Logarithmic scale, activity values

Fig. 4.4 (a) Comparison on a logarithmic scale of the conductivity ratio and the thermodynamic activity ratio of alkali oxide in several silica based glasses. Activity ratios are deduced from potentiometric measurements, (b) On the same scale, conductivity vs activity of AgX (X = Cl, Br, I) in phosphate glasses. Activity values are deduced from calorimetric measurements. 

In order to determine the volume of activation, first the rate constant, k, is calculated from the measured reaction rate, r, and the concentration, Ca, through eqn. 3.2-19. The exponent n can be obtained from experiments at different concentrations. The value of k is then plotted on a logarithmic scale versus the pressure, and Av (10 6 cm3/mol) is evaluated from the slope, a, of the resulting straight line (Fig. 3.2-2). For this purpose a, (MPa ), is multiplied by the gas constant, R (8.314 J mol 1 K 1), and the temperature, T(K). 

In order to investigate the influence of the pressure, polymerization tests were run at pressures of 120 - 190 MPa. As can be seen from Fig. 9.5-6, the rate of polymerization increases from (0.58 to 1.3) 10 3 mol ethylene/(l s). When r, r is plotted on a logarithmic scale versus the pressure, a value of activation volume of -32.5 ml/mol can be evaluated from the slope of the resulting straight line. The negative value is characteristic for polymerization reactions because the volume reduces in the transition state (see Chapter 3.2). 

Based on Eq. 12.1, optimum salinity follows the logarithmic mixing rule. Mohammadi et al. (2008) replaced the ratio of oil to surfactant concentration shown in Figure 12.5 by soap molar fraction and used the more generally effective salinity in the vertical axis. They did so because they could get these values from UTCHEM simulation models. Based on the logarithmic mixing rule, both axes in such activity maps are in logarithmic scales, and the upper and lower boundaries should be linear. 

Logarithms to the base 10 are called Briggsian or common logarithms. Before the advent of handheld scientific calculators, these were an invaluable aid to numerical computation. Section 2.6 on Powers of 10 was actually a tour on the logjo scale. Logarithmic scales give more convenient numerical values in many scientific applications. For example, in chemistry, the hydrogen ion concentration (technically, the activity) of a solution is represented as... 

Fig. 9.17 Nonlinear stress relaxation of the transient network model with a quadratic chain dissociation rate under a constant shear deformation for y = 0.5. The decay rate is fixed as (a) /3q = 0 and (b) /3q = 1. The total number Ve of active chains and the number Vg of chains that remain active from the initial state are shown on a logarithmic scale. These are normalized by the stationary value of Ve. The shear stress hxy, the first normal stress difference N, and the second normal stress difference N2 are shown in the unit of Ve B T. (Reprinted with permission from Ref. [19].)...

In Hansch analysis, the biological activity values (reciprocal molar doses C, on a logarithmic scale) are taken as the dependent variable (y variable), whereas different physicochemical properties of the compounds (e.g., logP values, MR) or of the substituents which are structurally modified (e.g., tt, cr, MR, Es) are taken as the independent variables x variables). Thus, regression analysis of the first three data columns of Table 1 leads to equation (7), whereas additional consideration of s values (first four data columns of Table 1) leads to equation (8). ... 

The underlying concept of all QSAR analyses is the additivity of substituent group contributions to biological activity values in the logarithmic scale. This additivity comes from the fact that QSAR models are linear free-energy related. All... 

FIGURE 8.6 Calculated activity coefficients for acetone and water at 1 atm based on the experimental values in Table 8.1. The values in Example 8.2 are the first points from the left in this plot, corresponding to Xacetone = 0.05. The curves are simple smoothed interpolations. Activity coefficient plots are almost always presented on semi-logarithmic coordinates, as is this one. In the text we often refer to plotting In (y,) that is equivalent to what we show here, plotting y,- on a logarithmic scale. 

Consider first the polarization curve (i.e., Tafel plot) for the anodic halfreaction occurring in corrosion of stainless steels (Fig. 16.8). The diagram for the active region is much the same as has been seen for other anodes (Figs. 15.4 to 15.7). As Eh is increased to a certain specific value, however, a sudden and dramatic drop in the anodic current density i occurs, corresponding to formation of an oxide film. At higher Eh, i remains constant at a very low level (the horizontal scale in Fig. 16.8 is logarithmic), and the metal has become passive, that is, effectively immune from corrosion. 

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