Semilogarithmic plot

A more accurate value of can be obtained by taking a ratio of slopes of the cui-ves of Fig. 12-43. Thus the ratio of the slope of the experimental cui ve of unaccomphshed moisture change versus drying time on a semilogarithmic plot [Eq. (12-32)] to the slope of the theoretical cui ve at the same unaccomphshed moisture change, again on a semilogaritmic plot, equals the quantity Df/d. If d is known, Df can be evaluated. 

Rgure 2 (a) Semilogarithmic plot of the positive relative ion yields of various certifiad... 

A parameter such as a rate constant is usually obtained as a consequence of various arithmetic manipulations, and in order to estimate the uncertainly (error) in the parameter we must know how this error is related to the uncertainties in the quantities that contribute to the parameter. For example, Eq. (2-33) for a pseudo-first-order reaction defines k, which can be determined by a semilogarithmic plot according to Eq. (2-6). By a method to be described later in this section the uncertainty in itobs (expressed as its variance associated with cb. Thus, we need to know how the errors in fcobs and cb are propagated into the rate constant k. 

Figure 2-11, Semilogarithmic plot of the hydrolysis of p-nitrophenyl glutarate in the presenee of p-methoxycinnamate ion 25.0°C, initial pH 7.53, reaction followed at 400 nm. The plot deviates from linearity after the first half-life.

Figure 3-4. Semilogarithmic plot of the concentration-time curves of Fig. 3-2.

If the data consist of Cb as a function of time, another approach can be used. As above, the smaller rate constant (say kj) estimated from a semilogarithmic plot of Cb at later times when Ca is negligible. This plot is extrapolated back to t = 0. This line is described by the equation [from Eq. (3-27)],... 

Carry out a manual Monte Carlo simulation of Scheme I, using [A]o = 100, [B]o = 0, n, = 7, n i = 3. Compare the equilibrium constant obtained in the simulation with the tme value. Make the semilogarithmic plot according to Eq. 3-40 and interpret its slope. 

Next a period of time T (T > T ) is allowed for the entire system to relax to its steady-state configuration. Then the pulse sequence is repeated, with a different value for t. In this way the decay of M is measured by sampling it via the 90° pulse. The sequence is called a 18(f, t, 90° sequence. l/T, is found from a semilogarithmic plot. 

A graph of the fraction of single-stranded DNA reannealed c/cq) as a function of CqI on a semilogarithmic plot is referred to as a c t (pronounced cot ) curve (Figure 12.20). The rate of reassociation can be followed spectrophoto-metrically by the UV absorbance decrease as duplex DNA is formed. Note that... 

Figure 50. Semilogarithmic plot of cathodic (Ec) and anodic (E) potentials against values of 1 IQ [cPQityd ] extracted from Figs. 52 and 53. Following Eq. (48), values of the coefficient of electrochemical relaxation (zr) and the coefficient of cathodic polarization (ze) can be deduced from the slopes. (Reprinted from T. F. Otero and H.-J. Grande, Reversible 2D to 3D electrode transition in polypyrrole films. ColloidSurf. A. 134,85, 1998, Figs. 4-9. Copyright 1998. Reproduced with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 Amsterdam, The Netherlands.)...

Figure 59. Semilogarithmic plot of the peak potential (Ep) vs. the scan rate (v). (Reprinted fromT. F. Otero, H.-J. Grande, andJ. Rodriguez, J. Phys. Chem. 101, 8525, 1997, Figs. 3-11, 13. Copyright 1997. Reproduced with permission from the American Chemical Society.)...

Figure 1. Semilogarithmic plot of brevetoxin ( iCi) in plasma over time after an intravenous injection of tritium-labeled PbTx-3. T 1/2 alpha = 30 sec T 1/2 beta = 112 min.

Thus, in the case of two-step reactions, different methods of determining the exchange CD generally yield different results (in contrast to the case of simple reactions discussed earlier) Extrapolation of the limiting anodic and cathodic sections of the semilogarithmic plots yields values and if, respectively, while the slope of the linear section in an ordinary plot of the polarization curve yields the value of ig. It is typical for multistep reactions that the exchange CD determined by these methods differ. 

