Time vs. reaction rate

The very informative semilogarithmic plot of over-all reaction rate vs. time was first published by Bartholome et al. (4, 6). Looking at the reaction rate-time curves given below one can see that even for the styrene system, which was shown to follow Smith-Ewart kinetics the best... 

Fig. 6.48. The role of non-equilibrium charge screening in eliminating the Coulomb catastrophe the dimensionless reaction rate vs time. Dotted curve - the Debye theory (no screening and similar particle correlation) broken curves - the solution of kinetic equations incorporating these correlations but neglecting screening full curves, screening is taken into account. Parameters L = 5, Da = Db. Curves 1 to 3 correspond to dimensionless concentrations ...

Acetone aldol condensation proceeds on either acidic or basic catalysts. On basic catalysts, the reaction products are mainly a,P-unsaturated ketones [5] whereas on acidic materials formation of aromatics and olefins is favored [6]. In our catalytic tests, the main reaction products were mesityl oxides (MO s) and isophorone (IP). MO is formed from the initial selfcondensation of acetone whereas IP is a secondary product arising from the consecutive aldol condensation between MO and acetone. Over all the samples the reaction rate diminished as a function of time-on-stream as shown in Fig. 1 for the MgjAlOx sample which lost about 60 % of its initial activity after 10 h-run. Initial reaction rates (r ) and product selectivities (S j) were calculated by extrapolating the reaction rates vs. time curves to zero. 

Figure 22 Reaction rate vs. time for different heating rate dynamic tests comparison between expaimental DSC data (points) and model predictimis (fiill lines). (After Kenny et al., ref. 44).

The present paper tests the assumed original and enhancement mechanisms with rates and conversions for a broad range of contaminants measured under a fixed mass concentration (50 mg/m ) feed condition. The plots compared are reaction rates vs. (1) dark adsorption, Ot. (2) second order rate constant for (OH ) (TCE absent) or (Cl ) (TCE present), and (3) the product of these gas phase second order rate constant times the reactant dark coverage. Where a second order gas phase rate constant was not available, we estimated its value from correlations of kci vs. koH for tke same class of compounds. 

Figure 50.2. Reaction progress data for a one-pot, two reaction sequence for the reaction of Scheme 50.2. (a) reaction heat flow vs. time (b) reaction rate vs. [5] (c) reaction rate/[6] vs. [5].

Rate vs. time curves are are presented as per cent C=C conversion per second by using the experimentally determined heat of polymerization of acrylate groups of 78 kJ.Mol (11). Extents of reaction were reproducible to within 0.7%, the accuracy depends on the accuracy of the heat of reaction. The distortion of DSC curves of fast reactions is discussed below in the section on shrinkage and conversion. 

The development of the reaction was followed by measuring pressure change (Ap), light emission (7), reaction rate (dAp/dt), and by chemical analysis. Pressure rise was recorded by a pressure transducer (A.C.B. 504H). Reaction rate (dAp/dt = W) was obtained by using a resistance-capacity circuit of suitable time constant, 6 = RC (76, 78), appropriate to the branching factor of the reaction, < . It was possible to record simultaneously pressure rise vs. time and rate vs. time or rate vs. pressure rise. 

This is found from the absolute value of the slope of a curve of concentration vs. time. An estimate of the reaction rate at time t may be found from the average reaction rate over a small time interval surrounding t. For those familiar with calculus notation, the following equations define reaction rate, but calculus is not needed for this skill ... 

FIGURE 5.13 Autocatalytic reaction of obidoxime chloride with k = 3.27 x lO mLfmg-wk)-1 (a) concentration vs. time and (b) rate vs. time. [Graph reconstructed from data by Rubnov et al., J. Pharm. Pharmcol., 51, 9 (1999).]... 

Fig. 4. Etch rate vs. time shows reaction to be self-retarding.

Monomer Concentration Effect. In bulk polymerizations such as those conducted in the present study, the dependence of polymerization rate on monomer concentration can be determined only on the basis of the dependence of rate on the extent of reaction. Reduction of the rate vs. time DSC traces to digital data files permits computer calculation of reaction rate as a function of monomer conversion. A computer program which yields print-out of the rate and time at given fractions of the total heat release allows computation of the order of reaction with respect to carbon-carbon double bond concentration. Assuming -80.0 cal gm l represents the... 

