phase is required as a function of the mole fraction at the constant temperature T0 and pressure P, an integration of the Gibbs-Duhem equation must be used. For this the infinitely dilute solution of the solute in the solvent must be... [Pg.256]

As shown in Example 1, the chemical potential of a solute can be of a more complicated form than given by Eqs. (43)-(45), even though the solution shows ideally dilute behavior. This can result from a transformation of the substance when it dissolves in the solution. [Pg.236]

Liquid-phase extraction is a procedure by which some fraction of a solute is taken out of solution by shaking the solution with a different solvent (in which the solute usually has greater solubility). The analysis of this process assumes that the shaking is sufficient so that equilibrium is established for the solute, i, between the two solutions. At equilibrium, the chemical potentials of the solute in the two solutions are equal. Assuming ideally dilute solutions, we can write... [Pg.244]

Transport numbers8 can be used to calculate the junction potentials from Eq. (5.10). Table 5.1 gives the experimental Ece l values and the values of E, calculated from Eqs. (5.2), (5.8), and (5.10). The reasonable agreement indicates that junction potentials for dilute solutions of 1 1 electrolytes calculated from Eq. (5.3) or (5.10) are credible. [Pg.175]

In this case the unitary value of the chemical potential of solute substance i can be estimated, as mentioned above, by extrapolating the chemical potential of dilute constituent i to xt = 1 from the dilute concentration range in which the linear relation of Eq. 5.22 holds. [Pg.51]

Figure 9.8. Schematic of the electric double layer under two different electrolyte concentrations. Colloid migration includes the ions within the slipping plane of the colloid denotes the electric potential in dilute solution denotes the electric potential in concentrated solution (adapted from Taylor and Ashroft, 1972)... Figure 9.8. Schematic of the electric double layer under two different electrolyte concentrations. Colloid migration includes the ions within the slipping plane of the colloid denotes the electric potential in dilute solution denotes the electric potential in concentrated solution (adapted from Taylor and Ashroft, 1972)...

See other pages where Potential of Dilute Solutions is mentioned: [Pg.219]    [Pg.219]    [Pg.1238]    [Pg.219]    [Pg.219]    [Pg.1238]    [Pg.63]    [Pg.500]    [Pg.431]    [Pg.309]    [Pg.29]    [Pg.363]    [Pg.35]    [Pg.175]    [Pg.34]    [Pg.381]    [Pg.527]    [Pg.300]    [Pg.253]    [Pg.398]    [Pg.262]    [Pg.300]    [Pg.196]    [Pg.129]    [Pg.129]   


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