First-order rate equations for

The reaction rate for simple fermentation systems is normally given by the Monod equation. This model indicates that the specific conversion rate is constant when applied to an immobilised cell system (Table 8.7). If a first-order rate equation for sugar consumption is used, (8.7.4.2) yields ... 

The concentration is proportional to the counts/min. Try a first order rate equation for which... 

Here, Cf is the mean concentration of foulant in the film whose thickness at any time t is 6f, and m and m are, respectively, the mass of foulant deposited and removed per unit area per unit time. Assuming the deposition rate to be independent of the foulant film thickness and the removal rate to be linearly dependent on the film thickness, we may write a first-order rate equation for the film growth. From Eq. (1) this equation is given by... 

A perfectly mixed vessel therefore can be considered as a batch vessel during the time required for the bubbles to sweep the vessel contents exactly once (i.c., up to /, = l/ 2 ). The definition of the singlebubble collection efficiency ( ) requires that the observed removal efficiency ( ) should equal after one bubble sweep. This assumes that all the oil drops that collide with a bubble stick to it. The solution of the First-order rate equation for a batch vessel for /j l/ 2 and ( = R yields ... 

Fig. 3.3 Fit of the experimental data to the integrated first-order rate equation for the process 2N2O5 - 4N02 +02 at 45°C inCCI4.

Where, i = 1 for the bubble phase, i = 2 for the cloud phase, and i = 3 for the emulsion phase. Note from the term on the right-hand side of Eqn. (1) that a first order rate equation for particulate collection is assumed (10). The inlet gas corresponds to the zero compartment, thus. 

For a monodisperse suspension the decay rate can be described by a first order rate equation. For a polydisperse suspension the decay rate is a sum of exponentials. Measurement of the decay rate permits computation of particle size [338]. 

FIRST-ORDER RATE EQUATION For comparison, the differential method will be applied to a first-order mechanism. The rate expression replacing Eq. (A) is... 

As with previous first-order rate equations for absorption and distribution, a first-order equation for the metaboUc rate can be written... 

With this, Equation 8 can be simplified further when replacing Ws by Wsf Assuming a first-order rate equation for the deposition process (as has proven a reasonable hypothesis in many cases), one obtains for the rate of change of particle concentration attributable to deposition ... 

Inserting this into equation (4-95), together with the first-order rate equation for B, we have... 

Both compoimds- A and B, decompose by first-order kinetics. Tlierefore, we can write a first-order rate equation for A and also one for B. 

Nitrogen was used as the diluent in the reaction. Its partial pressure remained approximately constant throughout the reaction at 154.6 °C = 8.1 mm and at 147.2 °C = 4.5 mmHg). The initial partial pressures of the peroxide (A) were 168 and 179 mm Hg at 154.6°C and 147.2 °C, respectively. Obtain a suitable first-order rate equation for the reaction, assuming an ideal gas. 

The set of coupled equations (5.2) can be readily solved using matrix methods. The advantage of this approach is that it can easily be generalized to treat any number of coupled first-order (or pseudo-first-order) rate equations. For simplicity consider a two-step process and define a column vector constructed from the concentrations... 

Figure 6-8b Test of first-order rate equation for bromine decomposition.

Figure 6-9a Test of first-order rate equation for fructose isomerization at 70 °C using xylose isomerase derived from T. neapolitana.

The first-order rate equation for this reaction can be written as... 

The distributed reactivity model explanation for the biphasic rate behavior commonly observed for desorption of HOCs from soils is that the soft-carbon sorbed, or labile fraction of the contaminant desorbs readily and reversibly, whereas the hard-carbon sorbed, or resistant component is released much more slowly. The slow desorption step has been attributed to non-Fickian diffusion into a tightly-knit SOM, polymerization, or entrapment within the SOM matrix. The rate model found in comparative analyses to be the most appropriate for description of such behavior (17) is a two-phase release model which couples first-order rate equations for both the slow, resistant, and rapid, labile fractions, < >r (= 1- (j) ... 

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