Solute defining activity

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

There are several different scales 011 which the activity of a solute may be defined.1 In thermodynamic expressions for a solute in a non-ideal solution the activity on the molality scale plays the same part that is played by the molality of a solute in an ideal solution. Since the activity is expressed in the same units as the molality, the ratio of the activity to the molality—the activity coefficient—is a pure number whose value is independent of these units it is also indopendont of the particular b.q.s. that has been adopted. Thus the numerical values of all activities and molalities would change in the same ratio, if at any time a new choice were made for the b.q.s. 

When a solute is added to an acidic solvent it may become protonated by the solvent. If the solvent is water and the concentration of solute is not very great, then the pH of the solution is a good measure of the proton-donating ability of the solvent. Unfortunately, this is no longer true in concentrated solutions because activity coefficients are no longer unity. A measurement of solvent acidity is needed that works in concentrated solutions and applies to mixed solvents as well. The Hammett acidity function is a measurement that is used for acidic solvents of high dielectric constant. For any solvent, including mixtures of solvents (but the proportions of the mixture must be specified), a value Hq is defined as... 

It has been emphasized repeatedly that the individual activity coefficients cannot be measured experimentally. However, these values are required for a number of purposes, e.g. for calibration of ion-selective electrodes. Thus, a conventional scale of ionic activities must be defined on the basis of suitably selected standards. In addition, this definition must be consistent with the definition of the conventional activity scale for the oxonium ion, i.e. the definition of the practical pH scale. Similarly, the individual scales for the various ions must be mutually consistent, i.e. they must satisfy the relationship between the experimentally measurable mean activity of the electrolyte and the defined activities of the cation and anion in view of Eq. (1.1.11). Thus, by using galvanic cells without transport, e.g. a sodium-ion-selective glass electrode and a Cl -selective electrode in a NaCl solution, a series of (NaCl) is obtained from which the individual ion activity aNa+ is determined on the basis of the Bates-Guggenheim convention for acr (page 37). Table 6.1 lists three such standard solutions, where pNa = -logflNa+, etc. 

The main equations used to extract thermochemical data from rate constants of reactions in solution were presented in section 3.2. Here, we illustrate the application of those equations with several examples quoted from the literature. First, however, recall that the rate constant for any elementary reaction in solution, defined in terms of concentrations, is related to the activation parameters through equations 15.1 or 15.2. 

For concentrated solutions, the activity coefficient of an electrolyte is conveniently defined as though it were a nonelectrolyte. This is a practical definition for the description of phase equilibria involving electrolytes. This new activity coefficient f. can be related to the mean ionic activity coefficient by equating expressions for the liquid-phase fugacity written in terms of each of the activity coefficients. For any 1-1 electrolyte, the relation is ... 

Reductants and oxidants are defined as electron donors and proton acceptors (Sect. 2.2.2). Because there are no free electrons, every oxidation is accompanied by a reduction and vice versa. In aqueous solutions, proton activities are defined by the pH ... 

In dilute solutions the activity of the solvent is essentially constant, so the ratio K /a may be defined to equal a new constant K, in terms of which Equation (65) becomes... 

Just as in aqueous solutions, the activity of solute i (acl) in non-aqueous solutions is related to its (molar) concentration (sj by aCii = yCiiCi, where g is the activity coefficient that is defined unity at infinite dilution. For non-ionic solutes, the activity coefficient remains near unity up to relatively high concentrations ( 1 M). However, for ionic species, it deviates from unity except in very dilute solutions. The deviation can be estimated from the Debye-Hiickel equation, -log yci = Az2 /1/2/ (1+aoBf1 2). Here, I is the ionic strength and / (moll-1), a0 is the ion size parameter... 

Equation 6-24 and the equations that follow from it apply to molal activities. However, the concentration can be substituted for activity in very dilute solution where the behavior of the dissolved molecules approximates that of the hypothetical ideal solution for which the standard state is defined. For any real solution, the activity can be expressed as the product of an activity coefficient and the concentration (Eq. 6-26). 

In treating ionic equilibria in aqueous solution, two activity scales have proved especially useful. The first is the traditional infinite dilution activity scale, which is defined in such a way that the activity coefficient yA = A /[A] approaches unity as the solution approaches pure water. One might refer to this scale as the fresh water scale. 

Allow earty termination V if lop [3 solutions are within jl.5 Angstroms RJvt.S.D. Define active site from Point v Atom Rle v Atom Number o Active site radius [TdF Detect Cavity ... 

