L-t plot

The value of EM depends not only on solvent, catalyst, and co-catalyst but - at least for isobutene - also on the monomer concentration. Kennedy and Thomas [85] found that for isobutene-AlCl3-alkyl chloride the slope of the log DP-l/T plots increases with increasing monomer concentration in such a way that the family of lines all cross at approximately the same temperature, near -50 °C which they called the inversion temperature. They interpreted this phenomenon in terms of a change in the relative importance of monomer transfer and solvent transfer with changing composition of the reaction mixtures. 

The temperature variation method is used often in solvent extraction studies. It can give reliable values of the enthalpy if care is taken to verify that the change in temperature is not causing new reactions, which perturb the system. Also, a reasonable temperature range (e.g., AT 50°C) should be used so that it is possible to ascertain the linearity of the In P vs. l/T plot upon which Eq. (3.17) is based. 

The slope of the In i vs. l/T plot is not as steep at the low temperature range. For high temperatures (liquid state) we obtain with a = 1... 

Using this equation, ln(r.) was evaluated at several temperatures at known coverages 6 = q/qx where qx is the equilibrium coverage at P0i = 6 cm.). The activation energy for adsorption, Ea, was evaluated from the ln(r,) vs. l/T plots, and it was found that at constant pressure the activation energy increased in a roughly linear fashion with coverage... 

Using equation (4), Torocheshnikov et al. (50) have calculated the values of <5C and K for Me3SnCl and Et3SnCl in acetone, acetonitrile, and dioxan. The molar enthalpy of complex formation, AH, can be obtained from a In K vs. l/T plot (Fig. 5) using the Van t Hoff relationship ... 

B. Interpretation of L-t plot and D from Phenomenological Transport Model... 

Figure 1.14. L-t plot results using the modified diffusion equation [Eq. (1.5)] for several values of x.

An alternative way to present the simulated spreading behavior is shown in Figure 1.33. The L-t plot was constructed by plotting the distance that an isoheight in the spreading profile travels from the initial sharp boundary (a position of constant thickness that changes with time) versus the number of... 

For determining Hb, it is sufficient to measure J(V) at few temperatures, extrapolate them until they meet and determine Vc. Hb can now be determined using Eq. (3.55). The trap density can also be determined from the slopes of In J-l / T plots using Eqs. (3.54) and (3.53). Trap densities determined by these simple direct methods agree with those derived by complicated fitting procedures [49],... 

Fig. 13. The log Pmax versus l/T plots for equimolar ester—oxygen mixtures [45]. Pmax is the maximum rate of reaction in torr. min . (1) Methyl n-hutyrate, P(total) = 240 torr. (2) Methyl propionate, P(total) = 500 torr. (3) Ethyl acetate, P(total) = 160 torr. (4) Methyl acetate, P(total) = 500 torr.

Fig. 5 (A) Travel length (L) as a function of time (i) obtained from Fig. 3B for monodisperse Zdol T = 26°C, under dry nitrogen and (B) L-t plot results using the modified diffusion equation (Eq. 7) for several values of t. (View this art in color at WWW. dekker. com.)...

The dc electrical conductivity of a number of N-(2-pyridyl)benzamide and N, N -dibenzoyl-2,6-diaminopyridine metal complexes, as a function of temperature (to 388 K) and radiation, was studied by Abou Sekkina et al. (61). Linear log versus l/T plots were obtained for all the Cu(II) and Ni(II) complexes, from which the activation energy, Ea, and other parameters could be calculated, using the expression... 

Using the ArC° = 0 ArH° constant) approximation for aqueous reactions such as ionization constants can lead to very poor results because these reactions commonly have heat capacity terms that vary considerably with temperature. A useful observation is that for a great many aqueous reactions, ArC° can be made much closer to zero, hence giving a much straighter line on a log A versus l/T plot, by transforming the reaction into the isocoulombic form. Isocoulombic refers to... 

Using the log K versus l/T plot, evaluate T for each value of x and plot X versus T (line ah in Fig. 

Because of the exponential form of the viscosity equation, mixtures of ceramic powder in thermoplastic binder are only significantly sensitive to temperature change above 70°C [3]. In an injection molding operation, it is usual to plot In q versus T for a constant shear rate, not a In q versus l/T plot at a... 

Finally, further advice in this context If you are interested in an analysis of characteristics of your particular compounds or stationary phases, you should consider van t Hoff plot, which are suitable for these questions. A In k versus l/T plot results in a straight line with the general formula y = ax + h. The slope represents the enthalpy differences and the y intersection the entropy values. We obtained some interesting results using the van t-Hoff plots, but a more detailed discussion is not within the scope of this book. Let us just discuss some of the conclusions that can be reached from this kind of analysis ... 

From In = f(l/T) plots, AH values can be obtained for each solute, which can then be plotted against In k. 

Fig. 5.8. Log K versus l/T plot for the cholesterol-tributyrin complex. (Parker and Bhaskar, 1968.)...

Thus, the slope of a ln(C) against l/T plot equals —E /2k. The data has minimal uncertainty so the slope can be calculated by the two-point difference method. Alternatively, a linear regression lit of ( /T, ln(G/S)) data points gives the slope. 

Rate constants for the two isomerization processes were calculated using A5 and A as described in Section 6.1.3. The comparison with the experimental values in a log k versus l/T plot is shown in Figure 6.21. As can be seen, the agreement is very good. 

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