Yield constant

However, an evaluation of the observed (overall) rate constants as a function of the water concentration (5 to 25 % in acetonitrile) does not yield constant values for ki and k2/k i. This result can be tentatively explained as due to changes in the water structure. Arnett et al. (1977) have found that bulk water has an H-bond acceptor capacity towards pyridinium ions about twice that of monomeric water and twice as strong an H-bond donor property towards pyridines. In the present case this should lead to an increase in the N — H stretching frequency in the o-complex (H-acceptor effect) and possibly to increased stabilization of the incipient triazene compound (H-donor effect). Water reduces the ion pairing of the diazonium salt and therefore increases its reactivity (Penton and Zollinger, 1971 Hashida et al., 1974 Juri and Bartsch, 1980), resulting in an increase in the rate of formation of the o-complex (ik ). 

A 4 km intercepting sewer with diameter D = 0.5 m is flowing half full. The DO consumption rate, rf, of the sewer biofilm is measured, and an average value of 0.6 g02 m-2 h-1 was estimated. The biofilm yield constant of the heterotrophic biomass was not measured but was estimated as Yf= 0.55 gCOD biomass produced per gCOD substrate consumed. Only aerobic heterotrophic transformations in the biofilm are expected to proceed. 

Suspended biomass growth results in the removal of readily biodegradable substrate. A yield constant, YHw, typically about 0.55 g COD biomass produced... 

It should be noticed that biomass growth and respiration for bulk water phase include details that are not taken into account in the simple half-order biofilm description. As an example and a consequence, the two yield constants, YHw and Yup are differently interpreted in terms of the substrate requirement of the biomass (Figure 5.5). 

In addition to the kinetics of the sewer processes described in Section 5.3, the stoichiometry of the transformations of the components is crucial for the mass balance. The stoichiometry of the biomass/substrate relationships is, according to the activated sludge model concept, determined by the heterotrophic biomass yield constant, YH, in units of gCOD gCOD-1. As depicted in Figure 5.5, the yield constant is an important factor related to the consumption of both Ss and S0 for the production of XBw. 

The biomass yield constant was, according to Poulsen (1997), about 0.38 gCOD gCOD-1. Aesoey et al. (1997) showed that 4.8 gCOD gN03-N-1 is removed when readily biodegradable substrate is available. If hydrolysis limits the transformations, this value was reduced to about 50%. 

The yield constant, Y, for the sulfate-reducing biomass is, according to Equation (6.19), in mass units ... 

The relatively low yield constant makes it acceptable to omit the growth process for the sulfate-reducing biomass in the concept. 

YHw Suspended biomass yield constant for heterotrophics 0.55 gCOD gCOD"1... 

YHf Biofilm yield constant for heterotrophic biomass 0.55 GCODg COD 1... 

The determination of the COD components depends on the fact that the substrate uptake can be experimentally related to the OUR curve. The heterotrophic yield constant, YHw, that is experimentally determined from procedure number 1, Section 7.2.1, relates the oxygen uptake to the readily biodegradable substrate that is consumed irrespective of its origin, being either directly available or continuously produced from hydrolyzable COD fractions. 

Ym yield constant for methane-producing biomass [gCOD, biomass (gCOD,substrate)-1]... 

The rates of uptake of substrate and oxygen are related to the biomass growth rate by appropriate yield constants ... 

This equation has a simple solution (recall that the averages <. .. > yield constants, independent on r) ... 

Another important consequence of the constant rate of release diffusion model is that it mimics many of the features that have commonly been attributed to surface reaction (matrix dissolution) control. If one were to account for changes in surface area over time, the predicted long-term dissolution rate due to surface reaction control would also yield constant element release. In surface reaction controlled models, the invariant release rate with respect to time is considered to be the natural consequence of the system achieving steady-state conditions. Other features of experiments commonly cited as evidence for surface reaction control, such as relatively high experimental activation energies (60-70 kJ/ mol), could be explained as easily by the diffusion-control model. These findings show how similar the observations are between proponents of the two models it is only the interpretation of the mechanism that differs. 

However, Hsieh and Kitchen 151 failed to consider the influence of their measurement temperature, 78 °C, on the stability of the poly(dienyl)lithium active centers (see section on Active Center Stability). As an example of this potential problem is the observation by two separate groups 47-152> that viscometric measurements of hydrocarbon solutions of poly(butadienyl)lithium fail to yield constant flow times (at 30 °C) following the completion of the polymerization, i.e., the flow times were found to increase with increasing time. This inability of the poly(butadienyl)lithium chain to exhibit constant solution viscosities renders it unsuitable for association studies of the type done by Hsieh and Kitchen 151). 

