Activity of the species

The activity a, of a species i is expressed as a function of the nature of the species under discussion. It is a dimensionless value. 

In the case of an ideal solid or liqitid solution, the activity of the compound belonging to that solution is expressed by  

in a solution, the compound is not in a single phase, its activity a, is expressed by  

In the case of a dissolved species (in low concentration), the activity is normally expressed by  

When the concentration of the compound in its phase is low (a solute in a solvent in the case of a liquid solution), its activity coefficient y, is near to 1. This means that the activity becomes equal to the ratio of its concentration to the reference concentration. For an electrolyte, as long as the concentrations are greater than 0.05 mol/L, the expression as a function of the concentrations involves too high a degree of approximation. Therefore we need to take account of the activity coefficient. 

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Experimentally deterrnined equiUbrium constants are usually calculated from concentrations rather than from the activities of the species involved. Thermodynamic constants, based on ion activities, require activity coefficients. Because of the inadequacy of present theory for either calculating or determining activity coefficients for the compHcated ionic stmctures involved, the relatively few known thermodynamic constants have usually been obtained by extrapolation of results to infinite dilution. The constants based on concentration have usually been deterrnined in dilute solution in the presence of excess inert ions to maintain constant ionic strength. Thus concentration constants are accurate only under conditions reasonably close to those used for their deterrnination. Beyond these conditions, concentration constants may be useful in estimating probable effects and relative behaviors, and chelation process designers need to make allowances for these differences in conditions. 

Thus the tendency for an electrochemical reaction at a metal/solution interface to proceed in a given direction may be defined in terms of the relative values of the actual electrode potential E (experimentally determined and expressed with reference to the S.H.E.) and the reversible or equilibrium potential E, (calculated from E and the activities of the species involved in the equilibrium). 

Previous Considerations have been confined to the effect of pressure and concentration upon coverage, but in an electrochemical equilibrium the activity and chemical potentials of the species adsorbing at the interface will also be a function of the potential difference A4>. For a solution containing unit activity of the species the effective pressure of the species at the interface is given by... 

Electrodes such as Cu VCu which are reversible with respect to the ions of the metal phase, are referred to as electrodes of the first kind, whereas electrodes such as Ag/AgCl, Cl" that are based on a sparingly soluble salt in equilibrium with its saturated solution are referred to as electrodes of the second kind. All reference electrodes must have reproducible potentials that are defined by the activity of the species involved in the equilibrium and the potential must remain constant during, and subsequent to, the passage of small quantities of charge during the measurement of another potential. 

Nemst Equation the thermodynamic relationship between the equilibrium potential of an electrochemical reaction and the activities of the species involved in that reaction. 

The rates increase up to a maximum at about 90 wt. % sulphuric acid (this point varies slightly according to the aromatic reactivity) and the increase with increasing acid concentration is consistent with the increase in the concentration of nitronium ions. The occurrence of a maximum indicates an opposing factor and is thought42 to be partly due to protonation of the aromatic (most of the measured compounds contain the group >X=0) but since it also occurs for PhNMe3, medium effects must be involved, i.e. the activities of the species present varies, whilst the concentrations remain the same. The kinetic equation for reaction of nitronium ion with an aromatic is... 

The recent discovery that a chiral phosphine ligand in a platinum(II) complex can give rise to a catalytic asymmetric hydrosilation of prochiral olefins seems to prove that a phosphine ligand can be included in the coordination sphere of platinum in an active catalytic species, but that when a phosphine ligand is so included, the activity of the species is reduced by several orders of magnitude. 

Smith (1996) summarized data on the spontaneous methemoglobin reductase activity of mammalian erythrocytes. Using nitrated RBCs with glucose as a substrate, the data reflect the ratio of the activity of the species to the activity in human RBCs. Activity in rat cells and human cells ranged from 1.3 to 5.0. Activity in cells of the cat and dog was similar to that in human cells, and that of the rabbit was 3.3 to 7.5 times greater. Most studies show that the spontaneous methemoglobin reductase activity of human erythrocytes is within an order of magnitude of that of other mammals (Smith 1996). 

Measurement of the potential of a galvanic cell, usually at zero current cell potential governed by the potential of an indicator electrode which responds to changes in the activity of the species of interest. 

This is a method involving a two-compartment cell with a salt bridge connection and having two identical indicator electrodes. The sample solution is placed in one compartment and a blank solution having the same total ionic strength in the other. Increments of a standard solution of the species to be determined are added to the blank compartment until the cell potential is zero. At this point, the activities of the species of interest in each compartment are equal and that of the sample solution can therefore be calculated. A concentrated standard solution should be used to minimize dilution errors. This method is particularly useful for the determination of trace amounts or where no suitable titrant can be found. 

It is practically impossible to measure 7 for solid electrodes. However, in some applications one needs only the change in 7 with certain parameters. For example, for the determination of the surface excess of a neutral organic species, one requires the change in the interfacial tension with the activity of the species. This can be measured if there is a reference potential 4>r at which the species is not adsorbed the change in the interfacial tension is then referred to this potential. One proceeds in the following way [2] ... 

