Subscripts with chemical reactions

We will generally not be concerned here with chemical reactions, so the Ri term can be omitted, in which case the subscript i denoting species is no longer required. In addition, for the turbulent flows of interest the molecular diffusion term in Eq. (2.1) may be neglected. [Although for the spatial scales of interest to us the molecular diffusion term may be neglected, molecular and turbulent diffusion are not independent, linearly additive, physical processes (Saffman, I960).] As a result of the above two simplifications, Eq. (2.1) becomes... 

Consider the case when the equilibrium concentration of substance Red, and hence its limiting CD due to diffusion from the bulk solution, is low. In this case the reactant species Red can be supplied to the reaction zone only as a result of the chemical step. When the electrochemical step is sufficiently fast and activation polarization is low, the overall behavior of the reaction will be determined precisely by the special features of the chemical step concentration polarization will be observed for the reaction at the electrode, not because of slow diffusion of the substance but because of a slow chemical step. We shall assume that the concentrations of substance A and of the reaction components are high enough so that they will remain practically unchanged when the chemical reaction proceeds. We shall assume, moreover, that reaction (13.37) follows first-order kinetics with respect to Red and A. We shall write Cg for the equilibrium (bulk) concentration of substance Red, and we shall write Cg and c for the surface concentration and the instantaneous concentration (to simplify the equations, we shall not use the subscript red ). 

Provided that equilibrium is maintained between the aqueous and micellar pseudophases (designated by subscripts W and M) the overall reaction rate will be the sum of rates in water and the micelles and will therefore depend upon the distribution of reactants between each pseudophase and the appropriate rate constants in the two pseudophases. Early studies of reactivity in aqueous micelles showed the importance of substrate hydropho-bicity in determining the extent of substrate binding to micelles for example, reactions of a very hydrophilic substrate could be essentially unaffected by added surfactant, whereas large effects were observed with chemically similar, but hydrophobic substrates (Menger and Portnoy, 1967 Cordes and Gitler, 1973 Fendler and Fendler, 1975). 

We will indicate the order of the chemical reaction with a subscript, so k2 is the rale constant of a second-order reaction. 

In the same way, you can recognize similarities between chemical reactions and the types of reactants that tend to undergo different types of reactions. With this knowledge, you can predict what will happen when one, two, or more substances react. In this section, you will often see chemical reactions without the subscripts showing the states of matter. They are omitted deliberately because, in most cases, you are not yet in a position to predict the states of the products. 

The subscript r is used to denote changes associated with a chemical reaction. Although symbols such as ArH should denote the integral enthalpy of reaction, ArH = H( 2) — H( i)> in practice this symbol is usually used to denote the change divided by the amount transferred, i.e. the change per extent of reaction, defined by the equation... 

Note that rB and v can also be defined on the basis of partial pressure, number concentration, surface concentration, etc., with analogous definitions. If necessary differently defined rates of reaction can be distinguished by a subscript, e.g. vp = vB 1dpB/dt, etc. Note that the rate of reaction can only be defined for a reaction of known and time-independent stoichiometry, in terms of a specified reaction equation also the second equation for the rate of reaction follows from the first only if the volume V is constant. The derivatives must be those due to the chemical reaction considered in open systems, such as flow systems, effects due to input and output processes must also be taken into account. 

B. Write a balanced chemical reaction, with subscripts indicating state or phase. 

Figure 2. A network of chemical reactions. Letters indicate carbon positions within reactants and prodncts. Isotopic compositions of these positions are indicated by Ss with alphabetical snbscripts. Reactions are designated by nnmbers and the

This analysis begins with the unsteady-state mass balance for component i in the well-mixed reactor. At high-mass-transfer Peclet numbers, which are primarily a function of volumetric flow rate q, the rate processes of interest are accumulation, convective mass transfer, and multiple chemical reactions. Generic subscripts are... 

This result will be employed in conjunction with the thermal energy balance for reactive systems. If there is only one chemical reaction, then subscript j is not required and dFi/vi is independent of component i ... 

The dimensionless scaling factor in the mass transfer equation for reactant A with diffusion and chemical reaction is written with subscript j for the jth chemical reaction in a multiple reaction sequence. Hence, A corresponds to the Damkohler number for reaction j. The only distinguishing factor between all of these Damkohler numbers for multiple reactions is that the nth-order kinetic rate constant in the 7th reaction (i.e., kj) changes from one reaction to another. The characteristic length, the molar density of key-limiting reactant A on the external surface of the catalyst, and the effective diffusion coefficient of reactant A are the same in all the Damkohler numbers that appear in the dimensionless mass balance for reactant A. In other words. 

Fig. 11. Active transport using the simple carrier. Formal kinetic schemes for (a) countertransport and (b) co-transport. A and B are the two substrates of the carrier E either of which (in countertramsport) or both which (in co-transport) combine with E to form EA, EB or EAB. Subscripts 1 or 2 refers to substrate at side 1 or 2 of the membrane. The rate constants b, d, f, g, k are defined in the figure. AT" is the equilibrium constant of the chemical reaction /I =4.42 in primary active transport (and is equal to unity in the case of secondary active transport). Af=A /A 2 in co-transport. The square brackets denote concentrations and terms such as /4, =[/l,]/Arj, where is the relevant dissociation constant, here = dj/gi. J is the net flux in the 1 ->2 direction. (Figure taken, with permission, from [30].)...

The rate of the mass transfer through the Nernst layer is defined by the rate of diffuse flow of reagents and products participating in chemical reactions on the interface. This rate was already reviewed as the adsorption rate in the process of film diffusion. It is based on the same Shchukarev equation (2.204). However, contrary to adsorption, here in the flow participate all ions formed in the process of dissolution, not just one ion. That is why in the equation (2.204) should be reviewed the flow of the mineral itself in solution, not of its individual ions, and its subscripts i should be replaced with ... 

Figure 2 indicates the different types of emulsions. Simple emulsions are labeled as oil-in-water (0/W) when they exhibit oil drops dispersed in an aqueous phase, or water-in-oil (W/O) if the opposite occurs, while multiple or double emulsions are symbolized either by W,/0/Wi or Oi/W/O . Wi (respectively 0 ) and W2 (respectively O2) indicate the most internal phase and the most external one. Note that phases with subscript I and 2 may be identical or different. If they are not the same a likely difference in chemical potential may drive a mass transfer process, a phenomenon that is advantageously harnessed for controlled-release applications. Bieniulsions are emulsions containing two different internal phase droplets, either of the same nature (but different size) or of different nature (whatever the size). The first kind of biemulsion is used to control some property, as, for example, emulsion viscosity, whereas the second may be used to produce controlled chemical reaction or mass transfer between the two internal phases. 

The Michaehs constants corresponding to various reactants are designated by K, with an identifying subscript /Ea, Kq, Kp, and Tq K[a, Kia, Kiq, etc. are used for inhibition or dissociation constants, and other special constants may be defined as well, if need arises. All such constants have dimensions of [concentration]. The overall equihbrium constant of the chemical reaction is designated K q. The maximum velocities in forward and reverse directions are designated V, and these have dimensions of [concentration/unit time]. The expressions Vi/Eo and V /Eq are turnover numbers, and have dimensions [time... 

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