First-order plot

To determine the reaction order we plot ln(%p-methoxyphenylacetylene) versus time for a first-order reaction, and (%p-methoxyphenylacetylene) versus time for a second-order reaction (Figure A5.1). Because the straight-line for the first-order plot fits the data nicely, we conclude that the reaction is first-order in p-methoxyphenylacetylene. Note that when plotted using the equation for a second-order reaction, the data show curvature that does not fit the straight-line model. 

The initial anhydride concentration was about 3 x 10 M, and the amine concentration was much larger than this. The reaction was followed spectrophoto-metrically, and good first-order kinetics were observed hence, the reaction is first-order with respect to cinnamic anhydride. It was not convenient analytically to use the isolation technique to determine the order with respect to allylamine, because it is easier to observe the cinnamoyl group spectrophotometrically than to follow the loss of amine. Therefore, the preceding experiment was repeated at several amine concentrations, and from the first-order plots the pseudo-first-order rate constants were determined. These data are shown in Table 2-1. Letting A represent... 

Figure 2-8. First-order plot of the hydrolysis of p-nitrophenyl glutarate at 25°C Reaction followed spectrophotometrically at 400 nm b = I cm, A = 0.900, pH 7.14.

Figure 3-13. First-order plot of simulated data for reactant A in Fig. 3-12.

We have next to consider the measurement of the relaxation times. Each t is the reciprocal of an apparent first-order rate constant, so the problem is identical with problems considered in Chapters 2 and 3. If the system possesses a single relaxation time, a semilogarithmic first-order plot suffices to estimate t. The analytical response is often solution absorbance, or an electrical signal proportional to absorbance or to another physical property. As shown in Section 2.3 (Treatment of Instrument Response Data), the appropriate plotting function is In (A, - Aa=), where A, is the... 

The data of Fig 26 can be converted into the extent of reaction plot of Fig 27. Fig 27 is a typical first-order plot and this and other data were interpreted to mean that the reaction is pseudo first-order in glycol and nitration proceeded via a N02+ mechanism... 

In a first-order reaction, the concentration of reactant decays exponentially with time. To verify that a reaction is first order, plot the natural logarithm of its concentration as a function of time and expect a straight line the slope of the straight line is —k. 

Fig. 3. a) First order plot of oxygen uptake in the Methylene-blue (MB)-sensitized photooxidation of GA 8.4 pM and 1.3 mM histidine (control) in phosphate buffer pH 7. b) Percentage radical scavenging activity for the control molecule Trolox and GA at pH 7.4 in phosphate buffer 10 mM (hydroxyl radical) and pH 10 in sodium carbonate buffer 50 mM (anion superoxide radical). 

Data must be collected over a relatively long period to determine whether a first-order plot is linear. Notice that the first five points on the plot in Example fall reasonably close to the dashed straight line. Only after more than 50% of the reactant has been consumed does this plot deviate substantially from linearity. 

The first-order plot is not linear, so the reaction cannot be first order. The straight line in the... 

Invariably, measurements of decay of reactive molecules in solid glasses are found to be nonexponential, that is, first-order plots of ln[intensity] versus time are upwardly curved, as shown in Figure 10.3. 

Determination of QMT effects often rests upon the temperature or isotope dependence of rates, as described above. Thus, the matrix site dispersity presents an immediate dilemma Which matrix sites should be compared at different temperatures or for different isotopes There have been different approaches to this problem. The most simple has been to compare the first 10-20% of the decay curves after irradiation is shut off First-order plots are generally linear in those time frames. However,... 

Figure 10.3. First-order plots of ln[Intensity] versus time, showing idealized exponential decay (dotted line), and nonexponential decay from statistical distribution of matrix sites (solid line).

The first order plot for the isomerization reaction shows a good linear fit (correlation coefficient = 0.998) while there is... 

Figure 8. First Order Plot of Isomerization Reaction at 183...

As may be seen from Figure 3, first order plots based on the conversions obtained by both methods were linear with slopes in close agreement. The apparent rate constant is 0.57 h"1 based on H2 evolution and 0.54 h"1 based on the formation of glycine salt thereby indicating that it is valid to use the simpler H2 evolution measurements when measuring the effects of process variables on the reaction. 

Figure 3 Comparison of first order plots for the formation of hydrogen and of glycine salt during ethanolamine dehydrogenation over unpromoted skeletal copper under standard conditions.

A mixture of Me3210PbCl and 210Pb(NO3)2 was used to study the rate of ionic trimethyl-lead uptake by exposed plant surfaces. More specifically, the mean cumulative activity of the lead toxicants transferred across tomato cuticle was measured daily over a six-day period. Reversed-phase HPLC was used to separate and identify the lead species crossing the plant cuticle. It was found that appreciably more trimethyllead(I) (75% of the theoretical) than inorganic lead(II) (39%) was transferred. The apparent rate constants derived from the first-order plot of time in days versus the difference in observed activity were 0.0788 and 0.0346 day-1 for transfer of the trimethyllead(I) and inorganic lead(II), respectively. 

S2 and are the slopes of the second and first order plots for the ionogenic reactions, respectively (see Figure 7)... 

The maximum concentration of SD ions, and their rate of formation were calculated from the extinction coefficient e424 = 3.8 x 103 which was obtained under the same standard conditions (see Reference [16]) t Value of xr at 0 °C S2 and S1 are the slopes of the second and first order plots for the ionogenic reactions, respectively (see Figure 7) ... 

Figure 1 shows typical first-order plots (log m versus time) for the reaction at 0 °C. The plots are curved towards the time-axis, indicating an acceleration. This acceleration only becomes evident at, or sometime after, the first half-life. The first-order rate-constants k1 in Table 1 correspond to the slopes of the rectilinear portion of the first-order plots. The kv is directly proportional to the initial concentration of the acid, as shown in Figure 2. The slope of this plot gives the second-order rate constant k2 in the rate expression ...

Figure 1 First-order plots of typical calorimetric and dilatometric experiments...

Fig. 5 (A) Typical time-resolved picosecond absorption spectrum following the charge-transfer excitation of tropylium EDA complexes with arenes (anthracene-9-carbaldehyde) showing the bleaching (negative absorbance) of the charge-transfer absorption band and the growth of the aromatic cation radical. (B) Temporal evolution of ArH+- monitored at Amax. The inset shows the first-order plot of the ion...

Fig. 9 (A) Transient absorption spectrum of the cation radical from anthracene (AnH) in CH2C12 at about 35 ps following the 532 nm charge-transfer excitation of the 0s04 complex with 30-ps (FWHM) laser pulse. The inset shows the steady-state spectrum of AnH+- obtained by spectroelectrochemical generation. (B) The decay of the charge-transfer transient by following the absorbance at Amax = 742 nm. The inset shows the first-order plot of the absorbance decay subsequent to the maximum...

First-order plots demonstrating the catalysis of transition-metai oxygenation by oxide surfaces. 

Fig. 1 a, b. Example of the first order plots of benzo[a]pyrene at two different concentrations a high b low... 

An example of first-order plots is shown in Fig. 1 for benzo[a]pyrene (i.e., B[a]P) sorption on three different soils (in terms of organic matter content) and two sediment samples (marine and fresh water) at two different concentrations [1]. It can be noted that the plots are linear at both concentrations, which would indicate that the sorption process is first order. The findings that the rate constants are not significantly changed with concentration is a good indication that the reaction is first order under the experimental conditions that were imposed. 

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