Reaction order plot

Fig. 30. Apparent reaction order plot for oxygen desorption from Ir(110) as function of coverage (124).

Fig. 43. CO reaction order plot for C02 formation on a platinum surface (132).

Fig.IF Calculation of the reaction order from the Tafel plots, a) Tafel lines for a series of concentrations of the electroactive jr species, b) Reaction-order plots derived from (a) for different...

Fig. 5. Reaction-order plots for the ORR process at the Pt/Nafion membrane interface. A unity reaction order is evaluated from the dependence of the apparent Jo on oxygen partial pressure [5], (Reprinted by permission of the Electrochemical Society).

FIGURE 2.21. Reaction order plot with respect to layer thickness for the reduction of 0.2 mAf Fe (aq) ion in 1.0 M HC104-supporting electrolyte at the Os-loaded redox metallopolymer. The linear regression line and the 98% confidence limits are shown. Note that k ME is independent of layer thickness in this case. 

Eor a pseudo-zero-order reaction a plot of [A]( versus time should be linear with a slope of -k, and a y-intercept of [A]o (equation 13.8). A plot of the kinetic data is shown in figure 13.7. Linear regression gives an equation of... 

Thus, for a second-order reaction, a plot of [A] versus f is linear, with a slope of k and an intercept of [A]o h Alternatively, a reaction can be shown to be second-order in A by observing the effect on the rate of changing the concentration of A. In this case, doubling the concentration of A produces a fourfold increase in the reaction s rate. 

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. 

Therefore, for this type of second-order reaction, a plot of 1/ca vs. t is linear, with the slope equal to k. The usual units of a second-order rate constant are liters per mole-second (M s" ). 

A reaction order determined by plotting the integrated rate equation is sometimes called the order with respect to time f this order has an unambiguous meaning only if the order is independent of time, which means that the plotted function is linear... 

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... 

Thus by measuring Vq at several values of c , the log-log plot yields the reaction order. This method also works if the rate equation includes the concentrations of other reactants, provided their concentrations are held constant throughout the series of measurements. 

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.

Determination of M . The end group concentration can be determined from Mn. However, M determinations permit only a control of the kinetic plots obtained by other methods. They are not suffidently accurate to allow unambiguous determinations of reaction orders. 

Fig. 1. 2.5-order plot for the reaction of adipic acid with diethylene glycol at 166 °C using Flory s data1. Critical study by Solomon3 ... 

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... 

Fig. 3. Reduced time plots, tr = (t/t0.9), for the contracting area and contracting volume equations [eqn. (7), n = 2 and 3], diffusion-controlled reactions proceedings in one [eqn. (10)], two [eqn. (13)] and three [eqn. (14)] dimensions, the Ginstling— Brounshtein equation [eqn. (11)] and first-, second- and third-order reactions [eqns. (15)—(17)]. Diffusion control is shown as a full line, interface advance as a broken line and reaction orders are dotted. Rate processes become more strongly deceleratory as the number of dimensions in which interface advance occurs is increased. The numbers on the curves indicate the equation numbers.

A plot illustrating that the order with respect to [H+] varies with [H+] during the reaction in which water is substituted for chloride ion in the complex (H20)5CrCl2+, Eq. (1-16). The ordinate shown is the (normalized) reaction rate, as in Eq. (1-18), and the abscissa is [H+], Both quantities are displayed on logarithmic scales. The apparent reaction orders with respect to [H+] are the limiting slopes, -1 at low [H+] and 0 at high [H+],... 

The relation between E and time can be used to determine the reaction order n in the equation v = k[A]". Following Wilkinson,16 we shall show the utility of a plot of t/E versus time, as suggested by the following expression ... 

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. 

FIGURE 13.15 The plots that allow the determination of reaction order, (a) If a plot of ln[A] against time is a straight line, the reaction is first order, (b) If a plot of 1/[A against time is a straight line, the reaction is second order. 

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... 

The curves in Figure 7.2 plot the natural variable a t)laQ, versus time. Although this accurately portrays the goodness of fit, there is a classical technique for plotting batch data that is more sensitive to reaction order for irreversible Hth-order reactions. The reaction order is assumed and the experimental data are transformed to one of the following forms ... 

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

Wetton and Higginson have briefly investigated the reaction between Fe(IlI) and Sn(II). Spectrophotometric data for the rate of disappearance of Fe(IlI) were obtained at 335 m/i. In the absence of substantial amounts of Fe(II) and Sn(lV) the kinetics in 1.0 M hydrochloric acid are of simple second order, indicating that Sn(II) is present as the monomeric species. The addition of Fe(ll) to the reacting system produces a pronounced retardation, the second-order plots showing curvature after 75 % reaction. The appropriate mechanism is... 

The rate of reduction of Tl(III) by Fe(II) was studied titrimetrically by John-son between 25 °C and 45 °C in aqueous perchloric acid (0.5 M to 2.0 M) at i = 3.00 M. At constant acidity the rate data in the initial stages of reaction conform to a second-order equation, the rate coefficient of which is not dependent on whether Tl(III) or Fe(II) is in excess. The second-order character of the reaction confirms early work on this system . A non-linearity in the second-order plots in the last 30 % of reaction was noted, and proved to be particularly significant. Ashurst and Higginson observed that Fe(III) retards the oxidation, thereby accounting for the curvature of the rate plots in the last stages of reaction. On the other hand, the addition of Tl(l) has no significant effect. On this basis, they proposed the scheme... 

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