Activity scales

Figure 5.5. The Scale Selection Page. A extreme values in data set B currently active scale (= default scale of extremes +/ - 5% when first opened) C tic-mark spacing, initially set by default.

All equilibrium constants in the present discussion are based on the concentration (not activity) scale. This is a perfectly acceptable thermodynamic scale, provided the ionic strength of the solvent medium is kept fked at a reference level (therefore, sufficiently higher than the concentration of the species assayed). This is known as the constant ionic medium thermodynamic state. Most modern results are determined at 25 °C in a 0.15 M KCl solution. If the ionic strength is changed, the ionization constant may be affected. For example, at 25 °C and 0.0 M ionic strength, the pXj of acetic acid is 4.76, but at ionic strength 0.15 M, the value is 4.55 [24]. 

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. 

At least a partial solution to this problem is attained by the conventional activity scale method [5, 6, 7, 9, 10, 11]. This procedure was first used by Bates and Guggenheim [8] when formulating the operational definition of pH (see [86a], chapter 1), on the basis of which the National Bureau of Standards in the USA developed a method for determining conventional hydrogen ion activities. The basic assumption is the use of the Debye-Hiickel relationship for the individual activity of chloride ions ... 

The individual activity coefficients calculated from (4.12), suitable for calibration of ISEs for chloride ions, the alkali metal and alkaline earth ions, are given in tables 4.1 and 4.2. Ion activity scales have also been proposed for KF [141], choline chloride [98], for mixtures of electrolytes simulating the composition of the serum and other biological fluids (at 37 °C) [106,107], for alkali metal chlorides in solutions of bovine serum albumine [132] and for mixtures of electrolytes analogous to seawater [140]. 

ISEs respond to the activities of ions. To prepare activity standards, the individual activity coefficients of the pertinent ions must be known. However, individual activity coefficients cannot be determined accurately and can only be calculated approximately. For a discussion of conventional activity scales see p. 73-6. 

When using standard solutions prepared on the basis of activities calculated from these activity scales, and provided there is no interfierence and that the prelogarithmic term in the E versus log a dependence is Nernstian or at least accurately known and constant, the sample activity can be determined from the ISE potentials obtained in the sample and in a standard solution (see (4.13), p. 74-6). 

The infinite dilution activity scale is useful for ionic equilibria in fresh waters, but for equilibria in sea water one gains precision by applying an ionic medium activity scale. Measuring pH in sea water gives less information than total alkalinity and total carbonate. Calculations on redox equilibria are simplified by introducing the master variable pE -----log e. ... 

The concentrations are then used instead of the activities in various-thermodynamic expressions (e.g., the equilibrium law, and Nernst s equation for the e.m.f.). Some physical chemists are suspicious of this method. However, it is just as thermodynamic as the traditional one, the only difference being that another activity scale is used. 

Here, is a constant, which defines the activity scale, and yA is the activity coefficient. For the moment we will disregard the units of concentration (mole fraction, moles per kg. solution, moles per kg. water). Changing to a new activity scale means that /xA is shifted by a constant and that all activities are multiplied by the same factor. 

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. 

The "ionic medium activity scale, on the other hand, is so defined that the activity coefficient, yA = A / [A] approaches unity as the solution approaches the pure solvent (in this case the ionic medium)—Le., when the concentrations go toward zero for all other species than water and the medium ions. 

In most cases a value for the overall activity of enzyme is not very interesting. Much more important are both the specific activity, scaled to the mass of catalyst, and the volumetric activity, based on the activity per unit volume ... 

The numerical value of the activity of j at the Henrian standard state is 1 on the Henrian activity scale, but y° on the Raoultian activity scale. 

Ionic strength ranges are applicable for the equations Yi yL where and y, are the activity coefficients on the mole fraction and molarity concentration/activity scales, respectively. The parameter A depends on T(K) according to the equation A = 1.92 x 106 (sT) 3/2 where e is the temperature-dependent dielectric constant of water B = 50.3 (eT) 1,2. For water at 298 K (25°C), A = 0.51 and B = 0.33. Applicable ionic strength range obtained from Stumm and Morgan (1981). 

A well known example is the establishment of solvent-independent ion activity scales e.g. pH). Furthermore, in electroanalytical chemistry and preparative chemistry it would be favorable not only to be able to predict the behavior of certain systems in a new solvent from the knowledge in some other solvent (most often water), but in advance also to use single ion properties to prepare mixed solvent media in which each ion interacts with the medium in a manner aspired. 

FIGURE 35.1. Representative profiles of the activity of the AChE molecular forms in soleus, EDL, and hemidiaphragm muscles. Profiles at the top of each column are from untreated muscles followed by profiles of activity of AChE molecular forms of muscles 24 h and 7 days, respectively, after receiving an acute dose of soman (100 pg/kg, s.c.). The AChE activity scale is in arbitrary units based on the pmole substrate hydrolyzed/min by the enzyme activity in each fraction. The sedimentation values of the AChE molecular forms are given in the profiles of untreated muscles above the associated peaks. Sedimentation values were determined by the location of the added sedimentation standards, P-galactosidase (16.0 S), catalase (11.1 S), and alkaline phosphatase (6.1 S), following velocity sedimentation of the gradients. 

Despite the recognition that GDH may be more important in its catabohe role, GDH activities have been difficult to correlate with nitrogen excretion because of the compheations of size-scaling GDH activities scale differendy with body size than do N-excretion rates (see Berges et al., 1993). Assays are also potentially complicated by the presence of assimdatory GDH in other organisms in samples. 

As equation 23 illustrates, a change in the activity scale convention merely changes kf. In an ideal constant ionic medium, equation 23 becomes... 

Both activity scales are thermodynamically equally well defined. In constant ionic medium, activity (= concentration) can frequently be determined by means of emf methods. 

Activity coefficients defined within the infinite dilution activity scale cannot be formulated theoretically for the ionic medium of seawater. Since the oceans contain an ionic medium of practically constant composition, the ionic medium activity scale might be used advantageously in studying acid-base and other equilibria in seawater (see also Appendix 6.2 in Chapter 6). 

Equilibrium constants are either or are defined in terms of the constant ionic medium activity scale. 

Constants based on activities (rather than concentrations), the activity scale being based on the infinite dilution reference state. 

Equilibrium constants in the form of concentration quotients are just as thermodynamically valid as the traditional thermodynamic constants, the main difference being the choice of activity scale and reference state. 

The pH values so measured are on a different activity scale they may be used to characterize and compare seawater samples and so serve as an index of acid-base balance and speciation. ... 

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