Logarithmic-linear expression

The relationship between the concentration and the perceived taste intensity of MSG was logarithmically linear like those of the four common tastes, although the slope for MSG was somewhat less steep than the others. It means that Weber-Fechner s law holds for all of the five taste substances. The relation of the taste intensity (S) to the concentration (x) can be expressed by... 

To decide if the experimental sorption behavior of a substance obeys the Freundlich isotherm or K, model, the approach generally used is to first linearize the isotherm by taking the logarithm of expression (10.2), which yields... 

On the other hand, measurements of shear stress versus shear rate, when plotted on logarithmic scales, may often be represented by a linear expression over a limited range of shear rate (in this case, from 7 to 158 s ). The equation which represents this behavior is usually called the power-law or the Ostwald-De Waele model ... 

Log arithmic-Mean Driving Force. As noted eadier, linear operating lines occur if all concentrations involved stay low. Where it is possible to assume that the equiUbrium line is linear, it can be shown that use of the logarithmic mean of the terminal driving forces is theoretically correct. When the overall gas-film coefficient is used to express the rate of absorption, the calculation reduces to solution of the equation... 

The intensity of "umami" increases linearly with a logarithmic increase in the concentration of MSG. The synergistic effect of MSG with 5 -ribonucleotides is expressed by the following relation... 

The logarithm of the micellar molecular weight (M) and consequently the aggregation number of sodium dodecyl sulfate at 25°C in aqueous sodium chloride solutions is linearly related to the logarithm of the CMC plus the concentration of salt (Cs), both expressed in molar units, through two equations [116]. Below 0.45 M NaCl micelles are spherical or globular, and Eq. (18) applies ... 

Increasing temperature permits greater thermal motion of diffusant and elastomer chains, thereby easing the passage of diffusant, and increasing rates Arrhenius-type expressions apply to the diffusion coefficient applying at each temperature," so that plots of the logarithm of D versus reciprocal temperature (K) are linear. A similar linear relationship also exists for solubUity coefficient s at different temperatures because Q = Ds, the same approach applies to permeation coefficient Q as well. 

For catalytic reactions and systems that are related through Sabatier-type relations based on kinetic relationships as expressed by Eqs. (1.5) and (1.6), one can also deduce that a so-called compensation effect exists. According to the compensation effect there is a linear relation between the change in the apparent activation energy of a reaction and the logarithm of its corresponding pre-exponent in the Arrhenius reaction rate expression. 

The expression is called absorbance and has a positive value if more light is absorbed from a substance spot than from a clean TLC plate surface. Usually, there is no linear relationship between the logarithmic signal and the sample mass in the layer. 

Therefore, the activation energy of quasi-equilibrium conductivity changes as a logarithm of concentration of adsorption particles which, when the linear dependence between Nt and P is available, corresponds to situation observed in experiment [155]. We should note that due to small value m function (1.91) satisfactorily approximates the kinetics oit) A - B n(i + t/t>) observed in experiments [51, 167, 168]. Moreover, substantially high partial pressures of acceptor gas, i.e. at high concentrations of Nt expression (1.81) acquires the shape ait) Oait/toc) it,Nty " when t>toc>. This suggests that for... 

Expressing the hydrogen ion concentration of a solution by a logarithmic function, such as the pH, is helpful in another way too many physicochemical properties of these solutions are linearly proportional to the logarithm of the hydrogen ion concentration. 

The basis for linear solvent strength theory is the assertion that the logarithm of the capacity factor is linearly related to the solvent strength. This is expressed in the Equation 87 90... 

Once the QFH formula for the excess chemical potential is linearized in (11.37), the logarithmic expression can be expanded to first order and all or part of the classical-average term can be integrated by parts to yield the Wigner-Kirkwood correction to the free energy. Then if (11.40) is reorganized, computation of the chemical potential can be viewed as a classical average with a modified interaction potential of the same form as (11.3). 

According to this method and under the hypothesis of weak solubility interactions, the logarithm of the partition coefficient of a sorbent layer with respect to a certain volatile species is the linear combination of five terms expressing the intensity of five basic interaction mechanisms. They are polarizability, polarity, two terms describe the hydrogen bonding considering the analyte acting as an acid and a base respectively, and... 

The values for 7 and 70 cannot be measured in absolute terms and the measurements are most conveniently made by expressing / as a percentage of / . This value is known as the percentage transmittance (T) and only shows a linear relationship with the concentration of the test substance if the logarithm of its reciprocal is used. It is therefore more convenient to report the measurements initially as this logarithmic function of 7 and 70, a parameter which is known as absorbance (A) ... 

Diffusion systems are based upon the ability of the antibiotic to diffuse through agar and cause the inhibition of the sensitive assay strains. Since the substrate to be assayed is applied in a "point source," diffusion occurs radially. A circular zone of inhibition forms and the size of the zone is a function of the concentration. This function is expressed as a linear relationship between the size of the zone of inhibition and the logarithm of the concentration. 

A plot of the logarithm of a rate constant (or an equilibrium constant) for one series of reactions versus the logarithm of the rate constant (or the equilibrium constant) for a related series of reactions. (Recall that at constant temperature and pressure the logarithm of an equilibrium constant is proportional to AG°, and the logarithm of a rate constant is proportional to AG ). An example of a linear free energy relationship is provided by the Hammett crp-equation. With equilibrium constants, this relationship is given by the expression ... 

To characterize the relative gas-chromatographic retentions of condensed aromatics and heteroaromatics, inclu g thienothiophenes, benzo[b]thiophene, dibenzothiophene, naphthobenzothiophenes, and anthrabenzothiophenes, a system of indices. In, was proposed, In this system a series of similar linearly condensed hydrocarbons (such as benzene, naphthalene, anthracene, tetracene, pentacene,...) was used as a reference scale. The logarithm of the corrected retention volume (adjusted to 0°), log Ft, depends linearly upon the number of condensed benzene rings (z) in the molecule, both in the polar and nonpolar phases. In is expressed by Eq. (58) ... 

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