Reciprocal reaction rate

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

Figure 2-11 shows a typical curve of the reciprocal reaction rate as a function of concentration for an isothermal reaction carried out at constant volume, For reaction orders greater than zero, the rate decreases as concentration decreases. The area under the curve gives the space time necessary to reduce the concentration of A from Qo to C -... 

A plot of the reciprocal reaction rate versus the reciprocal urea concentration should be a straight line with an intercept l/y ax and slope KJV. This type of plot is called a Lineweaver-Burkplot. The data in Table E7-7.1 are presented in Figure E7-7.1 in the form of a Lineweaver-Burkplot. The intercept is 0.75, so... 

Fig. 8.3 Reciprocal reaction rate along an adiabatic path.

The shape of the reciprocal reaction rate curve in Fig. 8.3 suggests that a combination of tubular and stirred tank type reactors might have some advantages over either one of them used by itself. If we consider the feed extent to be zero and inlet temperature Py, then for the stirred tank... 

Fig. 9.4 The curves of reciprocal reaction rate versus extent for a reversible exothermic reaction at several temperatures.

If the reciprocal reaction rate is plotted as a function of conversion the shadowed areas represent the residence time necessary to reach a given conversion x (Eqs. (61) and (62)). 

To be able to compare relative reactor sizes, one needs a knowledge of the form of the reaction rate expression in either graphical or analytical terms. In Section 8.2.1 we showed that the area under a plot of the reciprocal reaction rate (-1/r ) versus fraction conversion was equal to the ratio for Pfo flow reactor. In the case of a sin-... 

The dialytic regime is characterized by high surface reaction rate coefficients and by rate-limiting diffusion. The Sherwood number (Sh) characterizes the regimes. Sh is defined as the ratio of the driving force for diffusion in the boundary layer to the driving force for surface reaction alternatively, it is the ratio of the resistivity for diffusion to the resistivity for chemical reaction (reciprocal reaction rate coefficient). Diffusion limitation is the regime at Sh 1 and reaction limitation means Sh 1. The Sherwood number is closely related to the Biot, Nusselt, and Damkohler II numbers and the Thiele modulus. Some call it the CVD number. In the boundary-layer model it is a simple function of the thickness of the boundary layer, the diffusion coefficient, and the reaction rate coefficient. For simplicity a first-order reaction will be considered in the derivation below. 

Figure 6.3.8 Plot of reciprocal reaction rate 1 /rso2 versus SO2 conversion for the borderline case of isothermal operation at T=Ti = 440°C (see also Figure 6.3.4).

Figure 63.11 Plot of reciprocal reaction rate 1/rso2 versus SO2 conversion for four adiabatic steps with intermediate absorption (1 bar feed gas 8% SO2, 11% O2, restN2).

The performance, therefore, is related to the F/M or sludge age and the degradabiUty, K. As the F/M decreases or the sludge age increases, greater removals are achieved. It should be noted that the sludge age is proportional to the reciprocal of the F/M. The reaction rate coefficient, iC, as related to wastewaters characteristics. 

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

A straight line is produced when the logarithm of a specific reaction rate is plotted against the reciprocal of the absolute temperature. Temperature has a marked influence on the reaction rates, but the range between reactions that are too slow or too fast to measure is really quite narrow. 

In Fig. 28, the abscissa kt is the product of the reaction rate constant and the reactor residence time, which is proportional to the reciprocal of the space velocity. The parameter k co is the product of the CO inhibition parameter and inlet concentration. Since k is approximately 5 at 600°F these three curves represent c = 1, 2, and 4%. The conversion for a first-order kinetics is independent of the inlet concentration, but the conversion for the kinetics of Eq. (48) is highly dependent on inlet concentration. As the space velocity increases, kt decreases in a reciprocal manner and the conversion for a first-order reaction gradually declines. For the kinetics of Eq. (48), the conversion is 100% at low space velocities, and does not vary as the space velocity is increased until a threshold is reached with precipitous conversion decline. The conversion for the same kinetics in a stirred tank reactor is shown in Fig. 29. For the kinetics of Eq. (48), multiple solutions may be encountered when the inlet concentration is sufficiently high. Given two reactors of the same volume, and given the same kinetics and inlet concentrations, the conversions are compared in Fig. 30. The piston flow reactor has an advantage over the stirred tank... 

Observe that aok has units of reciprocal time so that aokt is dimensionless. The grouping OQkt is the dimensionless rate constant for a second-order reaction, just as kt is the dimensionless rate constant for a first-order reaction. Equivalently, they can be considered as dimensionless reaction times. For reaction rates governed by Equation (1.20),... 

This equation has two parameters t, the mean residence time (z = V/F) with dimensions of time and k, the reaction rate constant with dimensions of reciprocal time, applying for a first-order reaction. The concentration of reactant A in the reactor cannot, under normal circumstances, exceed the inlet feed value, Cao and thus a new dimensionless concentration, Cai, can be defined as... 

When the initial LA concentration is large, the quantity of substrate transferred to the aqueous phase allows the lipoxygenation to progress. This reaction consumes LA and produces HP, which favor the transfer of residual substrate between the two phases. Then catalysis and transfer have a reciprocal influence on each other. We demonstrated that the use of a non-allosteric enzyme in a compartmentalized medium permits the simulation of a co-operativity phenomenon. The optimal reaction rate in the two-phase system is reached for a high initial LA concentration 14 mM. Inhibition by substrate excess is observed in two-phase medium. 

Here X denotes lb-moles of benzene per lb-mole of pure benzene feed and x, denotes lb-moles of diphenyl per lb-mole of pure benzene feed. The parameters k, and k2 are unknown reaction rate constants whereas K, and K2 are known equilibrium constants. The data consist of measurements of Xi and x2 in a flow reactor at eight values of the reciprocal space velocity t. The feed to the reactor was pure benzene. The experimental data are given in Table 6.2 (in Chapter 6). The governing ODEs can also be written as ... 

If one has data on the reaction rate constant at several temperatures, this equation provides the basis for the most commonly used method for determining the activation energy of a reaction. If E is temperature invariant, a plot of in k versus the reciprocal of the absolute temperature should be linear with slope —(E/R). A typical plot is shown in Figure 3.9 for the reaction H2 + I2 - 2HI. The slope corresponds to an activation energy of 44.3 kcal/mole. 

The overall reaction rate r may be defined as the reciprocal of this mean reaction time. 

The reaction rate constant, k, is an exponential function of the reciprocal of the absolute temperature and is defined by Equation (3-6), the Arrhenius equation [169,170] ... 

Arrhenius plot plot of the logarithm of the reaction rate constant k versus the reciprocal of the absolute temperature T the plot is a straight line with slope of -Ea/R for uncomplicated reactions without autocatalysis or inhibitor depletion effects. 

In Figure 8.3 the log of reaction rate (time to threshold value) has been plotted against the reciprocal of absolute temperature to give the Arrhenius plot. 

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