Logarithmic Plot

Figure 9 Logarithmic plots of the heights of the first peak m the PCF against Taft s (1 parameters (a) formamide (b) formamidic acid.

The general function giving straight lines on double logarithmic plots is ... 

Solution of equation 6.4 is the now familiar exponential distribution which is linear in a semi-logarithmic plot In n L) versus L (Figure 6.11a)... 

FIG. 10 Micelle size distribution for H2T2 surfactants within the Larson model. The dashed lines show fits to the expected form for spherical micelles (main peak) and cylindrical micelles (tail). Inset shows the tail of the distribution on a semi-logarithmic plot to demonstrate the exponential decay predicted for the cylindrical micelles. (From Nelson et al. [120].)... 

Keeping the composition of copolymerization media constant the total comonomer concentration of which is varied. The absorbed dose was kept constant at 0.14 KGy for the AM-AANa and at 0.35 KGy for the AM-DAEA-HCl systems. The results are shown in Figs. 4 and 5, which show the rate of polymerization, Rp, the degree of polymerization, and the intrinsic viscosity increase with increasing monomer concentration. At comonomer concentration >2.1 M/L, DPn decreases with increasing comonomer concentration. From the logarithmic plots, exponents of the comonomer concentration for the AM-AANa system were determined to be [17,54]. 

From the logarithmic plot of the Arrhenius equation shown in Figs. 8 and 9, the overall activation energy, / p, was calculated to be 0.65 and 0.56 Kcal/mol for AM-AANa and AM-DAEA-HCl systems, respectively. However, the corresponding reported values for gamma radiation induced copolymerization of acrylamide with DMAEM-MC in aqueous solution was found to be 2.0 Kcal/mol [16]. 

Figure 53. Logarithmic plots of eigenvalues (- -) and reduced eigenvalues (—) for the two training sets, Al and A2.

Figure 54. Logarithmic plots of the PRESS values as a function of the number of factors (rank) used to construct the calibration.

Figure 56. Logarithmic plots of the PRESS values as a function of the number of factors (rank) using the same samples for calibration and validation. As factors are added, the errors continue to decrease. When all of the factors are used, the errors equal exactly zero.

Figure 63. Semi-logarithmic plot of the SSR (y-axis) vs. the concentration of Component 5 (x-axis) for each sample in A5.

Both sets of experiments seem to support the proportionality of crack opening displacement 5C = 2w and molecular mass Mc between crosslinks as indicated by the slope 1 in the double logarithmic plot (Fig. 7.5). Even if Mc had to be adjusted due to doubts about the front factor in Eq. (4.3), the proportionality would stay unaffected. Consequently, the size of the deformation zone ahead of the crack is determined by the length of the molecular strands in the chemical network. 

Each of the curves in Figure 5-3 exhibits two or three pH regions in which the slope of the logarithmic plot is approximately —1, with intermediate regions where the slope is small or zero. Lewis and Hanson (1967) showed that in the case of (E,)-4-nitrobenzenediazoate the portion of the curve with slope —1 at relatively high pH was consistent with the acidity constant K3 of the (E )-diazohydroxide determined either by titration or spectrophotometrically, the relevant results being (by... 

The logarithmic plot is not linear, of course, since this is not a first-order reaction. Note, however, that even In [A], is linear in time to about 50 percent reaction. One cannot use these procedures to establish the kinetic order without data taken to at least two half-times, and preferably longer. 

A logarithmic plot of tj versus (fr in Figure 10.13 shows that, using this definition of L, the curves for the slab or platelet and the spherical particle come very close together. 

Figure 5. Semi-logarithm plots of the fractional intensities of C2Hi+, C2H2+, and C2H + ions as functions of the pressure of C2Ht...

The temperature-factor parameter B and the scale factor k were determined by a least-squares procedure/ with observational equations set up in logarithmic form and with weights obtained from those in equation (9) by multiplying by (G (obs.))2. Since a semi-logarithmic plot of G2 (obs.)/Gf (calc.) against B showed a pronounced deviation from linearity for the last five lines, these lines were omitted from the subsequent treatments. They were much broader than the others, and apparently their intensities were underestimated. The temperature-factor parameter B was found by this treatment to have the value 1-47 A2. 

Fig. 16. Logarithmic plot of k against [Li] for benzene soln. at 30 °C (S. Bywater, D. J. Worsfold,...

Order respect to N-Br-amino acid concentration. With the aim of establishing the reaction order with respect to the N-bromoalanine concentration, we have obtained the values of the initial rates for different N-bromoamino acid concentrations with a fixed OH" concentration of 0.23M. The logarithmic plot shows to be a straight line (Fig. 3) with a slope of 1.07 0.03. This means that the decomposition reaction of N-Br-alanine is first order with respect to the N-bromoalanine concentration. From the plot of initial rate against initial N-bromoalanine concentration (Table 1) we can obtain for the pseudofirst order rate constant for N-bromoalanine decomposition a value of 0.0160 0.(XX)4 s-f... 

Fig. 3. Logarithmic plot showing compliance with first order rate law respect to N-Br-alanine concentration for the N-Br-alanine decomposition reaction. [Ala] = 0.02 M, [NaOH] = 0.23M, T = 298 K. 

C, the fourth parameter, represents the relationship between the first cumulant and the particlescattering factor. For values of 1/F( ) < 10, the double logarithmic plot of the first cumulant against the reciprocal particle-scattering factor yields a straight line, and the exponent v is related to the initial slope C oiF/q D, against by the equation... 

RIA PREC.dat Two hundred thirty-eight calibration data sets were collected and analyzed for repeatability (within group CV) and plotted against the mean concentration. In a double-logarithmic plot the pattern seen in Fig. 4.6 appears. 

Figure 7.2. A logarithmic plot of the exponential decay of Figure 7.1 showing the linear dependence of In(concentration) versus time...

Convert the concentration data into ratios, take the logarithms, and then prepare a logarithmic plot to determine whether the reaction is first order ... 

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