Rational scale

Although the p.z.c. is difficult to determine experimentally, and although the values obtained vary with the method used, it is of fundamental significance in electrochemistry, since it provides information on adsorption of ions and molecules, i.e. if the potential is negative with respect to the p.z.c. cations will tend to be adsorbed and anions repelled, and vice versa. The p.z.c. appears to be a natural reference point for a rational scale of potentials defined by... 

The composition of a mixture need not be given in terms of the mole fractions of its components. Other scales of concentration are frequently used, in particular, when one of the components, say. A, can be designated as the solvent and the other (or others), B, (C,...) as the solute (or solutes). When the solute is an electrolyte capable of dissociation into ions (but not only for such cases), the molal scale is often employed. Here, the composition is stated in terms of the number of moles of the solute, m, per unit mass (1 kg) of the solvent. The symbol m is used to represent the molal scale (e.g., 5 m = 5 mol solute/1 kg solvent). The conversion between the molal and the rational scale (i.e., the mole fraction scale, which is related to ratios of numbers of moles [see Eq. (2.2)] proceeds according to Eqs. (2.32a) or (2.32b) (cf. Fig. 2.4) ... 

The quantity Pb is independent of the concentration scale used, being a true property of the solntion, bnt the three standard chemical potentials Pb x), PbV) Pb°°(c) are not eqnal. Conseqnently, differences between the standard chemical potentials of a solnte in the two liqnid phases employed in solvent extraction also depend on the concentration scale nsed. Thus, Pb defined in Eq. (2.23) is specific for the rational concentration scale, and does not equal corresponding quantities pertaining to the other scales. Therefore, Eq. (2.30) might be rewritten with a subscript (x), to designate the rational scale, [i.e., with Z)b(x) and Pb(x)]- Similar expressions would then be... 

Nutt D, King LA, Saulsbury W, Blakemore C. Development of a rational scale to assess the harm of drugs of potential misuse. Lancet 2007 369 1047-53. 

Figure 2.9. An estimate of the detrimental effects of some NP-rich drugs and some synthetic drugs suggests that cannahis (with its important NP THC) is less harmful than some widely used legal substances. (See Nutt D, King LA, Saulsbury W, Blakemore C. (2007). Development of a rational scale to assess the harm of drugs of potential misuse. The Lancet, 369,1047-53.)...

Fig. 3. Variation of potential at the OHP, with respect to the solution potential, with the electrode potential in the rational scale calculated from eqn, (44) with

Unlike the double layer effect on the transfer coefficient, which presents a maximum at the pzc, the double layer effect on the reaction order is zero at the pzc. Inspection of Fig. 3 shows that the derivative (9A02/9 In [O] )e adopts positive and negative values, respectively, at both sides of the pzc, so that the apparent reaction order may be smaller or larger than the true order depending on the electode potential in the rational scale. 

Fig. 1.7 Surface tension of mercury in contact with aqueous solutions of the salt named. T = 291 K. Abscissas are measured relative to a rational scale in which the potential difference between the mercury and a capillary-inactive electrolyte is arbitrarily set equal to zero at the electrocapillary maximum. Taken from [19] with permission...

The cumulative probability functions listed in Table 2.1.6 can be used to give some measure of correlation between the various criteria for orbital size. Once a particular value for P is chosen, it can be equated to each of the expresssions in turn and the resulting transcendental equation solved numerically. The p values thus obtained for P = 0.50, 0.90, 0.95, and 0.99 are tabulated in Table 2.1.7. The significant quantites are the size ratios, with the Is p value as standard, which provide a rational scale of relative orbital size based on any adopted probability criterion. As the prescribed P value approaches unity, the size ratios gradually decrease in magnitude and orbitals in the same shell tend to converge to a similar size. 

Rational potential — is the - electrode potential in a reduced scale, as referred to potential of zero charge of the same electrode material in solution of given composition. This quantity is used in studies of the electric double layer as the so-called Grahame rational scale [i]. A detailed discussion of the rational p. was given by Antropov [ii]. 

Some further nomenclature is now necessary to describe absorption equilibria in ion exchange systems. For a species i, m and C, represent the molal and molar concentrations respectively, whilst A and Xi denote the mole fraction and equivalent ionic fraction of i respectively. Single ion activity coefficients are denoted yj and mean ionic activity coefficients by yj . Whether the latter quantities refer to the molar or molal concentration scales is decided by the choice of units defining concentration. Thermodynamic activities and activity coefficients for the resin phase using the equivalent or mole fraction concentration scale (rational scale) are sometimes defined differently and are discussed in a later section. Finally, the exchanger and external solution phases are differentiated by subscripts r and s respectively. 

The above equation leads to the conclusion that, for a simple charge transfer step, the proper standard of comparison is the condition = constant, i.e., the same potential on the rational scale (referred to the point of zero charge), since the charge on the metal is an arbitrary imposed value, and the effect of the substrate is expressed in the work function term. 

The standard potentials on the molal molar and rational scales E ) are related by... 

Fig. 22 Experimental values of the repulsion constant , u, in isotherm (93) for iodide adsorption at Bi-water interface (points are shown with their dispersion) as a function of the eiectrode potentiai in the rational scale, (p = E — Eo=o- The theoretical curve (solid line) was calculated from Eq. (92) for A = 0.71 with the use of experimental data for the compact- and diffuse-layer capacitances of the same interface in a surface-inactive electrolyte solution.

Grahame-Parsons isotherm to interpret these data was unsuccessful, despite a greater number of fitting parameters. The analysis with the use of isotherm (93) gave the values of the intermediate parameters, V and Wads, which are shown in these figures as a function of the electrode potential in the rational scale,... 

A simple modification introduced in a stirred tank bioreactor allowed us the establishment of B. Candida hairy root cultures for scopolamine and 6P-hydroxyhyoscyamine production with increased alkaloid concentration compared to the Erlenmeyer flask cultures [28], It is worth pointing out that these results are potentially applicable to perform the rational scale-up of the process [28]. 

D. Nutt, E. A King, W. Saulsbury, C. Blakemore (2007) Development of a rational scale to assess the harm of drugs of potential misuse. Lancet, 369, 1047-1053. http //www.wada-ama.org/Documents/World Anti-Doping Program/WADP-Prohibited-list/2014/WADA-prohibited-list-2014-EN.pdf (last access March 23, 2014). http //www.drugabuse.gov./PDF/RRCocaine.pdf(last access February 25, 2014). 

The derivatives in Equation 4.15 through Equation 4.17 are easily obtained from the expression of the chemical potential on the rational scale. 

In this step, pairwise comparison between the goal of the model and logistics components, logistics components with logistics components themselves, and logistics components with their individually KPIs is made. Comparison in ANP, as in AHP, uses ration scale of absolute number from number 1 (equal important) to... 

Scale-up of any engineering process is a great technical and economic challenge. Scale-up of granulation processes, in particular, is difficult and often problematic due to the inherently heterogenous nature of the materials used. However, recent improved understanding of the rate processes that control granulation improves our ability to do rational scale-up. 

The first four criteria are derived from feedback-control theory. A SHE performance indicator must be observable and quantifiable, i.e. it must be possible to observe and measure performance by applying a recognised data-collection method and scale of measurement. The nominal scale is the simplest type. This means that we must be able to tell whether the result represents a deviation from a norm or not. Usually, the SHE performance indicators are expressed on a ration scale of measurement. A typical example is the LTI-rate, i.e. the number of lost-time injuries per one million hours of work. 

---