Specific rate of product formation

The values of S and e may be estimated by calculating the slope and intercept of the plot of the specific rate of product formation ( /X)(dP/dt) against //. Clearly, for a purely growth associated product e will tend to zero but will dominate the expression for a growth independent product. 

The product of and p, that is, = V p) is often called the specific rate of product formation, r/p, (mass product/volume/time). When the product is formed during the stationary phase where no cell growth occurs, we can relate the rate of product formation to sabstrate consumption by... 

The specific rate of product formation is often given in terms of the Luedeking-Piret equation, which has two parameters a (growth) and P (nongrowth)... 

Thus the specific rate of product formation is given by... 

Figure 5.65. Dynamic relationship between specific rate of product formation and specific growth rate for various rates of the exponential decrease of the specific growth rate expressed with the aid of varied values of the constant K dapt (see Equ. 5.226). The steady-state relationship is obtained at large K values. (From Harder and Roels, 1982.)...

In the previous discussion, extreme cases concerning the stage of product synthesis were considered, but actual production may occur in both exponential and stationary phases of growth. In order to account for this, the specific rate of product formation, qp, is then given by the Luedeking-Piret equation ... 

Tripathi and co-workers [46] evaluated phenylacetyl carbinol biotransformation efficiency of harvested whole yeast cells, grown continuously under glucose-limited conditions at different dilution rates. They found that cells from increasing dilutions showed increasing specific rates of product formation. 

Rate of product formation, g-11 - h 1 j Specific growth rate, h 1... 

Measurements of overall reaction rates (of product formation or of reactant consumption) do not necessarily provide sufficient information to describe completely and unambiguously the kinetics of the constituent steps of a composite rate process. A nucleation and growth reaction, for example, is composed of the interlinked but distinct and different changes which lead to the initial generation and to the subsequent advance of the reaction interface. Quantitative kinetic analysis of yield—time data does not always lead to a unique reaction model but, in favourable systems, the rate parameters, considered with reference to quantitative microscopic measurements, can be identified with specific nucleation and growth steps. Microscopic examinations provide positive evidence for interpretation of shapes of fractional decomposition (a)—time curves. In reactions of solids, it is often convenient to consider separately the geometry of interface development and the chemical changes which occur within that zone of locally enhanced reactivity. 

The various k s are the rate constants for the specific reactions shown. Standard kinetic analysis of this mechanism predicts that the rate of product formation is given by... 

It is also useful at this stage to make the data more quantitative by converting the amount of product formation from the machine units, arbitrary integration units, or percentage obtained, directly to units of amount. Such a conversion requires access to a calibration curve that relates the machine units to more specific units of amount. An example of such a calibration curve for adenosine is shown in Figure 4.13. Having made the conversion, the initial rate of product formation determined earlier can now be plotted as a function of enzyme concentration as part of the optimization process. 

Contrary to what is true for pathways with no reversible steps, fast reversible steps preceding the rate-controlling step do affect the rate of product formation. The rate depends on the equilibrium constants of such steps and thus on the ratios of their forward and reverse rate coefficients. Specifically, equilibria favoring the reverse reaction reduce the rate. 

For the influence of the specific surface area of the semiconductor powder on the rate of product formation, two opposite effects are of major importance [81]. One is concerned with the rate of electron-hole recombination which increases linearly with surface area, and accordingly the reaction rate should decrease. The other is a linear increase in the reaction rate of the reactive electron-hole pair with the adsorbed substrates, which should increase product formation. It is therefore expected that, depending on the nature of semiconductor and substrates, the reaction rate, or increasing surface area. This is nicely reflected by the CdS/Pt-catalyzed photoreduction of water by a mixture of sodium sulfide and sulfite. The highest p values are observed with small surface areas and are constant up to 2 m g". From there a linear decrease to almost zero at a specific surface area of 6 m g" takes place. Upon further increase to 100 m g" this low quantum yield stays constant [82]. 

We can see that for type 1 processes, high growth rate is obligately linked to a high rate of product formation. Indeed, this is the case for all products produced by a fermentative mode of metabolism, eg ethanol, lactic add, acetone. Chemostat stupes have shown that for most aerobic processes vv en growth is limited by some nutrient other than the cariron source, the yield of product decreases with increase in specific growth rate (p or D p = dilution rate (D) in chemostat culture). Conversely, both the biomass yield and foe spedfic rate of substrate utilisation (qs g substrate g biomass h ) increase with spedfic growth rate. 

Cone, of enzyme-substrate complex Cone, of enzyme-product complex Specific rate of enzyme formation, mg" time" ... 

The phenomenon of "mass transfer with chemical reaction" takes place whenever one phase is brought into contact with one or more other phases not in chemical equilibrium with it. This phenomenon has industrial, biological and physiological importance, in chemical process engineering, it is encountered in both separation processes and reaction engineering. In some cases, a chemical reaction may deliberately be employed for speeding up the rate of mass transfer and/or for increasing the capacity of the solvent in other cases the multiphase reaction system is a part of the process with the specific aim of product formation. 

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