It can be seen from Fig. 15.2 that in semilogarithmic plots of AE vs. log/, the polarization characteristics are linear [i.e., obey the Tafel equation (6.3)]. Slopes b practically coincide for most metals and have values of 0.11 to 0.13 V. However, the absolute values of polarization recorded for a given current density (CD) vary within... 

Fig. 39.5. (a) Plot of plasma concentration Cp (pg 1 ) versus time t. Cp(0) is the extrapolated initial concentration at time zero. At the half-life time tm the plasma concentration is half that of Cp(0). (b) Semilogarithmic plot of plasma concentration Cp (pg 1 ) versus time t. The intercept B of the fitted line is the plasma concentration Cp at time 0. The slope jp is proportional to the transfer constant of... 

Fig. 39.6. (a) Time courses of plasma concentration Cp in the one-compartment open model for intravenous injection, with different contingencies for the transfer constant of elimination kfe and the volume of distribution Vp. (b) Time courses of plasma concentration Cp as in panel (a) on semilogarithmic plots. 

The semilogarithmic plot of the data is given in Fig. 39.8a. On this plot we can readily identify the linear 3-phase of the plasma concentrations between 30 and 240 minutes. The last three points (at 360, 480 and 720 minutes) have been discarded because the corresponding plasma values are supposed to be close to the quantitation limit of the detection system. 

Hence, the slope of the semilogarithmic plot of 1 - Cp tVC versus time t yields the transfer constant of elimination kp. From the known rate constant of infusion k, the transfer constant of elimination kp and a graphical estimate of one can then derive the plasma volume of distribution Vp, using the steady-state condition which has been derived above. 

From a semilogarithmic plot of Cp(t) versus r - x, one can again estimate the transfer constant of elimination kp. From the known values of Cp(x), k and kp one also obtains a new estimate of Vp. 

Fig. 39.13. (a) Semilogarithmic plot of the plasma concentration Cp (pg 1 ) versus time /. The straight line is fitted to the later part of the curve (slow P-phase) with the exception of points that fall below the quantitation limit. The intercept Bp of the extrapolated plasma concentration appears as a coefficient in the solution of the model. The slope is proportional to the hybrid transfer constant p, which is itself a function of the transfer constants of and ifcbpOf the model, (b) Semilogarithmic plot of the... 

These data are also shown in the semilogarithmic plot in Fig. 39.13a, which clearly shows two distinct phases. A straight line has been fitted by least-squares regression through the data starting from the observation at 90 minutes down to the last one. This yields the values of 1.086 and -0.001380 for the intercept log and slope ip, respectively. From these results we have computed the extrapolated p-phase values between 2 and 60 minutes. These have been subtracted from the experimental Cp values in order to yield the a-phase concentrations C ... 

The residual a-phase concentrations C are shown in the semilogarithmic plot of Fig. 39.13b. Least-squares linear regression of log C upon time produced 1.524 and -0.02408 for the intercept log and the slope respectively. 

Quinn et al. studied ET at micro-ITIES supported by micropipettes or microholes [16]. The studied systems involved ferri/ferrocyanide redox couple in aqueous phase and ferrocene, dimethylferrocene, or TCNQ in either DCE or o-nitrophenyl octyl ether. Sigmoidal, steady-state voltammograms were obtained for ET at the water-DCE interface supported at a micropipette. The semilogarithmic plot of E versus log[(/(j — /)//] was... 

The voltammograms at the microhole-supported ITIES were analyzed using the Tomes criterion [34], which predicts ii3/4 — iii/4l = 56.4/n mV (where n is the number of electrons transferred and E- i and 1/4 refer to the three-quarter and one-quarter potentials, respectively) for a reversible ET reaction. An attempt was made to use the deviations from the reversible behavior to estimate kinetic parameters using the method previously developed for UMEs [21,27]. However, the shape of measured voltammograms was imperfect, and the slope of the semilogarithmic plot observed was much lower than expected from the theory. It was concluded that voltammetry at micro-ITIES is not suitable for ET kinetic measurements because of insufficient accuracy and repeatability [16]. Those experiments may have been affected by reactions involving the supporting electrolytes, ion transfers, and interfacial precipitation. It is also possible that the data was at variance with the Butler-Volmer model because the overall reaction rate was only weakly potential-dependent [35] and/or limited by the precursor complex formation at the interface [33b]. 

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

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