Analyses of the defect chemistry and thermodynamics of non-stoichiometric phases that are predominately ionic in nature (i.e. halides and oxides) are most often made using quasi-chemical reactions. The concentrations of the point defects are considered to be low, and defect-defect interactions as such are most often disregarded, although defect clusters often are incorporated. The resulting mass action equations give the relationship between the concentrations of point defects and partial pressure or chemical activity of the species involved in the defect reactions. 

The equilibrium concentration (activity) of the species H+, OH", Ca2+, HCO3, C03" and C02(aq) are known for a given pco2- In addition to the four equilibria (Eq. 3.12 and footnote) the electroneutrality (charge balance) condition... 

In general, the formulation of the problem of vapor-liquid equilibria in these systems is not difficult. One has the mass balances, dissociation equilibria in the solution, the equation of electroneutrality and the expressions for the vapor-liquid equilibrium of each molecular species (equality of activities). The result is a system of non-linear equations which must be solved. The main thermodynamic problem is the relation of the activities of the species to be measurable properties, such as pressure and composition. In order to do this a model is needed and the parameters in the model are usually obtained from experimental data on the mixtures involved. Calculations of this type are well-known in geological systems O) where the vapor-liquid equilibria are usually neglected. 

A large number of publications deal with the construction and interpretation of potential -pH (Pourbaix) diagrams, and some of these have been included in Table HJ. Most of these studies avoid the question of activity coefficients because the stability fields are calculated for arbitrarily specified activities of the species in solution. 

Assume for the moment that there is a single irreversible reaction. Let be a progress variable describing the extent of reaction CKE 1. As Ej increases in infinitesimal increments d , the solution s analytical concentrations are perturbed and the activities of the species in solution change. Thus for each solute species sj, aj is a function of . 

The product of the molar concentrations (or, more accurately, the activities) of the species produced as a result of autoprotolysis. The autoprotolysis constant for water is K, equal to [H30+][0H ], or 1.0 x IQ i at 25°C. It is a temperature-dependent constant, increasing with... 

For the case in which phase II in Fig. 3 is a solid, it is not yet clear how the activities of the species Ox, Red, and C+ in the solid have to be defined on a strict thermodynamic basis, and how they could be determined. No experiments are known that would lead to a separation of the free energies of the equilibria la and Ib in the case of solids. When phase II is a solution phase, the activities of Ox, Red, and C+ are in principle accessible however, in that case also, it remains the problem that an extrather-modynamic assumption is necessary for quantifying the free energy of ion transfer between the liquid phases II and III. 

Furthermore, the equilibrium constant is also related to the equilibrium activities of the species involved. For convenience, the activities are often replaced by concentrations to yield the more practical expression... 

According to Nernst s equation, there should be linear relationship between the equilibrium potential of the metal/metal-ion electrode (M/M2+) and the logarithm of the concentration of 1VF+ ions [Eq. (5.13)]. This linear relationship was experimentally observed for low concentration of the solute MA, for instance, 0.01 mol/L and lower. For higher concentrations a deviation from linearity was observed, see, for example, Figure 5.12. The deviation from linearity is due to ion-ion interactions. In the example in Figure 5.12, the ion-ion interactions include interaction of the hydrated Ag+ ions with one another and with NO 3 ions. The linear relationship between the equilibrium potential E and the log of concentration is obtained if the square brackets in Eq. (5.13) signify the activity of species within those brackets. The activity of the species i is defined by the equation... 

Here asx is the activity of the bound species and ax and as are the activities of the species in the sample and of the binding site in the sensor, respectively. For the purpose of this discussion, the binding site can be thought of as a defined but separate component of the selective layer, such as in heterogeneous selective layers, or it may be a specific part of the uniform matrix, as in homogeneous selective layers. (More on the origins of selectivity are discussed later.) The free energy of interaction for reaction depicted in (1.1) is... 

Equation 2.16 shows that potentiometry is a valuable method for the determination of equilibrium constants, ffowever, it should be borne in mind that the system should be in equilibrium. Some other conditions, which are described below, also need to be fulhlled for use of potentiometry in any application. The basic measurement system must include an indicator electrode that is capable of monitoring the activity of the species of interest, and a reference electrode that gives a constant, known half-cell potential to which the measured indicator electrode potential can be referred. The voltage resulting from the combination of these two electrodes must be measured in a manner that minimises the amount of current drawn by the measuring system. This condition includes that the impedance of the measuring device should be much higher than that of the electrode. 

Therefore, the primary electrode reaction includes the sensed species. Such electrodes give a direct response according to the Nernst equation for the logarithm of the activity of the species. 

The individual rates vq and v i are affected by temperature, pressure, and the concentrations of the species in Eq. (5.36). At equilibrium, the left side of Eq. (5.37) will disappear and v]eq/v ]eq where eq is the equilibrium condition will be a function of temperature, pressure, and the equilibrium composition of the exchanger and aqueous solution phase. Because the activities of the species in Eq. (5.36) have an identical dependence, vleq/v leq depends on temperature, pressure, and the species activities (Denbigh, 1981). But this same relationship applies to the quotient of the right and left sides of Eq. (5.38) for the determination of the exchange equilibrium constant (Ksx) for the reaction in Eq. (5.36), which can be expressed as,... 

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