Thermodynamic potential factor

To account for reverse as well as forward reaction, the Monod (and dual Monod) equation can be modified by appending to it a thermodynamic potential factor, as shown by Jin and Bethke (2005), in which case the equation predicts the net rate of reaction. The thermodynamic factor Ft, which can vary from zero to one, is given... 

The kinetic factors Tb and Fa and thermodynamic potential factor Fj are largest where the electron donor and acceptor are abundant, and the reaction products are not. If under such conditions all three factors are equal to one, as is not uncommon, the reaction rate predicted by Equation 18.22 reaches its maximum value, rmax = nw k+ [X]. As the substrates are depleted with reaction progress, and reaction products accumulate, the factors eventually decrease toward zero, slowing the reaction to a near stop. 

Fig. 33.2. Factors controlling reaction rate (expressed per kg water, as r/nw) in the simulation of bacterial arsenic reduction, including kinetic factors FD and Fa, thermodynamic potential factor FT, and biomass concentration [X], Biomass concentration determines the rate early in the simulation, but later the thermodynamic drive exerts the dominant control.

The principal controls on the microbial reaction rate in our example, then, are biomass and thermodynamic drive (Fig. 33.2). Initially, in the presence of abundant lactate and arsenate, the rate is controlled by the size of the microbial population available to catalyze lactate oxidation. As the population increases, so does reaction rate. Later, as reactants are consumed and products accumulate, the reaction approaches the point at which the energy liberated by its progress is balanced by that needed in the cell to synthesize ATR Reaction rate is governed now by the energy available to drive forward the cellular metabolism, this energy represented by the thermodynamic potential factor Ft over the course of the experiment, the kinetic factors Fd and Fa play minor roles. 

Fig. 33.4. Factors controlling rates of microbial activity in the simulation depicted in Figure 33.3, for acetotrophic sulfate reduction (top) and acetoclastic methanogenesis (bottom). Factors include the thermodynamic potential factor Ft, kinetic factors FD = wac/C ac + Kq) and FA = mso4/(mso4 + K A), and biomass concentration [A],...

Since the infinite dilution values D°g and Dba. re generally unequal, even a thermodynamically ideal solution hke Ya = Ys = 1 will exhibit concentration dependence of the diffusivity. In addition, nonideal solutions require a thermodynamic correction factor to retain the true driving force for molecular diffusion, or the gradient of the chemical potential rather than the composition gradient. That correction factor is ... 

Bard AJ, Wrighton MS (1977) Thermodynamic potential forthe anodic dissolution of n-type semiconductors - A crucial factor controlling durability and efficiency in photoelectrochem-ical cells and an important criterion in the selection of new electrode/electrolyte systems. J Electrochem Soc 124 1706-1710... 

The second factor is associated with the fact that all electrolyte solutions exhibit finite resistance to the flow of current. Thus, the potential that is measured (Em eas) between the working and reference electrodes consists of two contributors, the real thermodynamic potential Cereal) and that arising from uncompensated solution resistance (IRU)... 

The vapor density, like the vapor pressure, can be used as a thermodynamic potential whose total change around a closed path is zero. According to this argument, the effect of the above five factors on vapor density can be mathematically expressed and summed to zero. Beginning at the product water outlet, move to salt water by adding M, compress the salt water to pressure p, and subject it to the thermal loss of latent heat transfer, the diffusion loss of mass transfer, and the viscous loss of pressure in cellophane and manifold passages. This returns the path to fresh water and a closed circuit. 

In DLVO theory, the secondary minimum can only be created by the van der Waals force, which is essentially independent of the salt concentration across the concentration range 0.001 M < c < 0.1 M. This force has to be balanced with a force that decays exponentially as a function of k, which means that it decays by a factor exp(-10) across this range. The unhappy consequence of this prediction is that the position of the secondary minimum, and therefore the interlayer d value, varies very rapidly as a function of k, in contradiction to the experimental results. A further unhappy consequence of this balance is that it always produces a primary minimum much deeper than the secondary minimum. The full, standard DLVO thermodynamic potential energy curve, which also includes a very-short-range Bom repulsion, is shown in Figure 1.13 [23], It is therefore a definite prediction of DLVO theory that charge-stabilized colloids can only be kinetically, as opposed to thermodynamically, stable. The theory does not mean anything at all if we cannot identify the crystalline... 