The thermodynamics properties of an electrolytic solution are generally described by using the activities of different ionic species present in the solution. The problem of defining activities is however somewhat more complicated in electrolytic solution than in solutions of nonelectrolytes. The requirement of overall electrical neutrality in the solution prevents any increase in the charge due to negative ions. Consider the 1 1 electrolyte AB which dissociates into A+ ions and B ions in the aqueous solution. 

The original form of the Debye-Hiickel equation permits the calculation of the mean activity coefficients of strong electrolytes in solutions defined by their molarity c. Should the value of this coefficient be expressed by molality, whioh is more advantageous in electrochemistry, it will be possible in the case of a sufficiently diluted solution to substitute into the equation (V-58) for = y m (see V-41e) and for molarities of all ions the product of their molalities and the density of the solvent s wqp°, so that ... 

Since, for dilute solutions, the activity a (Chap. 10) of water is considered to be constant and very close to 1.0, and the activities of the solutes may be represented by their concentrations, we can define a practical constant, Kw, called the ionic product of water ... 

Nucleation in the atmosphere is essentially multicomponent process. However, a commonly used classical approach incapable of the quantitative treatment of multicomponent systems due to (a) excessive sensitivity to poorly defined activity coefficients, density and surface tension of multicomponent solutions (b) strong dependence of nucleation rates on thermochemistry of initial growth steps where... 

There is a simple way to avoid these problems. One can define a pH scale in a completely arbitrary manner relative to the emf of a suitable cell. One can then relate the pH on this scale to an arbitrarily defined activity of hydrogen ions, simply be setting pH = —log an+. The dissociation constants of model compounds can then be determined in terms of this arbitrary scale. This method has been used by Donovan et ai. (1959) for protein titrations in concentrated aqueous solutions of guanidine hydrochloride and of urea, and by Sage and Singer (1962) for titrations in ethylene glycol. 

As seen in 32f, the molarity of a very dilute solution is proportional to its mole fraction, and hence for such solutions the activity coefficient y., defined by Oz/c, represents the compliance with Henry s law. As in the preceding case, 7, and 7n are both unity at infinite dilution, and the values are approximately equal in dilute solutions. With increasing concentration, however, y and 7n differ, and althou the latter still indicates the adherence to Henry s law, the former, like 7m, does not. Thus, at high dilutions 7n, 7values approximating to unity, but at appreciable concenis ations the three coefficients differ the actual relationships between them will be considered in the next section. 

Equation (6.27) is frequently used in the calculation of surface adsorption in dilute solutions. For strictly regular solutions, the activity coefficient is defined as... 

For the ideal solution the activity coefficients of the constituents are unity, and for the real solutions they are defined with respect to a suitable reference state with the limitation that the temperature of the reference state must be that of the solution. We will return to the activity coefficient concept later when we discuss models for the liquid mixtures. 

The ratio of activity and mole fraction defines the activity coefficient, a = Xs7s [76]. For an ideal solution the activity is equal to the mole fraction since the activity coefficient equals unity. 

In the case of pure solids such as Ag and AgCl the chemical potential is identical to the standard chemical potential at 25°C and 1 bar pressure. For solutions, the standard state of the solute is unit activity at the same temperature and pressure. In the case of electrolytes as solutes, the activity is defined on the concentration (molarity) scale, and the standard state is the hypothetical ideal state of unit molarity for which the activity coefficient ye is unity. Under these circumstances, the activity of the solvent, which does not appear explicitly in equation (9.2.9), is also unity to a good approximation when the solvent is water. For gases the standard state is a pressure of 1 bar (10 Pa) at 25°C. In the older literature the standard pressure was 1 atm (101,325 Pa). In data compilations appearing after 1982, the standard state of 1 bar and 25°C is always used for gases [G3]. 

Many chemical experiments are carried out in aqueous solutions and it is important to be able to define activities in these circumstances. However, the standard state we have used so far—the pure liquid at one atmosphere pressure—is singularly inappropriate. We usually wish to express concentrations in molality (moles per kilogram of solvent) and for an electrolyte, such as sodium chloride, the pure-liquid state at room temperature is not a suitable reference state. 

Like ions in aqueous solutions, the chemical activities of ions solids, and of water, also vary with concentration. Over the range of solute concentrations in soil solutions, however, the activity of water changes only negligibly from that of pure water. The chemical potentials of pure solids are defined as one, because any amount of the solid fixes the equilibrium activity of that substance in the aqueous solution. The activity of the aqueous solution is therefore independent of the amount of solid present. 

For dilute solutions, the activity coefficients do not change much with concentrations, and a simple concentration-based equilibrium constant called the molar selectivity coefficient, KAB, can be defined as... 

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