Ionic activity coefficient, conventional

The activity of any ion, a = 7m, where y is the activity coefficient and m is the molaHty (mol solute/kg solvent). Because it is not possible to measure individual ionic activities, a mean ionic activity coefficient, 7, is used to define the activities of all ions in a solution. The convention used in most of the Hterature to report the mean ionic activity coefficients for sulfuric acid is based on the assumption that the acid dissociates completely into hydrogen and sulfate ions. This assumption leads to the foUowing formula for the activity of sulfuric acid. 

At finite concentrations the effect of the solvent on the ion-ion interactions are superimposed on the solvent effect discussed above for infinite dilution. The former effect can be expressed as the mean ionic activity coefficient, y again, expressed conventionally on the molal scale, relative to infinite dilution in the solvent in question, which in dilute solutions, where the extended Debye-Huckel expression is deemed to hold, is ... 

Throughout this section the hydronium ion and hydroxide ion concentrations appear in rate equations. For convenience these are written [H ] and [OH ]. Usually, of course, these quantities have been estimated from a measured pH, so they are conventional activities rather than concentrations. However, our present concern is with the formal analysis of rate equations, and we can conveniently assume that activity coefficients are unity or are at least constant. The basic experimental information is k, the pseudo-first-order rate constant, as a function of pH. Within a senes of such measurements the ionic strength should be held constant. If the pH is maintained constant with a buffer, k should be measured at more than one buffer concentration (but at constant pH) to see if the buffer affects the rate. If such a dependence is observed, the rate constant should be measured at several buffer concentrations and extrapolated to zero buffer to give the correct k for that pH. 

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. 

For the above reasons, the IFCC recommendations on activity coefficients [19] and the measurement of and conventions for reporting sodium and potassium [21] and chlorides [25] by ISEs were developed. At the core of these recommendations is the concept of the adjusted active substance concentration (mmol/L), as well as a traceable way to remove the discrepancy between direct and indirect determinations of these electrolytes in normal sera. Extensive studies of sodium and potassium binding to inorganic ligands and proteins, water binding to proteins, liquid-junction effects and the influence of ionic strength have demonstrated that the bias between sodium and potassium reports obtained from an average ISE-based commercial... 

The application of COSMO-RS to the calculation of infinite-dilution activity coefficients in ionic liquids was surprisingly successful. As shown in Fig. 8.5, the activity coefficients of neutral compounds in ionic liquids are very well described. This was achieved without any special adjustment of COSMO-RS, which was developed and parameterized for neutral solvents, just by describing the ionic liquid as a 50 50 mixture of anions and cations. We only needed to take into account the convention of chemical engineers of counting a pair of an anion and a cation as... 

To obtain the pH, it is necessary to evaluate the activity coefficient of the chloride ion. So the acidity function is determined for at least three different molalities mci of added alkali chloride. In a subsequent step, the value of the acidity function at zero chloride molality, lg(flHyci)°, is determined by linear extrapolation. The activity of chloride is immeasurable. The activity coefficient of the chloride ion at zero chloride molality, yci, is calculated using the Bates-Guggenheim convention (Eq. 5) which is based on the Debye-Hiickel theory. The convention assumes that the product of constant B and ion size parameter a are equal to 1.5 (kg mol1)1/2 in a temperature range 5 to 50 °C and in all selected buffers at low ionic strength (I < 0.1 mol kg-1). 

In the case of an - electrolyte dissociating in solution as Aj,+ Bj, < is+Az+ + z/ Bz where v+z+ = v z to ensure electroneutrality, and the total number of particles formed by each molecule is v = v+ + z/, then the only activity that can be measured is that of the complete species, and the individual ions cannot be assigned meaningful chemical potentials. Under these circumstances, a mean activity coefficient is defined through the equation yv = y++ yvs. Since individual ionic chemical potentials are not measurable, it has become conventional to assign to the chemical potential of the hydrogen ion under standard conditions the value of zero, allowing relative chemical potentials for all other ions to be formulated. 

The mean ion activity coefficient values can be obtained from experiments where the effect of electrolyte concentration on the A sp value for a salt is determined. The mean values are then compared with those for KCl under the same solution conditions. The single-ion activity coefficient for Ca " " can then be computed if an assumption is made about the individual values for and Cl. These ions have the same magnitude of charge and similar electronic configuration, ionic radii, and ionic mobilities. On the basis of these properties, the Macinnes convention (1919) states that... 