From the principles of thermodynamics and certain thermodynamic data the maximum extent to which a chemical reaction can proceed may be calculated. For example, at 1 atm pressure and a temperature of 680°C, starting with 1 mole of sulfur dioxide and mole of oxygen, 50% of the sulfur dioxide can be converted to sulfur trioxide. Such thermodynamic calculations result in maximum values for the conversion of a chemical reaction, since they are correct only for equilibrium conditions, conditions such that there is no further tendency for change with respect to time. It follows that the net rate of a chemical reaction must be zero at this equilibrium point. Thus a plot of reaction rate [for example, in units of g moles product/(sec) (unit volume reaction mixture)] vs time would always approach zero as the time approached infinity. Such a situation is depicted in curve A of Fig. 1-1, where the rate approaches zero asymptotically. Of course, for some cases equilibrium may be reached more rapidly, so that the rate becomes almost zero at a finite time, as illustrated by curve B. 

The heat of desorption can be deduced more simply from the maximum in the rate of evolution. The maximum rate as well as the surface concentration at the maximum, both of which enter into Eq. (12), can be obtained directly from the curve of evolution rate vs time or temperature. The graphical integration required for n can be avoided in simple first-order reactions by adopting a procedure customary in the study of thermo-luminescence. On substituting for d In nidi from Eq. (9), Eq. (12) rearranges to... 

It is also worth underlining an additional important physical meaning of lAI provided it is sufficiently larger than one. It is the ratio of the lifetimes (on the catalyst surface) of the promoting ion and of the reactants involved in the catalytic reaction. Equivalently, it is the ratio of the NEMCA-promoted catalytic rate divided by the rate of consumption of the promoting ion on the catalyst surface (due to desorption or side reaction with one of the reactants). This latter rate, which at steady state equals I/2F can also be conveniently extracted from log (rate) vs time curves upon current interruption. ... 

The observed decomposition rate vs. time curves (already discussed for the alkali and alkaline-earth azides) show an initial deceleration in the rate. This may be surface desorption or, as suggested previously, may be a consequence of a reaction occurring at sites that are consun>ed as the decomposition proceeds. 

The oxidation reaction of lactate in the presence of LOx at 23°C and 37°C was completed in 10s to 4 min, depending, as expected, on the LOx and lactate concentrations. Despite the relatively long time needed for completion of the oxidation reaction at low enzyme concentrations, a calibration curve for a given film can be obtained at shorter times by monitoring t after a constant reaction time for different analyte concentrations. A calibration curve can be obtained also by plotting the initial rate of change of t, (dr/dtjo, which is related to the initial reaction rate, vs. lactate concentration. Such a calibration... 

In this system the product of the first reaction possesses an absorption maximum at 222 nm and the final product has k ax = 288 nm. The initial reactant is essentially nonabsorbing at these wavelengths. Hence, spectrophotometric observation at 222 and 288 nm allowed two simultaneous equations to be written, and thus Cb and Cc were determined as functions of time. From the known quantity c°, the concentration Ca was calculated with Eq. (3-28). The rate constant A , was then found from the plot of In Ca vs. time. An estimate of rate constant k was obtained from a plot of In Cb vs. time in the late stages of the reaction, and this value was refined by curvefitting the Cb and Cc data. Figure 3-6 shows the data and final curve fits. 

The model GASPP was used to correlate yield vs. time for the 20 C boost to 100 C reaction temperature. With the first run, a value of kg = 0.00198 cm/sec was required to achieve the low yield reported. His second run had a yield of 13750 at 4.68 hr. Model GASPP requires kg = 0.00294 cm/sec to give this result at 100 C. This rate constant is only 2% greater than the kg reported in Table I here for the lowest activity BASF TiCi s. On this basis,... 

Plot the concentrations of the A and C cells vs. iterations n over this time frame. Determine the initial reaction rate from the first linear portion of the [C] vs. n plot also determine k from this plot. Next plot 1/[A] vs. n and determine k from this plot. Compare this value of k with that from the initial reaction rate. Does the y-intercept agree with the expectation from Eq. (8.5) ... 

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