Straight line decomposition

Fig. 2. a 60 MHz broad-line JH NMR spectrum of bulk polyethylene at 20 °C. b Two-component analyses, dotted line straight line decomposition [45] dashed line symmetrical decomposition [46,47]... 

The activation parameters for an initiator can be deterrnined at normal atmospheric pressure by plotting In vs 1/T using initiator decomposition rates obtained in dilute solution (0.2 M or lower) at several temperatures. Rate data from dilute solutions are requited in order to avoid higher order reactions such as induced decompositions. The intercept for the resulting straight line is In and the slope of the line is —E jR therefore both and E can be calculated. 

A plot of rate versus concentration for the decomposition of N2O5 is a straight line. The... 

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... 

Adiabatic calorimetry. Dewar tests are carried out at atmospheric and elevated pressure. Sealed ampoules, Dewars with mixing, isothermal calorimeters, etc. can be used. Temperature and pressure are measured as a function of time. From these data rates of temperature and pressure rises as well as the adiabatic temperature ri.se may be determined. If the log p versus UT graph is a straight line, this is likely to be the vapour pressure. If the graph is curved, decomposition reactions should be considered. Typical temperature-time curves obtained from Dewar flask experiments are shown in Fig. 5.4-60. The adiabatic induction time can be evaluated as a function of the initial temperature and as a function of the temperature at which the induction time, tmi, exceeds a specified value. 

The points for Ag and Pd-Ag alloys lie on the same straight line, a compensation effect, but the pure Pd point lies above the Pd-Ag line. In fact, the point for pure Pd lies on the line for Pd-Rh alloys, whereas the other pure metal in this series, i.e., rhodium is anomalous, falling well below the Pd-Rh line. Examination of the many compensation effect plots given in Bond s Catalysis by Metals (155) shows that often one or other of the pure metals in a series of catalysts consisting of two metals and their alloys falls off the plot. Examples include CO oxidation and formic acid decomposition over Pd-Au catalysts, parahydrogen conversion (Pt-Cu) and the hydrogenation of acetylene (Cu-Ni, Co-Ni), ethylene (Pt-Cu), and benzene (Cu-Ni). In some cases, where alloy catalysts containing only a small addition of the second component have been studied, then such catalysts are also found to be anomalous, like the pure metal which they approximate in composition. 

Their kinetic data using 0.14 mmol Cr(CO)6 in 40 ml 95% aqueous methanol resulted in a straight line when H2 turnover frequency was plotted versus formate concentration, such that k2 = 1200/day for decomposition of HC02Cr(C0)5 , and (k2 + k ) k = 0.43 mol/L at 60 °C. They later used the same system to hydrogenate aldehydes. They published a review of their work in a Russian journal in 1994.138... 

The validity of Johnston s interpretation of the experimental facts in terms of the simple unimolecular dissociation (1) has been questioned by Lindars and Hinshelwood120 and by Reuben and Linnett121. These workers maintain that isothermal plots of k versus p are not smooth curves, but consist of a number of straight lines linked by markedly curved portions. To explain such behaviour they incorporate into their mechanism a collision-induced crossover of vibrationally excited N20 (XS) to repulsive 3II and 3E states. While we incline towards the simpler view held by Johnston105 and others106-116, we feel that this feature of the decomposition kinetics merits further investigation. 

Equation 1.34 is plotted for a number of hydrides in Fig. 1.25. As can be seen all the data points fit very well in a simple straight line whose slope is equal to AS -130 J mol" K [162]. This clearly shows that the entropy term is, indeed, a nearly constant value for all the solid state hydrogen systems. Figure 1.25 also shows that a low desorption temperature at 1 atm of pressure (more or less an operating pressure of a PEMFC) can only be achieved with hydrides having the forma-tion/decomposition enthalpies not larger than 50 kJ moF. For example, hydrides that desorb at room temperature such as LaNi and TiFe have AH 30 and 33.3 kJ mol", respectively [163]. However, too small an enthalpy term would require at 1 atm to be much below 0°C. From this point of view the enthalpy term is one of the most important factors characterizing any hydride. 

To account for the decomposition of TiCuH, we proceed as follows although both x and y in Reaction 7 vary with temperature, AH remains reasonably constant with temperature and composition, as seen by the straight line in Figure 2. Such behavior is, in fact, observed experimentally in most metal hydrides (14). This being the case, we approximate the enthalpy of formation of TiCuH by rewriting Reaction 7 (Reaction 8) and assume AH for this reaction to be —75... 

Heterogeneous and catalytic reactions also give straight lines over as wide ranges of temperature as can be investigated. For example, in the catalytic decomposition of ammonia on the surface of a tungsten wire the value of A remains constant over the range 904° to 1,129° abs. in a manner which confirms the equation completely. 

By means of the calibration, the absorption intensity curve is converted into a concentration versus time curve. The rate of decomposition is then obtained by differentiating this curve and plotted on a logarithmic scale versus the logarithm of the concentration. From the slope of the resulting straight line, an order of unity for the decomposition is evaluated, and from the intersection at the ordinate the rate-constant is obtained. 

According to these data the heat of activation for the decomposition of nitric oxide, to which reaction the factor k refers, is A = 82 10 kcal/mole.10 It should be especially noted that there is no systematic divergence between the data on the formation and on the decomposition of nitric oxide this fact justifies the assumption that the rate of decomposition is directly proportional to the square of the nitric oxide concentration.11 The investigation covered the temperature range from 2000°K to 2900°K in which the rate varies by a factor of 300. As appears from Fig. 13, except for the scattering due to the inevitable errors of the experiments and computations, the points actually do fall on a straight line in the coordinates lg kr, 1/Tm, i.e., the Arrhenius temperature dependence of the reaction rate holds. The thermodynamic relation between the rates of the direct and reverse reactions permits determining the heat of activation A for the formation of nitric... 

The maximum temperature of synthesis reaction was calculated for the substitution reaction example as a function of the process temperature and with different feed rates corresponding to a feed time of 2, 4, 6, and 8 hours. The straight line (diagonal in Figure 7.11) represents the value for no accumulation, that is, for a fast reaction. This clearly shows that the reactor has to be operated at a sufficiently high temperature to avoid the accumulation of reactant B. But a too high temperature will also result in a runaway due to the high initial level, even if the accumulation is low. In this example, the characteristics of the decomposition reaction... 

The plot of this rate vs. the partial pressure of N20 gives a straight line and from its slope an apparent rate constant for N20 decomposition is estimated to be 6.7x10 mol/g-Ag.min.atm. 

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