Bates and Alfenar (23) proposed that the activity of the chloride ion in NaCl solutions be taken as the activity standard. Using this chloride convention together with the published values of mean activity coefficients, the activity of any simple ionic species can be estimated. The equation used to estimate values of yNo3 and thus aNo3 for nitric acid solutions is... 

The Ionic Medium Scale This convention can be applied to solutions that contain a swamping concentration of inert electrolyte in order to maintiiin a constant ionic medium. The activity coefficient, f = A /[A], beconries unity as the solution approaches the pure ionic medium, that is, when all concentrations other than the medium ions approach zero ... 

Under certain conditions regarded as ideal, j is probably actually close to zero. This should be the case when solution X matches closely the primary standard solutions S in pH, composition, and ionic strength (which must not exceed 0.1). Then pH(X) doubtless approaches —log (mHyn), where mn is the molality (mol/kg of water) of hydrogen ion and 7h is its conventional activity coefficient on the numerical scale defined by the convention adopted for the assignment of values to pH(S). When, as in seawater, these conditions do not prevail, the meaning of the experimental pH(X) in terms of concentrations and activities becomes unclear. 

The electrochemical cell is completed by the external reference electrode, an Ag/AgCl or calomel electrode, which is in contact with the specimen by a liquid/liquid junction or salt bridge of KCl or sodium formate. The potential difference across the cell is logarithmically related to the activity of free calcium ions in the sample by Nernsfs equation. By convention, free calcium is converted from activity to concentration with its activity coefficient, which is itself dependent on ionic strength. 

In order for us to have flexibility in our modeling of natural water chemistry we need a way to obtain individual ion activity coefficients from mean values. To do so requires that we make an assumption, called the Macinnes convention (Macinnes 1919), which states = 7c - The convention is based on the observation that and Cr ions are of the same charge and nearly the same size, have similar electron structures (inert gas), and similar ionic mobilities. In support of this assumption, tracer diffusion coefficients, D°, of K+ and Cl" at infinite dilution are nearly equal at 19.6 and 20.3 X 10" cmVs (Lerman 1979). Also, limiting equivalent conductances, A°, of and Cl" are comparable at 73.50 and 76.35 cmV(ohm) (equiv.) at 25°C (Robinson and Stokes 1970),... 

The Macinnes convention leads to = Tci = 7 kci, We can now compute individual ion activity coefficients from their mean values measured in solutions of strong electrolytes using y Kci values as our starting point. (In the ideal strong electrolyte, cations and anions are unassociated with each other and thus do not form complexes [see Chap. 3].) It is important to remember that all such calculations must be done with y values for KCl and other salts measured at the same ionic strength, which is not the same molality except for monovalent-monovalent salts. 

The individual-ion activity coefficients for the free ions were based on the Macinnis (18) convention, which defines the activity of Cl to be equal to the mean activity coefficient of KCl in a KCl solution of equivalent ionic strength. From this starting point, individual-ion activity coefficients for the free ions of other elements were derived from single-salt solutions. The method of Millero and Schreiber (14) was used to calculate the individual-ion, activity-coefficient parameters (Equation 5) from the parameters given by Pitzer (19). However, several different sets of salts could be used to derive the individual-ion activity coefficient for a free ion. For example, the individual-ion activity coefficient for OH could be calculated using mean activity-coefficient data for KOH and KCl, or from CsOH, CsCl, and KCl, and so forth. 

PHRQPITZ offers two scaling conventions based on (9). In the first case no scaling is performed and individual-ion activity coefficients are computed directly from the equations of (9). In the second case, all individual-ion activity coefficients calculated from the equations of (9) are scaled according to the Macinnes convention (37). In this case the activity coefficient of CL is defined to be equal to the mean-activity coefficient of KCl in a KCl solution of equivalent ionic strength, 7gf(Mac)=7 KCi- The scaling factor for the ith ion is computed from the term (7ci /T and is multiplied through all other calculated individual-ion activity coefficients (9). That is... 

In principle, the conventions used for nonelectrolyte solutions developed in Chap. 11 could be employed for electrolyte solutions which are subject to the condition of electroneutrality. Agreement with experimental data could be obtained by choosing the molecular weight to be some fraction of the formula weight. However, these conventions generally lead to activity coefficients which are rapidly varying functions of composition. In order to avoid this, we formally define chemical potentials and activity coefficients for ionic components. The definition of chemical potentials for ionic components does not have operational significance since their concentrations cannot be varied independently. 

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