Reaction rate plot

The Q (initial reaction rate) plots were presented in Fig. 19. Note again that the data may be correlated well by straight lines for both models. The C2 values are correlated by the solid lines of Fig 20. Note that the dual-site values can again be correlated by a straight line, but that the single-site values of C2 show a definite curvature. Alternatively, the 0.975 atm value of the single-site C2 could be rejected, and the three high-pressure points... 

The apparent order of reductive dissolution of Mn(III/IV) oxides can be determined experimentally from the slope of the log of reaction rate plotted versus pH (Stone, 1987a) ... 

Effect of Temperature on Reaction Rate. Plots of Xgg vs. W/Fgg were obtained at Pg2 = 2.0 kPa and Pco 2.3 kPa for three different temperatures. The values of Rq obtained from these graphs were plotted against 1/T to obtain an activation energy of 1.273 x 105 J/mol. 

MM A. Figure 6 shows the over-all reaction rate plotted logarithmically vs. time in case of the y-emulsion polymerization of MM A. After the sharp rise of Ufir, a period of zero order of Ubf seems to follow. But then Ubf increases further and reaches a maximum at about 50% conversion. Soon afterwards, the curve drops sharply, and Ubf decreases almost as fast as if the radiation source were removed at this point. This decrease does not follow, or follows for only a short time, a first-order law with respect to monomer concentration. There also is no reaction of the second order with respect to [M]. 

The first order reaction rate plot of Pd-Pt catalysts on ASA and MPS are given in Fig. 3. 

Fig. 3. First order reaction rate plot of various catalysts, a. Pd-Pt/ASA and b. Pd-Pt/MPS (Table 3).

Figure 4. Initial reaction rates, plotted against increasing substrate concentrations for a reaction obeying the Michaelis-Menten kinetics, and assuming that = Ka = i-...

Fig. 7 b. Normalized reaction rate plotted against substrate concentration for a reaction obeying Michaelis-Menten kinetics in reverse micelles. The abscissa shows the two scales of concentration, overall and local (or water pool) with 1% water, v v, and the two corresponding K -values... 

Figure 8. Figure (a) shows how the length of the initiation period varies with the inverse of the TPP concentration, (phr h. Figure (b) shows maximum ionic "reaction rate" plotted against the square of the TPP concentration, (phr ). 

Figure 16.10 Predicted and actual reaction rate plots for the octyl bromide-potassium acetate system in the presence of polymer-supported TBMAC catalyst at 95°C and at 0.25 and 0.5 mol/l< g octyl bromide concentration levels. (Adapted from Satrio, J.A.B., Glatzer, H.J., and Doraiswamy, L.K., Chem. Eng. ScL, 55(21), 5013, 2000.)...

Fig. 2. Reaction rate plots for the addition of poly(butadienyl)lithium (PBDLi) (Mn=1400g/mol) to 1,1-diphenylethylene in cyclohexane at 25 °C with [PBDLi]=l.lx 10 mol/1...

Figure 6-9f Another form of residual plot to test Michaelis-Menten rate equation for fructose isomerization using xylose isomerase derived fiom T. neapolitana. Residuals in reaction rate plotted against experimental values of reaction rate.

In the reaction kinetics context, the tenn nonlinearity refers to the dependence of the (overall) reaction rate on the concentrations of the reacting species. Quite generally, the rate of a (simple or complex) reaction can be defined in temis of the rate of change of concentration of a reactant or product species. The variation of this rate with the extent of reaction then gives a rate-extent plot. Examples are shown in figure A3.14.1. In... 

The Arrhenius relation given above for Are temperature dependence of air elementary reaction rate is used to find Are activation energy, E, aird Are pre-exponential factor. A, from the slope aird intercept, respectively, of a (linear) plot of n(l((T)) against 7 The stairdard enAralpv aird entropy chairges of Are trairsition state (at constairt... 

Deming and Pardue studied the kinetics for the hydrolysis of p-nitrophenyl phosphate by the enzyme alkaline phosphatase. The progress of the reaction was monitored by measuring the absorbance due to p-nitrophenol, which is one of the products of the reaction. A plot of the rate of the reaction (with units of pmol mL s ) versus the volume, V, (in milliliters) of a serum calibration standard containing the enzyme yielded a straight line with the following equation... 

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. 

The result is shown in Figure 10, which is a plot of the dimensionless effectiveness factor as a function of the dimensionless Thiele modulus ( ), which is R.(k/Dwhere R is the radius of the catalyst particle and k is the reaction rate constant. The effectiveness factor is defined as the ratio of the rate of the reaction divided by the rate that would be observed in the absence of a mass transport influence. The effectiveness factor would be unity if the catalyst were nonporous. Therefore, the reaction rate is... 

A linear plot of the reciprocal of the reaction rate versus 1/(S) will allow the determination of Km and from experimental data. 