The surface diffiisivity (Dp) is known to be a function of adsorbed phase concentration and is equal to the corrected diffiisivity (D p) multiplied by a thermodynamic correction factor (dlnP/dlnCp). Assuming that the driving force for surface diffusion is the gradient of the chemical potential and that the mobility constant is a function of adsorbed phase concentration. Do and Do [6] have introduced the following form for the corrected sur ce diffiisivity ... 

Conversely, the correct approach to formulate the diffusion of a single component in a zeolite membrane is to use the MaxweU-Stefan (M-S) framework for diffusion in a nonideal binary fluid mixture made up of species 1 and 2 where 1 and 2 stands for the gas and the zeohtic material, respectively. In the M-S theory it is recognized that to effect relative motions between the species 1 and 2 in a fluid mixture, a force must be exerted on each species. This driving force is the chemical potential gradient, determined at constant temperature and pressure conditions [68]. The M-S diffiisivity depends on coverage and fugacity, and, therefore, is referred to as the corrected diffiisivity because the coefficient is corrected by a thermodynamic correction factor, which can be determined from the sorption isotherm. 

We can use standard electrode potentials and the Nernst equation to calculate the potential obtainable from a galvanic cell or the potential required to operate an electrolytic cell. The calculated potentials (sometimes called thermodynamic potentials) are theoretical in the sense that they refer to cells in which there is no current. As we show in Chapter 22, additional factors must be taken into account if a current is involved. 

Notice that the same problem would be encountered for the ratio <7n / N) in cases where the external potential prevents the thermodynamic potential to be a homogeneous function of degree one in either s or Sy and these two quantities would be increased by noninteger factors. These examples show that for confined fluids one has to be cautious to approach the thermodynamic limit properly. 

The values in Table 26-1 are called thermodynamic potentials, that is, they are ideal values. Several factors, such as overpotential, activation energy, complexation, and pH, can change these values. These will be discussed later. 

Anderson C-R, Coker D F, Eckert J and Bug A L R (1999), Computational study of molecular hydrogen in zeolite Na-A. I. Potential energy surfaces and thermodynamic separation factors for ortho and para hydrogen , J Chem Phys, 111, 7599. 

In chemical kinetics the concept of the order of a reaction forms the basis of a kinematics which constitutes a frame for most of the molecular theories of chemical reactions. The fundamental magnitudes of this kinematics are the concentrations and the specific rate constants. In simple cases only the time enters as an independent variable, whereas in a diffusion process both time and space are involved. Diffusion processes are generally described in terms of diffusion coefficients, volume concentrations and thermodynamic potential or activity factors. Partial volume factors and friction coefficients associated with the components of the diffusing mixture are also essential in the description. A feature of the macro-dynamical theory is that it covers any region of concentration. Especially simple equations are connected with the differential diffusion process (diffusion with small concentration differences), for which the different coefficients or factors mentioned above are practically constant. 

The thermodynamic potential of the Ag+ions in the solution, however, has been increased by an amount kT In 10, as a consequence of the increase in concentration by a factor 10. This increase must equal the product e Q, and the resulting double layer potential is therefore = ( kTf ) In 10 = 2.3( 7 /e) = 57 millivolts. More generally we have... 

If G w the area of contact will spontaneously change so as to decrease the thermodynamic potential. If G< w, A increases and the crack recedes if G > w, A decreases, and the crack extends GdA is the mechanical energy released when the crack extends by dA. The breaking of interfacial bonds requires the energy wdA and the excess (G-w)dA is changed in kinetic energy if there is no dissipative factor. 

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