Reaction vs. time

Figure 5. Per cent of final reaction vs. time, 1.5% calfskin gelatin, at 10° C., pH 6.0, 0.1 Ai sodium chloride...

Fig. 11 Time-resolved in-situ EDXRD data showing the intercalation of methylphosphonate into hexagonal [LiAl2(0H)6]Cl H20. a 3D stacked plot, b Plot of extent of reaction vs time for the (002) reflections of the host and product and the (004) reflection of the intermediate. Reproduced with permission from Chem Commun (2003) 15 1816-1817...

Fig. 14 Time-resolved data for the intercalation of methylphosphonate into hexagonal LiAl - Br. a 3D stacked plot, b Extent of reaction vs. time plots for host, intermediate and product...

Fig. 19 Extent of reaction vs time for the reaction between CaAl - NO3 and 1,2-BDA. The reflection at 8.7 A corresponds to the host material, that at 14.8 A to the 1,2-BDA intercalate, and the 11.2 A reflection to Ca(l,2-BDA). Reproduced with permission from Chem Mater (2000) 12 1990-1994...

A study of the completion of reaction vs. time was also made on the direct esterification of a typical olefin with a primary alkyl acid 0-phthalate. By titration of the reaction mass with 0.5N sodium hydroxide, we determined the rate of reaction using standard conditions of catalyst level, reaction temperature and olefin excess as previously described. The acid value reached a minimum and longer time cycles did not reduce this to any great extent. 

This system of equations was solved by a predictor-corrector method for several values of a, / , and y using a digital computer. It was not possible to examine values of ft above 50 (a = 0.001, y = 0) as the method broke down because of accumulated errors. Up to these values, although a step is formed in the extent of reaction vs. time curve, the rate of acceleration in the third phase of the reaction was much slower than observed in the experiments. 

Figure 2. Comparison of the course of reaction (degree of reaction vs. time) of samples composed of identical spherical particles of various diameter. Conventionally, dimension unit is 1 for the curve at the left (adapted from Fig. XI.23, Ref. [7]).

The results of in situ 14N NMR study of the reaction vs time at 150°C (Fig. 9(a)) in the presence of imidazole and DABCO show a pH increase from 3.2 to 6 in the first 2 h of the reaction and then an almost constant value of 6 during the rest of the synthesis. This value, which indicates quasi neutral conditions since pKa is 11.5 at 150°C, is precious when considering speciation, protonation of ligands and coordination of A1 atoms. 

Figure 3. Percent reaction vs. time for BA-DAB-BA (neat) and BA-DAB-BA (with I % initiator) at 177°C, isothermal air cure.

Figure 9. Fractional reaction vs. time for neat PP (a) and PP-MAPP-Cloisite 20A (b) Mass/%...

Chemists chart the total energy of a chemical reaction vs. time using a graph called an energy diagram. 

End Point vs Kinetic Methods. Samples may be assayed for enzymes, ie, biocatalysts, and for other substances, all of which are referred to as substrates. The assay reactions for substrates and enzymes differ in that substrates themselves are converted into some detectable product, whereas enzymes are detected indirectly through their conversion of a starting reagent A into a product B. The corresponding reaction curves, or plots of detector response vs time, differ for these two reaction systems, as shown in Eigure 2. Eigure 2a illustrates a typical substrate reaction curve Eigure 2b shows a typical enzyme reaction curve (see Enzyme applications). 

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. 

Thus, the technique consists of a transformation from the time differential dt to the area differential dQ, and the essential effect of this transformation is a reduction by one of the apparent order of the reaction. The variable 6 is the area under the curve of Cb vs. time from t = 0 to time t. With modem computer techniques for integrating experimental curves, this method should be attractive. 

The kinetics of the reactive compatibilization of nylon-6-PP by acrylic acid modified PP was investigated by Dagli et al. [47]. The compatibilization reaction in this system involved the reaction between the acid group of acrylic acid modified PP and the amine group of nylon-6. A typical intensive batch mixer torque (t) vs time (t) trace for a ternary blend showing an increase in mixing torque upon the addition of PP-g-AA to a binary PP-NBR (85 7.5) blend is shown in Fig. 3. The kinetic... 

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,... 

Fig. 2 shows the plot of ln[(CEcVCEc] vs. time during first 2 h. Quite good straight lines were obtained, and the pseudo first-order reaction rate constants for 120,130 and 140 °C were 0.002421, 0.002481 and 0.002545 h, respectively. From the Arrhenius plot of the first order reaction rate constants, one can estimate the activation energy as 41.5 kJ/mol. 

A plot of ln([ A]g / [A]) vs. time in hours for the conversion of an alkyl bromide to an alkene. The experimental data are shown in the table. The linearity of this plot verifies that this reaction obeys a first-order rate law. 

Case 11 Evaluation. When kinetic data in terms of reaction conversion vs. time are used to fit the kinetic model expressed by equation (28) with the value of a, 0.0102, determined by the best curve fit, the ealeulated eonversion vs. reaetion time over the entire reaction period presented in Figure 3.4 is in good agreement with the experimental data. 

The catalyst deactivation can be calculated with equation (27). Figure 3.5 shows that the slope of the plot of In(l-x) vs. reaction time is 0.0138 at the beginning of the reaction. If there is no catalyst deactivation, the data of In(l-x) vs. time should follow a straight line. The deviation from this straight line indicates that the total catalyst concentration decreases as the reaction progresses. Using equation (27), the value for a, proportional to total catalyst concentration, can be determined from the conversion X and reaction time. As shown in this figrrre, the value for a becomes 0.0054 at the end of the reaction. 

Figure 3.10 Reaction Conversion vs. Time Figure 3.11 Effect of Initial Substrate at Various Initial Substrate Charges. Charge on Total Reaction Time.

Figure 50.1. Comparison of conversion vs. time for the reaction of Scheme 50.1 using HPLC sampling of product concentration to in situ monitoring by FTIR spectroscopy and reaction calorimetry.

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].

Figure 16 Reaction rate determination of 1,2/1,4 ketal in LANA reaction (scheme 5). Yield, graphed on the y-axis vs. time on the x-axis, was estimated by RPLC on Zorbax C18. Column 25 cm x 4.6 mm (5 p). The mobile phase was 100 mM KH2P04 (pH 6.5) acetonitrile (45 55) at 1.0 ml/min. The column temperature was 35°C, and detection was at 254 nm.

The validity of the conclusion regarding the reaction scheme can be verified from Figure 5, which plots relative moles of each species vs time. There is a rapid rise in monoadduct and diadduct content initially. Shortly after initial mixing, a rapid decrease in monoadduct with a significantly slower decline in diadduct content is seen. Triadduct is slow to form and slow to react. 

Confirmatory values of K were obtained from plots of loge 0.025 vs. time in the early stages of the reaction,... 

Equation (13) appears to be a good approximation for describing isothermal chemiluminescence kinetics for homogeneous systems where oxidation takes place uniformly. However, as has been shown by several authors [53-58], the different sections of a polymer sample may oxidize with its autonomous kinetics determined by different rates of primary initiation. A chemiluminescence imaging technique revealed that the light emission may be spread from some sites of the polymer film and the isothermal chemiluminescence vs. time runs are then modified, particularly in the stage of an advanced oxidation reaction [59]. 

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