First-order rate plots

On this basis = 0.0170 sec , = 0.645 sec , and K = 0.739 mole.P at 25 °C. The corresponding activation parameters were determined also by Es-penson. By a method involving extrapolation of the first-order rate plots at various wavelengths to zero time, the absorption spectrum of the intermediate was revealed (Fig. 1). Furthermore, the value of K obtained from the kinetics was compatible with that derived from measurements on the acid dependence of the spectrum of the intermediate. Rate data for a number of binuclear intermediates are collected in Table 2. Espenson shows there to be a correlation between the rate of decomposition of the dimer and the substitution lability of the more labile metal ion component. The latter is assessed in terms of the rate of substitution of SCN in the hydration sphere of the more labile hydrated metal ion. 

Figure 2. First-order rate plots for the consumption of CO in a 100-mL batch reactor (catalyst solution is 5 mL of aqueous diglyme with .5M HtO, 1.0M H2SO,lf T = 100°C and Pco (initial) = 0.9 atm). Slopes of the three linear plots are 2 X 10 2, 4.4 X JO 2, and 9.3 X JO 2 hr1 for the respective Ru (CO)I2 initial concentrations of (I) 0.006M, (II) 0.012U, and (III) 0.024U.

The results of this study and similar studies carried out in other solvents are included in Table I and are plotted in Figure 2. Rate constants for scrambling of label, derived from the first-order rate plots of Figure 2, are listed in Table II. 

Fig. 13. Typical first-order rate plots showing effect of varying initial cupric...

No reaction at all took place at 25°C in the absence of carbon so that the measured rates could be completely ascribed to the action of the catalyst, Decolorizing Charcoal Cl77. The concentrations of both cobalt complexes were spectrophotometrically monitored with time and it was noted that the sums of the concentrations of the two species were always 2-3% short of the initial concentrations. Since the intercepts of the first-order rate plots at zero time also gave concentrations 2-3% lower than the initial values, these apparent discrepancies clearly pointed to a small amount of fast adsorption. The rates were independent of the shaking speed which marked the catalysis as surface-controlled. The kinetics of this surface reaction were, however, extremely complicated. Mureinik systematically varied the concentrations of the relevant species he found that the plot of the effective first-order rate... 

By way of example, Figure 6.2 shows a first order rate plot for the stirred contact of sodium form styrenesulfonate cation exchange resin (12% DVB) with 0.001 M hydrochloric acid solution at 25 C. The system data and calculated rate constant are given in Table 6.1. The activation energy may be found from the temperature dependence of the rate constant and was found to equal 16.7 kj eq. This same data is redeployed later according to more rigorous diffusion theory. 

Figure 1 shows the first-order rate plots for the neutral substrates and the plots for the anionic substrates are shown in Figure 2. The kinetic parameters may be evaluated from Equation (4). A plot of 1/(kobs l) 1/[C] yields a straight line for each of the systems with the values of kj, k2, and the association constants K determined from the slope and intercept of these plots. These values are given in Table I for the neutral and anionic substrates.

Figure 4 First-order Rate Plots of e-Caprolactone Polymerization ([M] = 1 [Initiator] = 0.5 x 10 )...

Figure 3 shows first order rate plots of the negative log of AP residual vs. time for solutions aged 505 to 625 hours. The individual AP residual points were determined by subtracting data points of Figure 2 from the values of the extrapolated (dotted) lines at the same analysis reaction times. 

FIGURE 16. First-order rate plots for the disappearance of the colored forms of 6 -chloro-8 -ni tro-1,3,3-trimethyli ndoli nobenzopyrylospi ran at 300°K A, form a in polymethylmethacrylate ... 

Homogenous atom-transfer radical polymerization of methyl methacrylate under microwave irradiation conditions has also been studied by Zhu et al. [23, 24]. In a typical run, a small amount of CuCl, N,N,N, N",N"-pentamethyl-diethylenetriamine, with ethyl 2-bromobutyrate as activator-initiator system, were placed in a 10-mL glass tube with 1 mL DMF and 5 mL methyl methacrylate. The tube was sealed and placed in a two-necked reaction flask filled with hexane, so that temperature was controlled by the boiling point of the solvent during reflux in a modified domestic microwave oven. Linear first-order rate plots, linear in-... 

Figure 8.7 Association of pHJiloprost with the membrane receptor of NCB-20 cells. Total ( ), non-specific ( ), and specific binding (A) of 15 nmolL pH]iloprost at 20°C are shown in A. A pseudo first-order rate plot of the data up to 900 s is shown in B. Beq is the specific [ Hjiloprost binding at equilibrium, and Bt is the specific binding at each time, t. (Reproduced from reference 28 with permission)...

The linear first order rate plot obtained once the equilibrium is established indicates that (i) the polymerization is first order with respect to monomer and (ii) the concentration of active centers remains constant during the polymerization. From figure 3, it is seen that the rate of polymerization increases with the size of the macroinitiator. Furthermore, the different overall rates of polymerization observed were higher than the one of a typical LRP of alkyl methacrylate with ethyl 2-isobutyrate under similar conditions. 

Solutions of triphenylarsine and [Fe(nmt)2] in acetonitrile take up oxygen slowly with formation of triphenylarsine oxide [133], The rate of oxygen consumption by triphenylarsine was slow (/1/2 = 10-50hr), but the first-order rate plots were linear over more than two half-times. For [Fe(mnt)2] = 1.93 x 10" M, [ni As] = 3.3 X 10 M, t,/2 = 36hr in oxygen. 

Figure 3. First-order rate plots for poly(propylene ether) diol formation at 50°C...

In all the reactions, the pseudo-first-order rate plots remained relatively linear, with only a slight amount of... 

Figure 4 shows the first-order rate plots for the polymerization of N—Ts—PTL at 4% concentration in DMF solution for various concentratjon of benzyl mercaptan 0.2, 0.1, 0.06 and 0.01 g/100 ml. The rate constants were 7.2, 7.09,7.1 and 7.2 ml g hr", These values are corrected for the rate increase for the spontaneous polymerization caused by solvent. The fairly constant values of rate constant over wide range of initiator concentration and for practically the entire course of polymerization demonstrates the rate of polymerization to be proportional to the monomer and initiator concentration. 

Fig. 4. First-order rate plots for polymerization of NTs—PTL at 4% concentration in a mixture of 1 1 DMF and toluene for various concentration of benzylmercaptan (g/100 ml) (o) 0.2 (o) 0.1 ( ) 0.06 ( ) 0.01 ( ) blank. (The data are redrawn from Reference [5].)...

First order rate plots for the polymerization of methyl acrylate initiated by V-70 and AIBN at 333 K in the presence of (TMP)Co and (TMP)Co-CH(C02CH3)CH3 are illustrated in Figure 5.7. AIBN has a half life of about 18 hours at 333 K in benzene and the much slower entry of radicals into solution compared to V-70 (ti/2(333K) = 11 minutes) permits attaining a near constant steady state radical concentration which simplifies the kinetic analysis. The rate of MA polymerization after the induction period follows first order rate behavior where the slope of ln([M]o/[M]/) versus time is proportional to the square root of the initiator concentration ([AIBN] ). This demonstrates that the rate of MA polymerization is controlled by the AIBN concentration and not by the organo-Co(TMP) mediator complex which is a signature criterion for a degenerative transfer (DT) process. 

FIGURE 4.10 First-order rate plots for seeded butyl lithium polymerizations for monomers in benzene, hexane, or tetrahydrofuran. (Data from Morton, M., AIChE Symp. Polymer Kinetics Catalyst Systems, December 1961.)... 

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