Activity coefficients number

Concentration and purity can both be traced to the minimum work of separation, W, where Tq is the sink temperature Ai is the number of moles of a species present in the feed x = and y is an activity coefficient. The value of Wprovides a target that is easily calculated and approachable in... 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

In liquid metal solutions Z is normally of the order of 10, and so this equation gives values of Ks(a+B) which are close to that predicted by the random solution equation. But if it is assumed that the solute atom, for example oxygen, has a significantly lower co-ordination number of metallic atoms than is found in the bulk of die alloy, dieii Z in the ratio of the activity coefficients of die solutes in the quasi-chemical equation above must be correspondingly decreased to the appropriate value. For example, Jacobs and Alcock (1972) showed that much of the experimental data for oxygen solutions in biiiaty liquid metal alloys could be accounted for by the assumption that die oxygen atom is four co-ordinated in diese solutions. 

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. 

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. 

As an example, take the molecule aminoazobenzene, one of the solutes listed in Table 39. When colorimetric measurements were made at room temperature on very dilute aqueous solutions of HC1, containing a trace of this substance, it was found that neutral molecules and (BH)+ ions were present in equal numbers when the concentration of the HCl was 0.0016 molal.1 At this low concentration the activity coefficient of the HCl is very near unity, and we may use (216) to find how far the vacant proton level provided by the aminoazobenzene molecule in aque-... 

A number of techniques are employed to determine activities or activity coefficients, depending upon the nature and type of the system. Often, procedures are used that are very specific for the system being studied. We will describe several commonly encountered examples. 

Note that a number of complicating factors have been left out for clarity For instance, in the EMF equation, activities instead of concentrations should be used. Activities are related to concentrations by a multiplicative activity coefficient that itself is sensitive to the concentrations of all ions in the solution. The reference electrode necessary to close the circuit also generates a (diffusion) potential that is a complex function of activities and ion mobilities. Furthermore, the slope S of the electrode function is an experimentally determined parameter subject to error. The essential point, though, is that the DVM-clipped voltages appear in the exponent and that cheap equipment extracts a heavy price in terms of accuracy and precision (viz. quantization noise such an instrument typically displays the result in a 1 mV, 0.1 mV, 0.01 mV, or 0.001 mV format a two-decimal instrument clips a 345.678. .. mV result to 345.67 mV, that is it does not round up ... 78 to ... 8 ). 

Figure 7.4 shows such functions for binary solutions of a number of strong electrolytes and for the purposes of comparison, for solutions of certain nonelectrolytes (/ ). We can see that in electrolyte solutions the values of the activity coefficients vary within much wider limits than in solutions of nonelectrolytes. In dilute electrolyte solutions the values of/+ always decrease with increasing concentration. For... 

Thermodynamic models are widely used for the calculation of equilibrium and thermophysical properties of fluid mixtures. Two types of such models will be examined cubic equations of state and activity coefficient models. In this chapter cubic equations of state models are used. Volumetric equations of state (EoS) are employed for the calculation of fluid phase equilibrium and thermophysical properties required in the design of processes involving non-ideal fluid mixtures in the oil and gas and chemical industries. It is well known that the introduction of empirical parameters in equation of state mixing rules enhances the ability of a given EoS as a tool for process design although the number of interaction parameters should be as small as possible. In general, the phase equilibrium calculations with an EoS are very sensitive to the values of the binary interaction parameters. 

In many drug solutions, it is necessary to use buffer salts in order to maintain the formulation at the optimum pH. These buffer salts can affect the rate of drug degradation in a number of ways. First, a primary salt effect results because of the effect salts have on the activity coefficient of the reactants. At relatively low ionic strengths, the rate constant, k, is related to the ionic strength, p, according to... 

Activity ax is termed the rational activity and coefficient yx is the rational activity coefficient This activity is not directly given by the ratio of the fugacities, as it is for gases, but appears nonetheless to be the best means from a thermodynamic point of view for description of the behaviour of real solutions. The rational activity corresponds to the mole fraction for ideal solutions (hence the subscript x). Both ax and yx are dimensionless numbers. 

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

A number of authors have suggested various mixing rules, according to which the quantity a could be calculated for a measured electrolyte in a mixture, starting from the known individual parameters of the single electrolytes and the known composition of the solution. However, none of the proposed mixing relationships has found broad application. Thus, the question about the dependence of the mean activity coefficients of the individual electrolytes on the relative contents of the various electrolytic components was solved in a different way. 

Potentiometry is used in the determination of various physicochemical quantities and for quantitative analysis based on measurements of the EMF of galvanic cells. By means of the potentiometric method it is possible to determine activity coefficients, pH values, dissociation constants and solubility products, the standard affinities of chemical reactions, in simple cases transport numbers, etc. In analytical chemistry, potentiometry is used for titrations or for direct determination of ion activities. 

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. 

Given a prediction of the liquid-phase activity coefficients, from say the NRTL or UNIQUAC equations, then Equations 4.69 and 4.70 can be solved simultaneously for x and x . There are a number of solutions to these equations, including a trivial solution corresponding with x[ = x[. For a solution to be meaningful ... 

Studies of the reaction between various substituted benzenes and nitric acid, which can take place in a number of different acid systems, have been reported in an extensive series of papers by the Marziano group, using correlations with the Me activity coefficient function. This reaction is a two-stage process,... 

Equation 8.2 is notable in that it predicts a species activity coefficient using only two numbers (z/ and di) to account for the species properties and a single value... 

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