Inversion plots

However, it is often observed that the correlation of addn/rearr vs. [alkene] is not linear, but curved.17-20,25-28 On the other hand, a double inverse plot of [4]/[5] (rearr/addn) vs. l/[alkene] is linear These results can be understood if a second intermediate, besides the carbene, contributes to the formation of product 4. The kinetic and mechanistic formulation of this scenario appears below (Section III.B). 

FIGURE 15. Inversion plot A, reaction of 2,4-dinitroanisole with cyclohexylamine at 80 °C ( ) B, reaction of 2,4-dinitroanisole with rc-butylamine (n-BA) in benzene in 80 C (O, data from Reference 143a)144. Reprinted with permission from Reference 144. Copyright (1983) American Chemical Society... 

The two kinetic parameters (< >(lim) and k /kr) can be resolved quite easily by means of a simple inverse plot. The limiting quantum yield for L = PPtu is quite substantial, having a value of about 0.15 0.03. 

In a SISO system we normally make a Nyquist plot of the total openloop transfer function B. If the system is closedloop stable, the (— 1,0) point will not be encircled positively (clockwise). Alternatively, we could plot l/Gu B). This inverse plot should encircle the (— 1, 0) point negatively (counterclockwise) if the system is closedloop stable. See Fig. 16.4. 

Figure 3.3 Inverse plot of the velocity of disappearance of NADH as a function of pyruvate concentration.

The inverse plot of a hyperbolic equation is linear, and so the inverse plot of Equation (15.1) is... 

Figure 15.5 shows inverse plots obtained at pH 7 and 3. The plots are obtained by using all the measurements performed. This yields a value of A /rnax of 96.52 and 67.52 at pH 3 and 7, respectively, with dissociation constants equal to 1.74 and 6.28 //M, respectively. 

FIG. 4.8. Double inverse plot of specific binding over total applied radioactivity as a function of increasing cell concentration (C) using the A431 cell line. 

Figure 7.3. (a) Comparison of the Langmuir isotherm calculated by react, phreeqc, and Equation (7.7). (b) Inverse plot and least squares fit for the equation results. 

The inverse plot gives the expected results for the equation results. An inverse plot of the computer program results gives a straight line, but with a different slope and intercept. 

Figure 2. Inverse plot of sorption of water by poly(ethyl methacrylate) top curve, calculated Henry s Law isotherm Bottom curve, experimental data...

An inverse plot of the van Deemter Equation (Fig. 8) illustrates the relationship between colunm efficiency and flow rate. 

Hofstee, B.H. (1959) Non-inversed versus inversed plots in enzyme kinetics. Nature, 184,1296-1298. 

A phase inversion plot was developed for the Cjg alkyldiphenyl oxide disul-fonate/alcohol ethoxylate blends at a temperature of 35°C (Fig. 5). The y-inter-cept in this plot is equivalent to the optimal composition of the surfactant film. This composition provides the lowest oil-water interfacial tension at a given temperature. If the ratio of nonionic surfactant to anionic surfactant is lower than the optimum, the system is too hydrophilic in nature and tends to form an oil-inwater emulsion. Similarly, if the ratio of nonionic surfactant to anionic surfactant is higher than the optimum, a water-in-oil emulsion forms. The plot shown in Figure 5 was developed by using electrical conductivity measurements as outlined by Raney [12] to identify the transition from a high-conductivity oil-in-water emulsion to a low-conductivity water-in-oil emulsion. 

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