On the (assumed) much longer time scale over which SeOj and Mn2+ begin to appear in the aqueous-solution phase from the decomposition of = Mn" - 0Se020H, Eqs. 4.52c-4.52e can be solved under an appropriate imposed condition regarding the time variation of [=MnM - 0SeO2OH] based on the surface oxidation-reduction kinetics. For example, under steady-state conditions that yield constant concentrations of the adsorbed and dissolved selenite species, Eqs. 4.52a and 4.52b lead to a constant concentration of adsorbed selenate and therefore a constant rate of selenate detachment from the mineral surface (Eq. 4.52c). If the reasonable assumption is also made that the proton reaction with =MnH - OH equilibrates rapidly, then... 

Plotting ([S]T - [S]0)/[CD]X vs. [CD]X gives the first estimated values for K1 1 and K1 2 from the intercept and the slope, respectively. The estimated values are substituted to Equation (3.134) to determine [CD], The stability constants are estimated after substituting the estimated [CD] values. Three or four iterations, after the first estimated values of K, K12, and [CD] are calculated from Equation (3.135) and Equation (3.133), yield constant values for the stability constants. However, the determination of the stability constants for higher order complexes is not possible with this approach. 

Here, the T s are stoichiometric or yield constants. To obtain an estimate of cell concentration (X) by this relationship, one must obtain an expression for the product formation rate (dP/dt) in terms of cell concentration... 

This question was studied by Hsu [HsulJ in the chemostat with Michaelis-Menten dynamics, and his work is presented here. The equations take the form (ignoring the yield constants)... 

In the classical model of the chemostat, discussed in Chapter 1, it is assumed (following Monod [Mol Mo2]) that the nutrient uptake rate is proportional to the reproductive rate. The constant of proportionality, which converts units of nutrient to units of organism, is called the yield constant. As a consequence of the assumed constant value of the yield, the classical model is sometimes referred to as the constant-yield model. 

The variables and the units are those which have been used since Chapter 1 S(t) is the nutrient concentration at time t, Xx(t) is the concentration of plasmid-bearing organisms at time t, and X2(0 is the concentration of plasmid-free organisms at time t S is the input concentration of the nutrient, and D is the washout rate of the chemostat. These are the operating parameters. The mj term is the maximal growth rate of x, and a, is the Michaelis-Menten (or half-saturation) constant of x,. These are assumed to be known (measurable) properties of the organism that characterize its growth and reproduction. A plasmid is lost in reproduction with probability q, and y is the yield constant. 

With fight metal cations it is valid to use the yield constant (Yo), maximum specific growth rate (km), specific decay rate (ka), and half maximum velocity constant (kg), as defined for the Monod model as the kinetic parameters to categorize toxicity data. It is suggested that this procedure be applied to all substances. 

Equation 3 is a more specific formula for the metabolism of acetic acid and is developed from an oxidation-reduction balance using the appropriate yield constants as defined. 

The dynamic model presented herein builds on that reported previously (I) by incorporating the interactions between volatile acids, pH, alkalinity, gas production rate, and gas composition. The model is developed from material balances on the biological, liquid, and gas phases of a continuous-flow, complete mixing reactor. Appropriate relationships such as yield constants, an inhibition function, Henry s law, charge balances, and ionization equilibria are used to express the interactions between variables. The inputs and outputs for the reactor and the reactions considered are illustrated in Figure 2. 

The studies presented herein should be considered only semiquanti-tative in nature since it has been necessary to make several simplifying assumptions in developing the model, and reliable values for many of the parameters are not available. Reasonable estimates of /I = 0.4 day Kg = 0.0333 mmole/liter, and Yx/a = 0.02 mole/mole were made from the data of Lawrence and McCarty (5). For acetic acid, Yco2/x and Ych4/x are equal and were determined from the basic stoichiometry (Equation 3) as 47.0 moles/mole. An order of magnitude estimate of Ki = 0.667 mmole/liter was made using the 2000-3000 mg/liter of total volatile acids that Buswell (6) considers to be inhibitory. The estimates for Kg and Kj are not as reliable as those for Jl and the yield constants because Kg and Ki must be expressed as concentrations of unionized acid. 

The values for the organism yield constants are assumed to be somewhat higher than for acetic acid since they are expressed on a molar basis and more than one species may participate in the reaction. The yield constants for carbon dioxide and methane are developed from the oxidation-reduction balances. 

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