Plot of In Kp versus

The effect of D on kp was discussed by Stannett et al. (1979) in some detail, and they concluded that their results, shown as a plot of In kp+ versus 1 ID, agree with Laidler s equation, according to which In kp varies rectilinearly with 1 ID. Their Figure 3 shows results for EVE and IPVE which include their rate-constants for the bulk polymerisations which we now know should be characterised by a first-order rate-constant, and it includes results obtained at a very high concentration of monomer, where the significance of the formal kp+ is far from obvious. Therefore their conclusion cannot be accepted now, and it is clear that the relation between kp+ and D needs to be investigated with a Class A monomer, e.g., isobutene, and at low m. 

Equation (11.58) shows that a plot of In Kp versus 1/Thas a slope equal to —AH°/R. Since AH° is almost constant, at least over moderate ranges of temperature, the plot is often linear. 

These considerations should be taken into account when one attempts to compare heats of mixing reported by various authors as given in Table III. SQ-called entropies of mixing reported by various authors are even more complicated. For example, the entropy defined from the plot of In Kp versus IjT has the significance of... 

Similarly, from a plot of In (k/T) versus 1/T, the enthalpy of activation for each process may be obtained. This is also illustrated for the determination of the activation enthalpy for the propagation of degradation of a vinylidene chloride/methyl acrylate (five mole percent)/4-vinylpyridine (0.1 mole percent) copolymer in figure 7. The slope of the plot of In (kp/T) versus 1/T (figure 7) is given by -AH /R and the enthalpy of activation, AH, for the propagation reaction is calculated to be equal to 27.92 kcal/mol. The activation parameters for both the initiation and propagation reactions are recorded in table 3. 

A plot of In (kp/T) versus 1/T (Figure 6) allows evaluation of the enthalpy of activation, AH, from the slope, and the entropy of activation, aS, from the intercept. 

Figure 4.7 Negative-ion mass spectrometry data for 02 (—)-(H20) for equilibrium constants obtained from the ion intensities as shown in Figure 4.6, plotted as In Kp versus 1,000/r. The intercept multiplied by R is the standard entropy, while the slope multiplied by R is the heat of reaction. The plots for the n — 0 to n — 1 complex and the n — 6 to n = 7 complex have approximately the same intercept. Data from [16].

Figure 4.10 BCD data plotted as In Kp versus 1.000/7. Chlorobenzene and chloro-naphthalene dissociate via an intermediate molecular ion. They are designated DEC(2) for dissociative electron capture by a two-step process. The slope in the high-temperature region multiplied by R is equal to the EDEA. Given the electron affinity of the dissociating species, in this case Cl(—), the C—Cl bond dissociation energy can be measured. Data from [17-19].

If Kp is measured at several temperatures and the data plotted as In Kp versus 1/T, the slope of the line yields a value of AH° for the reaction through Eq. (11.58). Consequently, it is possible to determine heats of reaction by measuring equilibrium constants over a range of temperature. The values of the heats of reaction obtained by this method are usually not so precise as those obtained by precision calorimetric methods. However, the equilibrium method can be used for reactions that are not suited to direct calorimetric measurement. Later we will find that certain equilibrium constants can be calculated from calorimetrically measured quantities only. 

Figure 5 is a plot of permeability factor Kp versus (Ap/Ah)mf and contains the boundary Vmf = 50 mm S 1. Figure 6 is a plot of rcd/ps versus (Ap/Ah)mf-md contains the boundary X= 0.001 nf s kg-1. By using both Figs. 5 and 6, it is possible to propose the following three criteria relating to the potential modes of pneumatic conveying in conventional pipelines. 

From measurements of the concentration C, of the compound i as a function of exposure time, the first-order photolysis rate constant, kp(/1), is then determined by calculating the slope of a plot of In C, /C,0 versus time (see Section 12.3). Since the... 

In equation 6.61, Ac is the reactant (Fe ) and the reaction product is Fe+. In the batch reactor, for not too high reactant conversions, the plot of Fe" concentration versus time gives a sdaight line. Then, at r 0 and taking into account that at 254 nm Kp 5+ is large ... 

AS can be readily obtained from Eqs. (2-58) and (2-70). Alternatively, if the Arrhenius energy of activation is of interest, it may be obtained in the usual manner from a plot of In/ versus 1/T, and can be related to the transition-state thermodynamic parameters through Eqs. (2-58), (2-70), (2-81), and (2-82). In carrying out these calculations, the role of the choice of standard state in relation to the numerical values of AS and AG should be firmly kept in mind. Since AH° and A are independent of the standard state for ideal systems, the standard state is automatically determined by the units used for the rate constant [Eq. (2-72)] (unless a conversion factor such as that for going from to Kp is used). For nonideal systems, no additional... 

Hence a plot of In/ versus E is linear the slope yields an and the intercept yields the propagation rate constant kp provided that the layer thickness L can be determined. Hence we note that the variation of peak time with layer thickness and applied potential is diagnostic. 

Unfortunately, by omitting to plot the primary data, i.e., kx versus c0, they missed the most interesting feature of their results and were misled by the plots of kp. Their results plotted by us are shown in Figures 4 and 5, where we see that with increasing c0 the kx... 

In the study of the reaction of 2,4,6-trinitrotoluene with base (NaOMe, under first-order conditions), kinetic and equilibrium data for reaction in methanol-DMSO have been obtained. Since it has been found that plots of logarithms of rate and equilibrium constants versus the mole fraction of DMSO are linear, the value in pure methanol have been extrapolated (Kp = 12.4 lmol-1)213. 

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