The laboratory studies utilized small-scale (1-5-L) reactors. These are satisfactoiy because the reaction rates observed are independent of reac tor size. Several reac tors are operated in parallel on the waste, each at a different BSRT When steady state is reached after several weeks, data on the biomass level (X) in the system and the untreated waste level in the effluent (usually in terms of BOD or COD) are collected. These data can be plotted for equation forms that will yield linear plots on rec tangular coordinates. From the intercepts and the slope or the hnes, it is possible to determine values of the four pseudo constants. Table 25-42 presents some available data from the literature on these pseudo constants. Figure 25-53 illustrates the procedure for their determination from the laboratory studies discussed previously. 

These equations hold if an Ignition Curve test consists of measuring conversion (X) as the unique function of temperature (T). This is done by a series of short, steady-state experiments at various temperature levels. Since this is done in a tubular, isothermal reactor at very low concentration of pollutant, the first order kinetic applies. In this case, results should be listed as pairs of corresponding X and T values. (The first order approximation was not needed in the previous ethylene oxide example, because reaction rates were measured directly as the total function of temperature, whereas all other concentrations changed with the temperature.) The example is from Appendix A, in Berty (1997). In the Ignition Curve measurement a graph is made to plot the temperature needed for the conversion achieved. 

Figure 11.1 A plot of the reaction rate as a function of the substrate concentration for an enzyme catalyzed reaction. Vmax is the maximal velocity. The Michaelis constant. Km, is the substrate concentration at half Vmax- The rate v is related to the substrate concentration, [S], by the Michaelis-Menten equation ...

Let us consider cases 1-3 in Fig. 4.4. In case 1, AG s for formation of the competing transition states A and B from the reactant R are much less than AG s for formation of A and B from A and B, respectively. If the latter two AG s are sufficiently large that the competitively formed products B and A do not return to R, the ratio of the products A and B at the end of the reaction will not depend on their relative stabilities, but only on their relative rates of formation. The formation of A and B is effectively irreversible in these circumstances. The reaction energy plot in case 1 corresponds to this situation and represents a case of kinetic control. The relative amounts of products A and B will depend on the heights of the activation barriers AG and G, not the relative stability of products A and B. 

A plot of the reciprocal reaction rate versus the reciprocal urea concentration should give a straight line with an intercept and... 

Prepare a plot of reaction rate (-dC /dt) versus f(C ). If the plot is linear and passes through the origin, the rate equation is consistent with the data, otherwise another equation should be tested. Figure 3-17 shows a schematic of the differential method. 

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" ). 

If k is much larger than k", Eq. (6-64) takes the form of Eq. (6-61) for the fraction Fhs thus we may expect the experimental rate constant to be a sigmoid function of pH. If k" is larger than k, the / -pH plot should resemble the Fs-pH plot. Equation (6-64) is a very important relationship for the description of pH effects on reaction rates. Most sigmoid pH-rate profiles can be quantitatively accounted for with its use. Relatively minor modifications [such as the addition of rate terms first-order in H or OH to Eq. (6-63)] can often extend the description over the entire pH range. 

The activation enthalpies and entropies are in principle dependent on temperature (eq. 12.22)), but only weakly so. For a limited temperature range they may be treated as constants. Obtaining these quantities experimentally is possible by measuring the reaction rate as a function of temperature, and plotting ln(k/T) against T" (eq. 12.24). 

Figure 4 Reaction kinetics plot showing the use of a differential method of rate determination of PP-N6-PP-g-AA ternary blend. Source Ref. 47.

Determination of the instantaneous rate at a particular concentration. To determine the rate of reaction, plot concentration versus time and take the tangent to the curve at the desired point. For the reaction N20s(g) — 2N02(g) + 02(g), it appears that the reaction rate at [N205] = 0.080 M is 0.028 mol/L - min. 

Substrate and product inhibitions analyses involved considerations of competitive, uncompetitive, non-competitive and mixed inhibition models. The kinetic studies of the enantiomeric hydrolysis reaction in the membrane reactor included inhibition effects by substrate (ibuprofen ester) and product (2-ethoxyethanol) while varying substrate concentration (5-50 mmol-I ). The initial reaction rate obtained from experimental data was used in the primary (Hanes-Woolf plot) and secondary plots (1/Vmax versus inhibitor concentration), which gave estimates of substrate inhibition (K[s) and product inhibition constants (A jp). The inhibitor constant (K[s or K[v) is a measure of enzyme-inhibitor affinity. It is the dissociation constant of the enzyme-inhibitor complex. 

The inhibition analyses were examined differently for free lipase in a batch and immobilised lipase in membrane reactor system. Figure 5.14 shows the kinetics plot for substrate inhibition of the free lipase in the batch system, where [5] is the concentration of (S)-ibuprofen ester in isooctane, and v0 is the initial reaction rate for (S)-ester conversion. The data for immobilised lipase are shown in Figure 5.15 that is, the kinetics plot for substrate inhibition for immobilised lipase in the EMR system. The Hanes-Woolf plots in both systems show similar trends for substrate inhibition. The graphical presentation of rate curves for immobilised lipase shows higher values compared with free enzymes. The value for the... 

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