Graphical methods, kinetic

That is, ipKa = pH at the point where Eq. (6-66) holds. Because the larger of the two constants is usually much greater than the smaller one, this often may be interpreted that pA o = pH when k = k J2 (see Fig. 6-10). Graphical methods for estimating K by using all of the kinetic data are considered later. 

The plotting of Dixon plot and its slope re-plot (see 5.9.5.9) is a commonly used graphical method for verification of kinetics mechanisms in a particular enzymatic reaction.9 The proposed kinetic mechanism for the system is valid if the experimental data fit the rate equation given by (5.9.4.4). In this attempt, different sets of experimental data for kinetic resolution of racemic ibuprofen ester by immobilised lipase in EMR were fitted into the rate equation of (5.7.5.6). The Dixon plot is presented in Figure 5.22. 

Wang, X., Stoll, D.R., Carr, P.W., Schoenmakers, P.J. (2006). A graphical method for understanding the kinetics of peak capacity production in gradient hquid chromatography. J. Chromatogr. A 1125, 177-181. 

The kinetic data below were reported for an enzyme catalyzed reaction of the type E + S ES E + P. Since the data pertain to initial reaction rates, the reverse reaction may be neglected. Use a graphical method to determine the Michaelis constant and Fmax for this system at the enzyme concentration employed. 

Warning if a chemical process comprises several reaction steps, only the progress of the slowest step can be followed kinetically. These graphical methods of determining k are only useful for obtaining the rate-determining step (RDS) of such reactions. Although the reaction may appear kinetically simple, it is wisest to assume otherwise. 

A linear graphical method for analyzing the initial rate kinetics of enzyme-catalyzed reactions. In the Hanes plot, [A]/v is plotted as a function of [A], where v is the initial rate and [A] is the substrate concentration ". ... 

ATOM PERCENT EXCESS OXYGEN ISOTOPE EXCHANGE COMPARTMENTAL ANALYSIS ISOTOPE EXCHANGE KINETICS GRAPHICAL METHODS... 

Figure 14.8 Graphical method of evaluating the performance of N tanks in series for any kinetics.

Figure 6.2 Graphical method of analyzing the kinetics of a reaction obeying equation 6.16. The logarithm of [B] is plotted against time. The rate constant for the slower process is obtained from the slope of the linear region after the faster process has died out. The rate constant for the faster process is obtained by plotting the logarithm of A (the difference between the value of [B] at a particular time and the value of [B] extrapolated back from the linear portion of the plot) against time for the earlier points. The rate constants for this example are 20 and 2 s 1, respectively.

A useful empirical approach to the design of heterogeneous chemical reactors often consists of selecting a suitable equation, such as one in Table 3.3 which, with numerical values substituted for the kinetic and equilibrium constants, represents the chemical reaction in the absence of mass transfer effects. Graphical methods are often employed to aid the selection of an appropriate equation140 and the constants determined by a least squares approach<40). It is important to stress, however, that while the equation selected may well represent the experimental data, it does not... 

Yang, S. T. and M. R. Okos, "A New Graphical Method for Determining Parameters in Michaelis-Menten Type Kinetics for Enzymatic Lactose Hydrolysis "Biotechnol. Bioeng. 34 (1989) 763 - 773. 

Simple, graphical methods for testing the fit of rate data to Equation 9 and for estimating the kinetic parameters k2 and KR involve using linearized forms of Equation 9. By far the most widely used linear form is that of Kitz and Wilson (14). Taking reciprocals of both sides of Equation 9, we obtain... 

Accurate comparison of results requires knowledge of reaction site density per unit surface area. Calcite materials used for kinetic study have included natural marbles, limestones, hydro-thermal crystals of Iceland spar, tests of calcareous organisms and laboratory and commercial precipitates. Surface areas, estimated by BET methods and graphical methods (based on particle size distribution) range from about 0.005 to 2 m g . There are apparent discrepancies between graphical and BET surface areas and the question is raised as to which type of surface area estimate is most representative of the reacting surface area. 

Hamlin WE, Chulski T, Johnson RH, Wagner JG. A note on the photolytic degradation of antiinflammatory steroids. J Am Pharm Assoc (Sci Ed) 1960 49(4) 253-255. Pawelczyk E, Knitter B, Knitter K. Kinetics of drug decomposition. Part 50 graphic method for calculation of zero-order rate constants of indomethacin photodegradation. Pharmazie 1977 32(8-9) 483 85. 

Numerical solutions have been presented for the impedance response of semiconducting systems that accoimt for the coupled influence of transport and kinetic phenomena, see, e.g., Bonham and Orazem. Simplified electrical-circuit analogues have been developed to account for deep-level electronic states, and a graphical method has been used to facilitate interpretation of high-frequency measurements of capacitance. The simplified approaches are described in the following sections. 

Systems that are governed by reaction kinetics show well-defined behaviors as a function of temperature and potential. If the system can be described as being controlled by a single activation-energy-controlled process, graphical methods can be used to cause the data to superpose. 

These equations are solved graphically as in Figure 9.13 in which the left-hand side of the integrated form of the kinetic equations is the ordinate and the term 1/T is the abscissa. The graphical method involves the best approximation of the curve to a straight line [28]. 

Although computer software is now readily available to fit enzyme kinetic data to the Michaelis-Menten and related equations, it can be instructive to use simple graphical methods in some cases. The most convenient of these (though not necessarily the most accurate) are based on doublereciprocal methods that convert the hyperbolic rate equations into much simpler linear forms for plotting. 

Lineweaver-Buik double-reciprocal plot a graphical method for analyzing the kinetics of enzyme-catalyzed reactions (6.6)... 

Similar methods may be used for analysis of selectivity, yield, and concentration maxima in other types of parallel or sequential reaction schemes with either reversible or irreversible steps. However, when the kinetics involve other than first-order rate laws, convenient analytical solutions cannot be obtained, in general, and step-by-step calculations are probably more convenient. Also, the graphical method illustrated in Figure 4.15 is not applicable for parallel or sequential schemes because normally the rate of appearance or consumption of intermediates of interest depends on the concentration of more than one species and representation of rate in a single (—r) versus C relationship is not possible. 

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